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    <title>Neuropsychology | Reality Bending Lab</title>
    <link>https://realitybending.github.io/tag/neuropsychology/</link>
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    <description>Neuropsychology</description>
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      <title>Neuropsychology</title>
      <link>https://realitybending.github.io/tag/neuropsychology/</link>
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    <item>
      <title>PhD in Psychology / Neuroscience</title>
      <link>https://realitybending.github.io/jobs/phd/</link>
      <pubDate>Tue, 22 Nov 2022 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/jobs/phd/</guid>
      <description>&lt;p&gt;
  &lt;i class=&#34;fa fa-calendar  pr-1 fa-fw&#34;&gt;&lt;/i&gt; Flexible

  &lt;i class=&#34;fa fa-location-pin  pr-1 fa-fw&#34;&gt;&lt;/i&gt; University of Sussex, Brighton, UK&lt;/p&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img alt=&#34;&#34; srcset=&#34;
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               width=&#34;760&#34;
               height=&#34;343&#34;
               loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;h2 id=&#34;new-opportunities&#34;&gt;New Opportunities&lt;/h2&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img src=&#34;https://media.licdn.com/dms/image/v2/D4E22AQE87QMg9zXFlw/feedshare-shrink_1280/B4EZeomw49HYAk-/0/1750880424520?e=1754524800&amp;amp;v=beta&amp;amp;t=4cHB_CcBSi5EHaA1YREwROCpBG3lMfM2mev49jiAvWY&#34; alt=&#34;&#34; loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;11 December 20205&lt;/strong&gt;: &lt;a href=&#34;https://www.sussex.ac.uk/study/phd/degrees/psychology-phd&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Sussex Psychology PhD Program&lt;/a&gt;&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Fully funded for local and international students (i.e., pays university fees + gives you a salary)&lt;/li&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Selection is based on the candidate&amp;rsquo;s CV as well as on the project proposal&lt;/li&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Get in touch with potential supervisors before applying!&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;11 December 20205&lt;/strong&gt;: &lt;a href=&#34;https://www.sussex.ac.uk/study/fees-funding/phd-funding/view/1863-SEDarc-%28ESRC%29-PhD-scholarships-for-research-in-the-Social-Sciences&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;SEDarc PhD Scholarship&lt;/a&gt;&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; 3.5 years fully funded scholarship&lt;/li&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Project must fit within the SEDarc themes (e.g., data science)&lt;/li&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Selection is based on the candidate&amp;rsquo;s CV as well as on the project proposal&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;12 January 2026&lt;/strong&gt;: &lt;a href=&#34;https://www.sussex.ac.uk/study/phd/degrees/sussex-neuroscience-4-year-programme-phd&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Sussex Neuroscience 3+1 PhD Program&lt;/a&gt;&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Fully funded for local and international students (i.e., pays university fees + gives you a salary)&lt;/li&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; You don&amp;rsquo;t need to chose a supervisor before applying. The first year is made of 3 different rotations in different labs&lt;/li&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Selection is based mostly on the candidate&amp;rsquo;s CV&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id=&#34;what-you-will-get&#34;&gt;What you will get&lt;/h2&gt;
&lt;p&gt;Doing a PhD at Sussex with Dominique Makowski means:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Joining a dynamic team with a vibrant lab life&lt;/li&gt;
&lt;li&gt;A supervisor that actually supervises 🤯&lt;/li&gt;
&lt;li&gt;A super interesting research topic&lt;/li&gt;
&lt;li&gt;A French-style thesis defense to celebrate your accomplishments 🧀🍷&lt;/li&gt;
&lt;/ul&gt;
&lt;div class=&#34;alert alert-warning&#34;&gt;
  &lt;div&gt;
    &lt;p&gt;&lt;strong&gt;Don&amp;rsquo;t rely on what is written!&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Ask directly &lt;a href=&#34;https://realitybending.github.io/people/&#34;&gt;members of team&lt;/a&gt; (current and past) about their experience in the lab!&lt;/p&gt;
  &lt;/div&gt;
&lt;/div&gt;
&lt;h2 id=&#34;how-to-do-a-phd-in-psychology&#34;&gt;How to do a PhD in Psychology?&lt;/h2&gt;
&lt;ol&gt;
&lt;li&gt;The first step is usually to contact the potential supervisor to discuss a rough research project outline. Write an email with your CV, your research interests and - if you have - some ideas for a research project that matches your supervisor&amp;rsquo;s line of research. If you &lt;strong&gt;don&amp;rsquo;t have ideas yet&lt;/strong&gt;, it&amp;rsquo;s perfectly fine! I will likely propose some avenues of research that might match your interest, and refine them down the line.&lt;/li&gt;
&lt;li&gt;Ideally, you would also want to come up with a plan for &lt;a href=&#34;https://www.sussex.ac.uk/study/phd/degrees/psychology-phd#funding-fees&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;funding&lt;/strong&gt;&lt;/a&gt;. This is the most challenging part, unfortunately. There are typically 4 types of profiles: 1) the &lt;em&gt;student and the supervisor&lt;/em&gt; come up with a tentative research project, with which the student then applies to scholarship opportunities. 2) the &lt;em&gt;supervisor&lt;/em&gt; already has a scholarship for a specific project that he obtained a grant for, and will recruit a PhD for that specific research project; 3) the &lt;em&gt;student&lt;/em&gt; already secured a scholarship that allows them to pursue a PhD with the supervisor of their choice (e.g., some schemes exist from countries for their nationals to do their PhD abroad). 4) Self-funding, which we don&amp;rsquo;t recommend unless you&amp;rsquo;re one of the lucky few with money to spare.&lt;/li&gt;
&lt;/ol&gt;
&lt;h3 id=&#34;funding-opportunities&#34;&gt;Funding Opportunities&lt;/h3&gt;
&lt;p&gt;Funding is a complicated topic, and often the main barrier between one&amp;rsquo;s goal and its achievement. Keep in mind that there are many other possibilities and case-by-case considerations.&lt;/p&gt;
&lt;p&gt;Here are some scholarship opportunities for funded PhDs in the UK:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;The &lt;a href=&#34;https://archive.sussex.ac.uk/study/scholarships/1525-Psychology-Doctoral-Research-Studentship-UK-and-International&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Sussex Psychology Doctoral Research Studentship&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://www.sussex.ac.uk/research/centres/sussex-neuroscience/phd/4yearphd&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Sussex Neuroscience 3+1 years PhD&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://www.sussex.ac.uk/study/fees-funding/phd-funding/view/1807-Sussex-AI-PhD-studentships&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Sussex AI PhD&lt;/strong&gt;&lt;/a&gt; (you will need a primary supervisor from the &lt;em&gt;School of Engineering and Informatics&lt;/em&gt; but I can be a cosupervisor)&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://www.sussex.ac.uk/study/fees-funding/phd-funding/view/1639-SEDarc-%28ESRC%29-PhD-scholarships-for-research-in-the-Social-Sciences&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;SEDarc studentships&lt;/strong&gt;&lt;/a&gt; (see also &lt;a href=&#34;https://sedarc.ac.uk/thematic-pathways/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;here&lt;/a&gt;)&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://www.senss.ac.uk/studentships-overview&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;South and East Network for Social Sciences (SENSS)&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://wellcome.org/grant-funding/schemes/four-year-phd-programmes-studentships-basic-scientists&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Welcome Trust PhD Studentships&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://www.ukri.org/what-we-do/developing-people-and-skills/find-studentships-and-doctoral-training/get-a-studentship-to-fund-your-doctorate/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;UKRI studentship&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://southcoastdtp.ac.uk/funding/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;South Coast Biosciences Network (SoCoBio)&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://www.chevening.org/scholarships/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Chevening Scholarship&lt;/strong&gt;&lt;/a&gt; (International only)&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://phd.learningplanetinstitute.org/en/join-us&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;FIRE French scholarships&lt;/strong&gt;&lt;/a&gt; (must be a collaboration with a Paris-based lab)&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://www.daad.de/en/study-research-teach-abroad/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;DAAD scholarships&lt;/strong&gt;&lt;/a&gt; (Germans)&lt;/li&gt;
&lt;li&gt;The &lt;a href=&#34;https://www.sussex.ac.uk/study/fees-funding/phd-funding/view/1625-China-Scholarship-Council-CSC-University-of-Sussex-Joint-Scholarships-2024&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Joint China Scholarship&lt;/strong&gt;&lt;/a&gt; (China)&lt;/li&gt;
&lt;li&gt;Scholarship Opportunities for &lt;strong&gt;Singaporeans&lt;/strong&gt;:
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://www.gov.uk/government/news/compilation-of-scholarships-and-fellowships-for-singaporeans&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;gov.uk information&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://www.psc.gov.sg/scholarships/postgraduate-scholarships/lee-kuan-yew-scholarship&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Lee Kuan Yew Scholarship&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://www.a-star.edu.sg/Scholarships/for-graduate-studies/national-science-scholarship-phd&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;A*STAR Scholarship&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://www.smu.edu.sg/MOE-start/overseas-pg-scholarship&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;SMU Postgraduate Scholarship&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://www.ntu.edu.sg/hass/admissions/graduate-programmes/hips2024&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;NTU&amp;rsquo;s Humanities International PhD/Postdoctoral Scholarship (HIPS)&lt;/strong&gt;&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;As well as other options:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Partnership&lt;/strong&gt;: If an external partner agrees to cover half the cost (approx. £35k over three years), the university can match the other half of the cost. Useful for applied projects and collaborations with &lt;strong&gt;startups, private companies or NGOs&lt;/strong&gt;. If you&amp;rsquo;re thinking of developing a product, a software or a service, this could be a good option.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Collaboration&lt;/strong&gt;: Many universities allow some form of co-supervisorship. This means that you could do the main part of your PhD in another university, and come to Sussex sporadically as part of a collaboration. Note that official frameworks can exist for this type of configurations, such as the &lt;a href=&#34;https://u-paris.fr/cotutelle-internationale-de-these/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;em&gt;cotutelles&lt;/em&gt;&lt;/a&gt; in France.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;Check-out this &lt;a href=&#34;https://www.sussex.ac.uk/study/phd/apply&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;em&gt;how to apply&lt;/em&gt;&lt;/a&gt; guide for additional information.&lt;/p&gt;
&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    More info are available on the university&amp;rsquo;s &lt;a href=&#34;https://www.sussex.ac.uk/schools/psychology/study/phd&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;PhD in psychology&lt;/strong&gt;&lt;/a&gt;, &lt;a href=&#34;https://www.sussex.ac.uk/study/phd/degrees/psychology-phd#funding-fees&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Funding&lt;/strong&gt;&lt;/a&gt;, &lt;a href=&#34;https://www.sussex.ac.uk/study/phd/degrees/cognitive-science-phd&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;PhD in cognitive science&lt;/strong&gt;&lt;/a&gt; and &lt;a href=&#34;https://www.sussex.ac.uk/research/centres/sussex-neuroscience/phd&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;PhD in neuroscience&lt;/strong&gt;&lt;/a&gt; information page.
  &lt;/div&gt;
&lt;/div&gt;
&lt;h3 id=&#34;other-pots-of-money&#34;&gt;Other Pots of Money&lt;/h3&gt;
&lt;p&gt;Mostly for those already registered as PhD students.&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://editing.press/bassi&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Laura Bassi Scholarship&lt;/a&gt;: Masters and PhD on &amp;ldquo;neglected&amp;rdquo; research topics.&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id=&#34;questions-and-answers&#34;&gt;Questions and Answers&lt;/h2&gt;
&lt;h3 id=&#34;clinical-psychology-phd-or-dclinpsy&#34;&gt;Clinical Psychology PhD or DClinPsy?&lt;/h3&gt;
&lt;p&gt;Unfortunately, the University of Sussex does not offer at the moment a PhD in &lt;em&gt;&lt;strong&gt;Clinical Psychology&lt;/strong&gt;&lt;/em&gt; that includes clinical placements and internships in hospitals. However, if you are interested in working with patients, it is entirely possible to have a research project that involves clinical populations, and specialize in &amp;ldquo;clinical&amp;rdquo; research. Some people then complement this kind of PhD with clinical trainings (e.g., psychotherapy) to transition from research to practice.&lt;/p&gt;
&lt;h3 id=&#34;how-to-become-a-neuropsychologist&#34;&gt;How to become a Neuropsychologist?&lt;/h3&gt;
&lt;p&gt;Neuropsychology is both an approach (focusing on the relationship between the brain and its output in the form of behaviour and thought) and a practice (involving neuropsychological assessments and rehabilitation). The latter is considered a specialization of Clinical Psychology, which means that one must be a clinical psychologist to be a clinical neuropsychologist. As said above, the University of Sussex unfortunately does not offer, at the moment, a formal PhD in clinical psychology or clinical neuropsychology. However, joining the &lt;strong&gt;Reality Bending Lab&lt;/strong&gt; will get you well-prepared to eventually pursue this type of program, as the methods and mindset that we have draws heavily on neuropsychology (the use of neuropsychological tests, the focus on neurocognitive theories, etc.). In fact, some of our past members have become brilliant neuropsychologists, so feel free to ask them!&lt;/p&gt;
&lt;h3 id=&#34;how-to-work-on-psychedelics&#34;&gt;How to work on psychedelics?&lt;/h3&gt;
&lt;p&gt;Psychedelics and altered states of consciousness are a hot topic in psychology and neuroscience. Unfortunately, it is still &lt;em&gt;extremely&lt;/em&gt; difficult to get authorizations to work with these substances. I would not recommend to base your PhD project on this potentiality, as it&amp;rsquo;s too risky that things might not work out (due to ethical, administrative, or political reasons). That said, we do have projects running in collaborations with experts in the field, and are always on the lookout for opportunities to work on these topics. Additionally, we think it&amp;rsquo;s also very interesting to study how altered states of consciousness can be induced &lt;em&gt;without&lt;/em&gt; external substances (e.g., through meditation, hypnosis, sensory deprivation, neural stimulation, &amp;hellip;), which might be a more sustainable and ethical way to approach these phenomena.&lt;/p&gt;
&lt;h2 id=&#34;application-advice&#34;&gt;Application Advice&lt;/h2&gt;
&lt;p&gt;A few tips for your writing up your application dossier, in particular pertaining your CV and cover letter.
Note that these are general guidelines that also apply to other contexts (master&amp;rsquo;s programs, industry jobs, etc.).&lt;/p&gt;
&lt;p&gt;The key thing is to keep in mind that we receive a &lt;em&gt;&lt;strong&gt;lot&lt;/strong&gt;&lt;/em&gt; of applications (few hundreds for some positions). The first mistake you want to avoid is to have a generic, impersonal application: do address specific people (and &lt;strong&gt;do not make mistakes in the spelling of their names&lt;/strong&gt;, it happens often and is a turn-off), and try to concisely paint a profile of yourself that the recruiter can easily picture and form an image of: what is your background, where do you come from, what are your expertise, interests and goals. This should really be one tightly written paragraph (you can expand on this in your CV). We often see long and convoluted CVs and cover letters, that try to show &amp;ldquo;a bit of everything&amp;rdquo;, leaving the reader with little more than a sense of confusion.&lt;/p&gt;
&lt;p&gt;Next, after providing a clear depiction of who you are, you want to show that you have &lt;strong&gt;done your homework about where you are applying&lt;/strong&gt;: be specific about the people of the department (e.g., &amp;ldquo;I am particularly interested in working with Dr. X because of their work on Y&amp;rdquo;), or the papers (&amp;ldquo;I particularly enjoyed your paper on X because of Y&amp;rdquo;). This shows that you are motivated and that you are not just sending the same application to 100 different places. That being said, do not list &lt;em&gt;everything&lt;/em&gt; that is written on someone&amp;rsquo;s website or profile, because it makes it look like you just copied and pasted it. Be genuine, personal and specific. It is tempting to use AI to generate these kinds of things, but I would advise against it. Putting it the time, effort, and hard work will pay off.&lt;/p&gt;
&lt;p&gt;Finally, you want to show that you are a good fit for the position, and show that you have experience in the methods that are used in the lab, that you have experience in the field, etc.&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>Research Assistant in Psychology / Neuroscience</title>
      <link>https://realitybending.github.io/jobs/assistant/</link>
      <pubDate>Thu, 02 Feb 2023 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/jobs/assistant/</guid>
      <description>&lt;p&gt;
  &lt;i class=&#34;fa fa-calendar  pr-1 fa-fw&#34;&gt;&lt;/i&gt; Flexible

  &lt;i class=&#34;fa fa-location-pin  pr-1 fa-fw&#34;&gt;&lt;/i&gt; University of Sussex, Brighton, UK&lt;/p&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img alt=&#34;&#34; srcset=&#34;
               /media/ResearchAssistant_hu_12d205e384adbd5c.webp 400w,
               /media/ResearchAssistant_hu_13f4f996d205587a.webp 760w,
               /media/ResearchAssistant_hu_36fd80c5ae7ceb1c.webp 1200w&#34;
               src=&#34;https://realitybending.github.io/media/ResearchAssistant_hu_12d205e384adbd5c.webp&#34;
               width=&#34;760&#34;
               height=&#34;428&#34;
               loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;p&gt;Working as a research assistant (RA) is a formidable opportunity to take on before - eventually - signing up for a PhD. It is a flexible and varied position, and a perfect position to develop key research skills like writing, data analysis or neuroimaging; and eventually later pursue a postgraduate program in psychology/neuroscience/neuropsychology.&lt;/p&gt;
&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Funded RA positions at Sussex can be seen on the &lt;a href=&#34;https://www.sussex.ac.uk/about/jobs/research-assistant-ref-10411&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;recruitment page&lt;/a&gt;.
  &lt;/div&gt;
&lt;/div&gt;
&lt;h2 id=&#34;sussex-psychology-placement-year&#34;&gt;Sussex Psychology Placement Year&lt;/h2&gt;
&lt;p&gt;Students at the University of Sussex can also opt for a &lt;a href=&#34;https://www.sussex.ac.uk/study/undergraduate/courses/psychology-with-a-professional-placement-year-bsc&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;placement year&lt;/a&gt; between the second and third year of their studies. All undergraduates within the School are eligible to complete a placement year.&lt;/p&gt;
&lt;p&gt;While it might seem like it would &amp;ldquo;add&amp;rdquo; one year and &lt;em&gt;delay&lt;/em&gt; the end of the studies, the experience that you could gain is quite invaluable. Doing a full-year placement year in a research lab is the best way to take on larger projects and acquire a comprehensive research experience. Beyond providing you with a massive headstart for the final year, it is a great opportunity to learn new skills and meet many researchers, which will help you refine your career trajectory and maximize your chances of &lt;strong&gt;achieving your goals&lt;/strong&gt;.&lt;/p&gt;
&lt;p&gt;More information &lt;a href=&#34;http://www.sussex.ac.uk/psychology/internal/students/placements&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;here&lt;/strong&gt;&lt;/a&gt;.&lt;/p&gt;
&lt;h2 id=&#34;sussex-junior-research-associate-jra&#34;&gt;Sussex Junior Research Associate (JRA)&lt;/h2&gt;
&lt;p&gt;Sussex also offers short &lt;strong&gt;summer internship&lt;/strong&gt; opportunities for undergrads interested in developing your research skills and experience. You can apply to the &lt;a href=&#34;http://www.sussex.ac.uk/suro/jra&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Sussex Junior Research Associate (JRA) program&lt;/strong&gt;&lt;/a&gt; to become a research associate and undertake an intensive eight-week research project over the summer break. Find out more information on &lt;a href=&#34;http://www.sussex.ac.uk/suro/applying&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;how to apply here&lt;/strong&gt;&lt;/a&gt;.&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;See this &lt;a href=&#34;https://realitybending.github.io/post/2024-03-12-jingjra/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;blogpost&lt;/strong&gt;&lt;/a&gt; for a testimony.&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id=&#34;sosocbio-undergraduate-summer-studentship&#34;&gt;SoSocBio Undergraduate Summer Studentship&lt;/h2&gt;
&lt;p&gt;Undergraduates residing in the UK can apply for a paid 6 weeks (30hr per week) internship between 1 July and 30 September.&lt;/p&gt;
&lt;p&gt;More information &lt;a href=&#34;https://southcoastbiosciencesdtp.ac.uk/undergraduate-summer-studentship-programme/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;here&lt;/strong&gt;&lt;/a&gt;.&lt;/p&gt;
&lt;h2 id=&#34;international-junior-research-associate-ijra&#34;&gt;International Junior Research Associate (IJRA)&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;See here: &lt;a href=&#34;https://www.sussex.ac.uk/suro/current/ijra&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;https://www.sussex.ac.uk/suro/current/ijra&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id=&#34;other-bursaries&#34;&gt;Other Bursaries&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://www.the-bns.org/grants&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Neuropsychology International Fellowship (NIF)&lt;/strong&gt;&lt;/a&gt;: Small bursaries from the British Neuropsychological Society to support small research internship.&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id=&#34;volunteer-research-assistant&#34;&gt;Volunteer Research assistant&lt;/h2&gt;
&lt;p&gt;Check the &lt;a href=&#34;https://realitybending.github.io/jobs/intern/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;voluntary internships&lt;/a&gt; page for more information.&lt;/p&gt;
&lt;div class=&#34;alert alert-warning&#34;&gt;
  &lt;div&gt;
    &lt;p&gt;&lt;strong&gt;Don&amp;rsquo;t rely on what is written!&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Ask directly &lt;a href=&#34;https://realitybending.github.io/people/&#34;&gt;members of team&lt;/a&gt; (current and past) about their experience in the lab!&lt;/p&gt;
  &lt;/div&gt;
&lt;/div&gt;
</description>
    </item>
    
    <item>
      <title>Research Projects</title>
      <link>https://realitybending.github.io/jobs/projects/</link>
      <pubDate>Thu, 02 Feb 2023 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/jobs/projects/</guid>
      <description>&lt;p&gt;
  &lt;i class=&#34;fa fa-calendar  pr-1 fa-fw&#34;&gt;&lt;/i&gt; Flexible

  &lt;i class=&#34;fa fa-location-pin  pr-1 fa-fw&#34;&gt;&lt;/i&gt; University of Sussex, Brighton, UK&lt;/p&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img alt=&#34;&#34; srcset=&#34;
               /media/research_diagram_hu_2cf0bff64356c4b7.webp 400w,
               /media/research_diagram_hu_9696fb68ea7b6a6f.webp 760w,
               /media/research_diagram_hu_29eaf40393a7ff0f.webp 1200w&#34;
               src=&#34;https://realitybending.github.io/media/research_diagram_hu_2cf0bff64356c4b7.webp&#34;
               width=&#34;760&#34;
               height=&#34;578&#34;
               loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;h2 id=&#34;projects&#34;&gt;Projects&lt;/h2&gt;
&lt;p&gt;Research in the &lt;strong&gt;Reality Bending Lab&lt;/strong&gt; focuses primarily on the physiological and neurocognitive underpinnings of reality perception and aspects of &lt;strong&gt;reality bending&lt;/strong&gt; (e.g., fiction, deception, fake news, illusions, and altered states of consciousness such as through meditation or immersion). Possible projects include (but are not limited to):&lt;/p&gt;
&lt;h3 id=&#34;how-do-we-know-what-is-real-and-what-does-it-change&#34;&gt;How do we know what is real? And what does it change?&lt;/h3&gt;
&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Real vs. Fake&lt;/strong&gt;: This project will typically involve presenting some real vs. &amp;ldquo;fake&amp;rdquo; stimuli (e.g., fake news, AI-generated images, &amp;hellip;) to participants and investigate what interindividual/cognitive/emotional factors allows them to discriminate between the two.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Emotion regulation via fiction&lt;/strong&gt;: believing that something is unreal (regardless of whether it actually is or is not) seem to have some ripple effect on various facets of our body and brain, such as emotions. This project studies the characteristics and potential use of fiction as an emotion regulation strategy. This project can be focused on negative emotions (with threatening/unpleasant stimuli) or &amp;ldquo;positive&amp;rdquo; emotions (e.g., sexual arousal, attractiveness).&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Authenticity &amp;amp; Neuroaesthetics&lt;/strong&gt;: This project investigates the effect of believing that an artwork is &amp;ldquo;forged&amp;rdquo; (e.g., an imitation of a great painter) on our appraisal of beauty.&lt;/li&gt;
&lt;/ul&gt;
&lt;h3 id=&#34;assessment-of-bodily-and-cognitive-abilities-and-their-relationship&#34;&gt;Assessment of bodily and cognitive abilities and their relationship&lt;/h3&gt;
&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Neuropsychological assessment of Cognitive Control&lt;/strong&gt;: This project focuses on the development, validation and improvement of a neuropsychological task to reliably measure &amp;ldquo;cognitive control&amp;rdquo; (executive functions). This project requires some interest in neuropsychological assessment, task development and associated technical skills (programming, game development).&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Physiological Control&lt;/strong&gt;: development of measures (questionnaires, physiological tasks) measuring the ability to voluntarily regulate one&amp;rsquo;s physiology (e.g., heart rate, autonomic reactions, etc.).&lt;/li&gt;
&lt;li&gt;Relationship between &lt;strong&gt;Interoception&lt;/strong&gt; and higher-order functions: This project involves measuring various aspects of our relationship with our body (e.g., by measuring cardiac activity) and analyzing its relationship with cognitive abilities (e.g., Self control, emotion regulation) or higher-order constructs (e.g., primal world beliefsLinks to an external site.).&lt;/li&gt;
&lt;li&gt;Secondary &lt;strong&gt;EEG data analysis&lt;/strong&gt;: Investigating an existing dataset containing resting state EEG signal, from which one would extract features to try predicting dispositional indices (such as primal world beliefs).&lt;/li&gt;
&lt;/ul&gt;
&lt;h3 id=&#34;non-invasive-induction-of-altered-states-of-consciousness&#34;&gt;Non-invasive induction of altered states of consciousness&lt;/h3&gt;
&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Emotion regulation via distancing&lt;/strong&gt;: by instructing people to change their state of mind (e.g., &amp;ldquo;see the events in a detached manner, like a fly on the wall&amp;rdquo;), we hope to manipulate aspects of the sense of reality - such as absorption and psychological distance - and compare its effect (in particular on emotions) with that of other emotion regulation strategies.&lt;/li&gt;
&lt;li&gt;Can we &lt;strong&gt;manipulate the state of consciousness&lt;/strong&gt; and observe actual effects on the performance at various cognitive tasks? For instance, via hypnosis or mindfulness-like instructions, sound stimulation (binaural beats, drumming, &amp;hellip;), sensory deprivation (&amp;ldquo;floating&amp;rdquo; tanks). We study the role of expectations and try to isolate the mechanism of change.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Qualitative + quantitative&lt;/strong&gt; project: Investigation into the world of &amp;ldquo;reality shifters&amp;rdquo;, people claiming that have shifted between realities. Understand their language, personality, etc.&lt;/li&gt;
&lt;/ul&gt;
&lt;h3 id=&#34;metascience--data-science--software-development&#34;&gt;Metascience / Data science / Software development&lt;/h3&gt;
&lt;ul&gt;
&lt;li&gt;Investigation of &lt;strong&gt;scientific practices&lt;/strong&gt;: to what extent scientists engage in &amp;ldquo;new&amp;rdquo; practices (e.g., open science, slow science, preregistration, registered reports, &amp;hellip;) and what factors (e.g., career level, time, ideology, &amp;hellip;) are driving their adoption (or lack thereof). This might involve things like validating assessment tools (such as questionnaires or gamified measures like quizzes), distributing it widely and analysing the results.&lt;/li&gt;
&lt;li&gt;Improving access of &lt;strong&gt;R&lt;/strong&gt; to psychologists: R outputs can be complex, and we are developing tools to facilitate its understanding (e.g., the reportLinks to an external site. package). This project involves implementing functions in R to help communicate and interpret statistical results. This project requires some interest in programming and stats.&lt;/li&gt;
&lt;li&gt;Neurophysiological signal analysis in &lt;strong&gt;Python&lt;/strong&gt;: implementation and validation of new algorithms in Python, related for instance to chaos theory, EEG signal analysis, etc. This project requires some interest in programming, computer science and mathematics.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Psychophysiological methods&lt;/strong&gt;: what is the optimal electrode configuration for recording skin conductance responses (often used as a marker of emotions).&lt;/li&gt;
&lt;li&gt;Role of beauty in science: Is the impact of research publications related to the aeshetic qualities of figures.&lt;/li&gt;
&lt;/ul&gt;
&lt;h3 id=&#34;other--collaborations&#34;&gt;Other / Collaborations&lt;/h3&gt;
&lt;ul&gt;
&lt;li&gt;With &lt;a href=&#34;https://canvas.sussex.ac.uk/courses/30420/pages/theodoros-karapanagiotidis-2-2&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Theodoros Karapanagiotidis&lt;/a&gt;: project involving secondary behavioural data analysis, exploring questions about the nature of thoughts, their patterns, the impact of mood and ongoing experience , and how they vary in in real-life settings. By analysing existing data, students will be able to examine the links between ongoing thoughts, brain structure and function, and their potential implications for mental health and well-being.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;Some of these projects share strong links with philosophical concepts (e.g., the &lt;a href=&#34;https://en.wikipedia.org/wiki/Paradox_of_fiction&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;paradox of fiction&lt;/a&gt;) and/or carry some clinical relevance (e.g., for the understanding and treatment of mood/psychotic/dissociative disorders). Also, note that the lab is radically engaged in open science and, ultimately, quantitative methodologies: thus, &lt;strong&gt;most projects would typically require a substantial use of R&lt;/strong&gt; (or Python) at some stage. However, it&amp;rsquo;s totally okay not to feel proficient at these skills at the start, but the important thing is to be interested and motivated to learn.&lt;/p&gt;
&lt;p&gt;Projects might be conducted individually, in pairs, or in a group, depending on needs. Attending weekly lab meetings is also expected.&lt;/p&gt;
&lt;h2 id=&#34;skills&#34;&gt;Skills&lt;/h2&gt;
&lt;p&gt;Joining the &lt;strong&gt;Reality Bending Lab&lt;/strong&gt; will help you develop unique skills that your might not find in other labs, that will give an edge to your profile for future applications. These include:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Neuroimaging (EEG)&lt;/li&gt;
&lt;li&gt;Psychophysiology (multimodal bodily recordings)&lt;/li&gt;
&lt;li&gt;Computational Bayesian modelling with R&lt;/li&gt;
&lt;li&gt;Advanced programming with Python&lt;/li&gt;
&lt;li&gt;Open science best practices (using GitHub and various cutting edge tools)&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id=&#34;advice-for-students&#34;&gt;Advice for Students&lt;/h2&gt;
&lt;h3 id=&#34;choosing-options&#34;&gt;Choosing Options&lt;/h3&gt;
&lt;p&gt;Most psychology programs are proposing some optionality, i.e., some modules that you can pick.
While many of them look interesting, you often have to make hard choices.
Many students pick what looks interesting, from various psychology domains (e.g., a bit of social psychology, a module from cognitive, one from clinical etc.).
They might also believe that picking a variety of options will provide them with a &lt;strong&gt;multidisciplinary profile&lt;/strong&gt;, which might be valued later on.&lt;/p&gt;
&lt;p&gt;While this is, in principle, true, in practice, &lt;strong&gt;a &amp;ldquo;consistent&amp;rdquo; profile is often much more appealing to recruiters&lt;/strong&gt;. For instance, having a set of clinically-relevant options, or cognitive/neuroscience ones, will give you an edge (and sometimes, even for say a &amp;ldquo;neuroscience&amp;rdquo; opportunity, recruiters would prefer a clearly clinical profile rather than a &amp;ldquo;jack of all trades master of none&amp;rdquo; type of one). &lt;strong&gt;Make your choices wisely, and make them with a plan.&lt;/strong&gt;&lt;/p&gt;
&lt;blockquote&gt;
&lt;p&gt;But I &lt;em&gt;don&amp;rsquo;t know&lt;/em&gt; what I want to do later, so I want to keep most doors open.&lt;/p&gt;&lt;/blockquote&gt;
&lt;p&gt;Yes, that&amp;rsquo;s a common issue. You can still keep doors open while at the same time having a coherent profile. You &lt;em&gt;should&lt;/em&gt; at least have an idea of what subbranch of psychology you &lt;em&gt;don&amp;rsquo;t&lt;/em&gt; want to do (e.g., social psychology).&lt;/p&gt;
&lt;p&gt;For psychology students at Sussex, if you would like to work with me, I recommend picking some of the following options:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Cognitive Neuroscience &lt;em&gt;(must have)&lt;/em&gt;&lt;/li&gt;
&lt;li&gt;Conscious and Unconscious Mental Processes&lt;/li&gt;
&lt;li&gt;Biological Psychology of Mental Health&lt;/li&gt;
&lt;li&gt;Perspectives on Psychology&lt;/li&gt;
&lt;li&gt;Self Regulation: The Science of Achieving Your Goals&lt;/li&gt;
&lt;li&gt;Attention: Distraction, Daydreaming and Diversity&lt;/li&gt;
&lt;li&gt;Drugs, Brain and Behaviour&lt;/li&gt;
&lt;/ul&gt;
&lt;div class=&#34;alert alert-warning&#34;&gt;
  &lt;div&gt;
    &lt;p&gt;&lt;strong&gt;Don&amp;rsquo;t rely on what is written!&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Ask directly &lt;a href=&#34;https://realitybending.github.io/people/&#34;&gt;members of team&lt;/a&gt; (current and past) about their experience in the lab!&lt;/p&gt;
  &lt;/div&gt;
&lt;/div&gt;
</description>
    </item>
    
    <item>
      <title>Sussex Psychological Methods MRes: Tips and Advice</title>
      <link>https://realitybending.github.io/post/2024-03-19-mres/</link>
      <pubDate>Tue, 19 Mar 2024 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2024-03-19-mres/</guid>
      <description>&lt;p&gt;Ola! I&amp;rsquo;m &lt;a href=&#34;https://realitybending.github.io/authors/AnafNeves/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Ana&lt;/a&gt;. As I&amp;rsquo;m starting to approach the end of the year, it might be a good time to reflect and share my experience of doing a research masters in psychological methods at the University of Sussex, during the 2023/2024 academic year. First, I will talk a little bit about the modules I took; then I will mentioned all the reasons why you should choose to work with the Reality Bending Lab (ReBeL) and lastly, I will share some &lt;strong&gt;gems on how to survive the masters&lt;/strong&gt; 💎. Hopefully this blog will help you decide whether this degree is for you! Shall we start?&lt;/p&gt;
&lt;h2 id=&#34;overview-of-the-modules&#34;&gt;Overview of the Modules&lt;/h2&gt;
&lt;p&gt;Since this is a &lt;strong&gt;research masters&lt;/strong&gt; (MRes) aiming to prepare students for a future career as psychology researchers, the modules will have a significant focus on different research frameworks and practices, statistics and coding. During the Autumn semester you will have three main modules: 1) a (re)introduction to statistical models; 2) an introduction to Qualitative Methods; and 3) an introduction to better quality research practices. This term is super heavy on its content (no jokes) and will feel like a lot to do and learn (see below for tips on how to survive). However, there are plenty of materials to help you through this term, such as the R tutorials from our own in-house celebrity Professor Andy Field.&lt;/p&gt;
&lt;p&gt;The Spring semester is less content heavy and more practical focus. There are again, three main modules: 1) a theoretical and practical module on how to use advanced statistical methods; 2) an introduction to the Bayesian framework; and 3) an introduction to Python programming and how to use it to implement experiments. This has been a delightful term, not because it is &lt;em&gt;easy&lt;/em&gt;, but because the focus is less on &lt;strong&gt;memorising&lt;/strong&gt; and more on &lt;strong&gt;learning how&lt;/strong&gt;. Similarly, there are plenty of amazing materials to help you through this term such as optional zoom meetings to help you understand the materials and continuous communication on discord between lecturers and students.&lt;/p&gt;
&lt;p&gt;Additionally, there will be a research module that runs both in Autumn and Spring, and a dissertation module that starts in January and ends in August (i.e., when the dissertation project is due).&lt;/p&gt;
&lt;h2 id=&#34;the-internship&#34;&gt;The Internship&lt;/h2&gt;
&lt;p&gt;Critically, you will also do an &amp;ldquo;internship&amp;rdquo; as part of this masters (named the &amp;ldquo;research process&amp;rdquo; module 🤷‍♀️). This is by far &lt;strong&gt;the most exciting part&lt;/strong&gt; of this masters as you will learn first-hand what is like to be a researcher. You can essentially chose any psychology researcher from Sussex to work with, providing you with a great network and experience. Now&amp;hellip; you may be wondering &lt;strong&gt;what lab to choose?&lt;/strong&gt; And oh boy, do I have the answer for you!&lt;/p&gt;
&lt;p&gt;Introducing the &lt;strong&gt;Reality Bending Lab (ReBeL)&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Rebel is led by &lt;a href=&#34;https://realitybending.github.io/authors/dominique-makowski/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Dr. Dominique Makowski&lt;/a&gt;. He will be your Mr. Miyagi during the Autumn and Spring term (and also your lecturer for the Bayesian Module). His patience, humour, straightforwardness and unmatched theoretical and pragmatic knowledge will be one of the big reasons why you will desire to be a researcher at the end of this masters (PS: no payment has been received in exchange for this testimony). The lab focus a lot on &lt;strong&gt;innovation&lt;/strong&gt; hence you will learn new ways to collect neuroscientific data and use new statistical methods. There will also be a big focus on &lt;strong&gt;collaboration&lt;/strong&gt;. Yes you will work independently, however more likely than not you will have the support of everyone in the lab, and you will be giving support yourself (getting a bit of experience on supervision and mentoring). &lt;strong&gt;Curiosity&lt;/strong&gt; is welcome and encouraged. Ask your questions, get involved in all aspects of the process if possible, and take advantage of the fact you will have a &amp;lsquo;mentor&amp;rsquo; for the whole academic year.&lt;/p&gt;
&lt;p&gt;During my time at ReBeL, I have been involved in various projects, such as &amp;ldquo;Exploring the Correlation between Interoception and Primal World Beliefs&amp;rdquo; and a meta-analysis of a widely used questionnaire of Interoception. These projects have taught me a lot, from how to collect and analyse both physiological and behavioural data, access and collect data for a meta-analysis, and report the work I did in oral and written format. Throughout the year, with the guidance and expertise of everyone involved in the lab, I gained a lot of confidence in my abilities as a researcher. Which is why I found this internship the most influential aspect of my masters.  Ultimately, at the ReBeL lab, you will not only &lt;strong&gt;investigate exciting concepts and topics but you will also have first hand experience on what it actually takes to be a researcher&lt;/strong&gt; (including the need to have a twitter account, apparently).&lt;/p&gt;
&lt;h2 id=&#34;survival-tips&#34;&gt;Survival Tips&lt;/h2&gt;
&lt;p&gt;Now&amp;hellip; You might be wondering.. &amp;ldquo;How in the world will I do all of this in one academic year?&amp;rdquo; Here are some tips that helped me gain the most of this masters without loosing my mind.&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Unsurprising tip&lt;/strong&gt;: DO THE WEEKLY WORKSHOPS/TUTORIALS. They will provide with the majority of code, steps and knowledge necessary to complete the assignments.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Life saving tip&lt;/strong&gt;: do meal prep for the 48-hour assignments. If you are anything like me you will rather lose sleep then a delicious home-made meal. However, with the short time window to complete these assignments, meal prepping will help you feel less anxious about &amp;ldquo;not having enough time&amp;rdquo; to complete it all whilst still giving your mind everything it needs to function (i.e., sleep and nutrients).&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Qualitative tip&lt;/strong&gt;: as part of the January assignments, you will be asked to analyse 5 interviews using a qualitative method. If you come from a mostly quantitative background like me, you will be unfamiliar to how long it takes to code qualitative data. Do not make the same mistakes as I did and start that assignment as early as possible.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Student formatting tip&lt;/strong&gt;: when lectures say &amp;ldquo;I want it in APA format&amp;rdquo; some will expect you to write a piece of work that equates a publication level piece of work. When in doubt, ask them!&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Practical life skills tip&lt;/strong&gt;: communication is key with your supervisors. Especially during your internship; be honest about what you can and can not do, your preferred ways of working, your goals and dreams, and mostly important when you need help.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Ultimate tip&lt;/strong&gt;: do consider part-time , especially if you want/need to be working more than 20 hours a week on top of doing this masters. It is full on, and even as part-time all the lectures will be taught in the first year and hence there is still a lot of work to do. But it is possible, and can even be &lt;em&gt;enjoyable&lt;/em&gt;.&lt;/li&gt;
&lt;/ul&gt;
</description>
    </item>
    
    <item>
      <title>How to Assess Task Reliability using Bayesian Mixed Models</title>
      <link>https://realitybending.github.io/post/2024-03-18-signaltonoisemixed/</link>
      <pubDate>Mon, 18 Mar 2024 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2024-03-18-signaltonoisemixed/</guid>
      <description>&lt;p&gt;Using reliable tasks when assessing inter-individual differences is a key issue for differential psychology and neuropsychology, and many research areas are clouded with mixed evidence stemming out of the suboptimal computation of individual scores (e.g., tasks with not enough trials, scores consisting in computing the difference, aka the &lt;strong&gt;contrast&lt;/strong&gt; between two conditions; see &lt;a href=&#34;https://osf.io/preprints/psyarxiv/8ktn6&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Rouder et al., 2024&lt;/a&gt;). As such, measuring and reporting the reliability of the paradigms used could be an important step for &lt;strong&gt;increasing results replicability&lt;/strong&gt;.&lt;/p&gt;
&lt;p&gt;Recently, a new approach has emerged, suggesting to assess task sensitivity to inter-individual differences by leveraging mixed models (&lt;a href=&#34;https://doi.org/10.1177/09637214231220923&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Rouder et al., 2024&lt;/a&gt;).
In essence, the idea is to fit a statistical model that tests for the &lt;strong&gt;general population level&lt;/strong&gt; effect of a manipulation in a given task/experiment (e.g., the impact of a variable &lt;strong&gt;Difficulty&lt;/strong&gt; on another variable &lt;strong&gt;RT&lt;/strong&gt;), and incorporates a &lt;strong&gt;random effect&lt;/strong&gt; for each participant. This &amp;ldquo;full&amp;rdquo; mixed model essentially models the general population level by taking into account all the inter-individual effects and - as a side effect - &lt;strong&gt;estimates the effects of interest for each participant separately&lt;/strong&gt;.&lt;/p&gt;
&lt;p&gt;When fitting these models under a Bayesian framework, one can easily estimate the &amp;ldquo;variability&amp;rdquo; (or certainty) of the effect in each participant. This is great, because it allows us to assess a &amp;ldquo;signal-to-noise&amp;rdquo; ratio, an index of how much the interindividual variability (how participants vary) is larger than the intraindividual variability (e.g., how much participants vary across trial, or how precisely participants&amp;rsquo; effects are estimated).&lt;/p&gt;
&lt;p&gt;In this &amp;ldquo;Signal-To-Noise Ratio as Effect Reliability&amp;rdquo; framework, an ideal task/manipulation would have a strong inter-individual variability (i.e., participants would on average vary a lot) and a low intra-individual variability (each participant would have very consistent effects), which leads to a reliable measure of interindividual effects.&lt;/p&gt;
&lt;p&gt;Let&amp;rsquo;s see how we can do that in R using the &lt;code&gt;brms&lt;/code&gt; package for fitting Bayesian mixed model. First, let&amp;rsquo;s start to generate 4 datasets with different levels of inter-individual and intra-individual variability.&lt;/p&gt;
&lt;details&gt;
  &lt;summary&gt;Show code&lt;/summary&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-r&#34; data-lang=&#34;r&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;library&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;easystats&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;library&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;tidyverse&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;library&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;brms&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;library&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;patchwork&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Make function to generate data&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;generate_data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;kr&#34;&gt;function&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;25&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;effect_sd&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0.4&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;intercept_sd&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.4&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;noise&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.8&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;df&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;{&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;df&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;data.frame&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;kr&#34;&gt;for&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;participant&lt;/span&gt; &lt;span class=&#34;kr&#34;&gt;in&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;:&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;20&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;{&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;x&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;y&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;effect_sd&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;*&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;x&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;intercept_sd&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;y&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;y&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;noise&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;df&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rbind&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;df&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;data.frame&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Difficulty&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;x&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;RT&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;y&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;                               &lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;paste0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;S&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)))&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;p&#34;&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;df&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;$&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Name&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;name&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;df&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;p&#34;&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Generate 4 datasets&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;df1&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;generate_data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;20&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;effect_sd&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0.5&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;intercept_sd&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.5&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;1. Intercept and Effect&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;df2&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;generate_data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;20&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;effect_sd&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0.1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;intercept_sd&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.5&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;2. Intercept Only&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;df3&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;generate_data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;20&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;effect_sd&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0.5&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;intercept_sd&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;3. Effect Only&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;df4&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;generate_data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;200&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;effect_sd&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0.5&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;intercept_sd&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.5&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;4. More trials&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Plot data&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;rbind&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;df1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;df2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;df3&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;df4&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;|&amp;gt;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;ggplot&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;x&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Difficulty&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;y&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;RT&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;color&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;fill&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;geom_point2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;alpha&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.5&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;geom_smooth&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;method&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;lm&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;se&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;kc&#34;&gt;TRUE&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;alpha&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;theme_minimal&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;scale_fill_material_d&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;scale_color_material_d&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;facet_wrap&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;~&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Name&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;scales&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;free&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/details&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img alt=&#34;&#34; srcset=&#34;
               /post/2024-03-18-signaltonoisemixed/fig1_hu_8c4e561a613a9b8e.webp 400w,
               /post/2024-03-18-signaltonoisemixed/fig1_hu_43c54a6c4684fff.webp 760w,
               /post/2024-03-18-signaltonoisemixed/fig1_hu_733432bfea2875c2.webp 1200w&#34;
               src=&#34;https://realitybending.github.io/post/2024-03-18-signaltonoisemixed/fig1_hu_8c4e561a613a9b8e.webp&#34;
               width=&#34;760&#34;
               height=&#34;760&#34;
               loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;p&gt;In each of the dataset, we simulated the data of &lt;strong&gt;20 participants&lt;/strong&gt; undergoing a task with &lt;em&gt;n&lt;/em&gt; trials varying in &lt;strong&gt;difficulty&lt;/strong&gt;, and we recorded their &lt;strong&gt;reaction time (RT)&lt;/strong&gt;. Note that while in our example &lt;em&gt;difficulty&lt;/em&gt; is a continuous variable, it would work the same if it was categorical variable (e.g., effect of condition B over A, intervention vs. baseline, incongruent vs. congruent, etc.).&lt;/p&gt;
&lt;p&gt;When we fit a linear regression of the form &lt;em&gt;RT ~ difficulty&lt;/em&gt;, we are estimating two parameters; the &lt;em&gt;intercept&lt;/em&gt; (which can be seen as the &amp;ldquo;baseline&amp;rdquo; RT, i.e., &lt;strong&gt;participants&amp;rsquo; baseline processing speed&lt;/strong&gt; when the difficulty is 0) and the &lt;em&gt;slope&lt;/em&gt; (how much participants are impacted by this variable). These two parameters are in principle independent (a participant can be very fast regardless of the difficulty, and another one could be equally fast at baseline - same intercept - but very slow when the task is difficult - strong slope).&lt;/p&gt;
&lt;p&gt;We simulated 4 datasets with different participant characteristics:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Dataset 1&lt;/strong&gt;: Both the RT intercept (&lt;strong&gt;the &amp;ldquo;baseline&amp;rdquo; RT&lt;/strong&gt;) and the effect of the manipulation (the &lt;strong&gt;effect of difficulty&lt;/strong&gt;) vary across participants.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Dataset 2&lt;/strong&gt;: Not much interindividual variability in the effect (only the baseline RT varies).&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Dataset 3&lt;/strong&gt;: Not much interindividual variability in the baseline RT (only the effect of difficulty varies from participant to participant).&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Dataset 4&lt;/strong&gt;: Same as dataset 1, but with more trials (200 instead of 20). As you can see, the &amp;ldquo;precision&amp;rdquo; ribbon around the regression line is much narrower, indicating that the effect is more precisely estimated.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;We expect that reliability of the paradigm to measure 1) the sensitivity to &lt;strong&gt;difficulty&lt;/strong&gt; and 2) the &lt;strong&gt;baseline RT&lt;/strong&gt; will be higher in dataset 4 (because more trials) than in dataset 1. Moreover, the sensitivity to &lt;strong&gt;difficulty&lt;/strong&gt; will be particularly low in dataset 2 (where only the baseline RT is set to varies), and similarly for baseline RT in dataset 3 &lt;em&gt;mutatis mutandis&lt;/em&gt;.&lt;/p&gt;
&lt;p&gt;Now, let&amp;rsquo;s fit a Bayesian linear mixed model to each of these datasets (note that we specify the effect of Difficulty as a random &lt;em&gt;slope&lt;/em&gt; in addition to estimating the random intercept).&lt;/p&gt;
&lt;details&gt;
  &lt;summary&gt;Show code&lt;/summary&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-r&#34; data-lang=&#34;r&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;model1&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;brms&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;brm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;RT&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;~&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Difficulty&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Difficulty&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;|&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;df1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;iter&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;600&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;model2&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;brms&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;brm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;RT&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;~&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Difficulty&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Difficulty&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;|&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;df2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;iter&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;600&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;model3&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;brms&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;brm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;RT&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;~&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Difficulty&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Difficulty&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;|&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;df3&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;iter&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;600&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;model4&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;brms&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;brm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;RT&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;~&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Difficulty&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Difficulty&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;|&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;df4&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;iter&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;600&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/details&gt;
&lt;p&gt;This model basically computes the overall relationship (Intercept + Slope) between difficulty and RT, as well as &lt;strong&gt;for each participant&lt;/strong&gt;.
We can then extract the &lt;strong&gt;posterior distribution&lt;/strong&gt; of these individual effects (i.e., the value of the &lt;strong&gt;Intercept&lt;/strong&gt; and the &lt;strong&gt;Slope&lt;/strong&gt; for each participant).&lt;/p&gt;
&lt;details&gt;
  &lt;summary&gt;Show code&lt;/summary&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-r&#34; data-lang=&#34;r&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Random effects extraction&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;extract_individual&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;kr&#34;&gt;function&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;df&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;{&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;coefs&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;coef&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;summary&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;kc&#34;&gt;FALSE&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;$&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rbind&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;as.data.frame&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;coefs[&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Intercept&amp;#34;&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;|&amp;gt;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;nf&#34;&gt;pivot_longer&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;everything&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;names_to&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Participant&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;values_to&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Value&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;|&amp;gt;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Parameter&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Intercept&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;as.data.frame&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;coefs[&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Difficulty&amp;#34;&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;|&amp;gt;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;nf&#34;&gt;pivot_longer&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;everything&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;names_to&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Participant&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;values_to&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Value&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;|&amp;gt;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Parameter&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Difficulty&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;p&#34;&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;re1&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;extract_individual&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;1. Intercept and Effect&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;re2&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;extract_individual&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;2. Intercept Only&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;re3&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;extract_individual&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model3&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;3. Effect Only&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;re4&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;extract_individual&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model4&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;4. More trials&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Plot Random effects&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;rbind&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;re1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;re2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;re3&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;re4&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;|&amp;gt;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;ggplot&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;x&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Value&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;y&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;fill&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;ggdist&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;stat_slabinterval&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;adjust&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;linewidth&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.5&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;size&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.5&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;scale_fill_material_d&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;theme_minimal&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;facet_grid&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;~&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Parameter&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;scales&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;free&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/details&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img alt=&#34;&#34; srcset=&#34;
               /post/2024-03-18-signaltonoisemixed/fig2_hu_78e660234b2c4fd1.webp 400w,
               /post/2024-03-18-signaltonoisemixed/fig2_hu_fb7aeb0fd86ae2f8.webp 760w,
               /post/2024-03-18-signaltonoisemixed/fig2_hu_1735dde7047b1b34.webp 1200w&#34;
               src=&#34;https://realitybending.github.io/post/2024-03-18-signaltonoisemixed/fig2_hu_78e660234b2c4fd1.webp&#34;
               width=&#34;570&#34;
               height=&#34;760&#34;
               loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;p&gt;Each participant&amp;rsquo;s &amp;ldquo;score&amp;rdquo; (for the baseline RT score, i.e., the intercept; and the effect of difficulty, i.e., the slope) is represented by &lt;strong&gt;a distribution&lt;/strong&gt;.
This distribution is wider when there is less trials, which can be interpreted as more uncertainty about the exact estimate.
Some datasets have a low interindividual variability for some parameters (e.g., dataset 2 has not much interindividual variability in the effect of difficulty).&lt;/p&gt;
&lt;p&gt;We can now compute, for each participant, the &amp;ldquo;mean&amp;rdquo; of its effects (for the intercept and the slope), as well as its own effect SD (intra-individual variability).&lt;/p&gt;
&lt;details&gt;
  &lt;summary&gt;Show code&lt;/summary&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-r&#34; data-lang=&#34;r&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;scores&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rbind&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;re1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;re2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;re3&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;re4&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;|&amp;gt;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;summarize&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;Mean&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;mean&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Value&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;SD&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;sd&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Value&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;.by&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Name&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Parameter&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Participant&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;head&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;scores&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/details&gt;
&lt;table&gt;
  &lt;thead&gt;
      &lt;tr&gt;
          &lt;th style=&#34;text-align: left&#34;&gt;Name&lt;/th&gt;
          &lt;th style=&#34;text-align: left&#34;&gt;Parameter&lt;/th&gt;
          &lt;th style=&#34;text-align: left&#34;&gt;Participant&lt;/th&gt;
          &lt;th style=&#34;text-align: right&#34;&gt;Mean&lt;/th&gt;
          &lt;th style=&#34;text-align: right&#34;&gt;SD&lt;/th&gt;
      &lt;/tr&gt;
  &lt;/thead&gt;
  &lt;tbody&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;1. Intercept and Effect&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Intercept&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;S1&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.37&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.20&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;1. Intercept and Effect&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Intercept&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;S10&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;-1.05&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.20&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;1. Intercept and Effect&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Intercept&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;S11&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.88&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.19&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;1. Intercept and Effect&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Intercept&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;S12&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;-0.30&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.18&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;1. Intercept and Effect&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Intercept&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;S13&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.16&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.19&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;1. Intercept and Effect&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Intercept&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;S14&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.57&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.19&lt;/td&gt;
      &lt;/tr&gt;
  &lt;/tbody&gt;
&lt;/table&gt;
&lt;p&gt;Finally, we can compute the &lt;strong&gt;Signal-to-Noise Ratio&lt;/strong&gt; for each parameter for each dataset, which is the ratio of the interindividual variability (the SD of the individual mean scores) over the average intraindividual variability (the average of the individual SDs).&lt;/p&gt;
&lt;details&gt;
  &lt;summary&gt;Show code&lt;/summary&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-r&#34; data-lang=&#34;r&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;summarize&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;scores&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;          &lt;span class=&#34;n&#34;&gt;SNR&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;sd&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Mean&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;/&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;mean&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;SD&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;          &lt;span class=&#34;n&#34;&gt;.by&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Name&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Parameter&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;/details&gt;
&lt;table&gt;
  &lt;thead&gt;
      &lt;tr&gt;
          &lt;th style=&#34;text-align: left&#34;&gt;Name&lt;/th&gt;
          &lt;th style=&#34;text-align: left&#34;&gt;Parameter&lt;/th&gt;
          &lt;th style=&#34;text-align: right&#34;&gt;SNR&lt;/th&gt;
      &lt;/tr&gt;
  &lt;/thead&gt;
  &lt;tbody&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;1. Intercept and Effect&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Intercept&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;2.87&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;1. Intercept and Effect&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Difficulty&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;3.00&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;2. Intercept Only&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Intercept&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;2.57&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;2. Intercept Only&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Difficulty&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.55&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;3. Effect Only&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Intercept&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;0.88&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;3. Effect Only&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Difficulty&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;2.59&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;4. More trials&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Intercept&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;8.88&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;4. More trials&lt;/td&gt;
          &lt;td style=&#34;text-align: left&#34;&gt;Difficulty&lt;/td&gt;
          &lt;td style=&#34;text-align: right&#34;&gt;7.97&lt;/td&gt;
      &lt;/tr&gt;
  &lt;/tbody&gt;
&lt;/table&gt;
&lt;p&gt;As predicted, the &amp;ldquo;reliability&amp;rdquo; of the paradigm to measure the interindividual effect of difficulty on RT is low in dataset 2 (where only the baseline RT varies), moderate in dataset 1 and 3, and high in dataset 4 where there are more trials.&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>Junior Research Assistant (JRA) at Sussex: is it worth it?</title>
      <link>https://realitybending.github.io/post/2024-03-12-jingjra/</link>
      <pubDate>Thu, 02 Nov 2023 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2024-03-12-jingjra/</guid>
      <description>&lt;p&gt;Hi all, I am &lt;a href=&#34;https://realitybending.github.io/authors/jingxiong-xu/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Jing&lt;/a&gt;, and I thought I would share my experience as a Psychology Junior Research Assistant (JRA) at the University of Sussex, as many students might wonder how it is really like. Obviously, I cannot speak for all the labs, but I hope my experience can give you a general idea of what to expect.&lt;/p&gt;
&lt;p&gt;I worked as a JRA during summer 2023 at the Reality Bending Lab (ReBeL). And to put it simply, I think it was &lt;strong&gt;the most valuable experience&lt;/strong&gt; during my undergraduate journey &lt;em&gt;(PS: I have &lt;strong&gt;not&lt;/strong&gt; written this at gunpoint)&lt;/em&gt;. During these three months, I was supervised by Dr Makowski to work on a piece of original research, that thought me a lot about programming, cognitive neuropsychology, physio recordings and how real research is done. Additionally, know that it is possible to stay in the same lab next academic year, to do your final year &lt;strong&gt;dissertation with a strong head start&lt;/strong&gt; in terms of skills and knowledge.&lt;/p&gt;
&lt;img src=&#34;poster.jpg&#34; align=&#34;right&#34; width=&#34;40%&#34;&gt; 
&lt;p&gt;I had the pleasure of joining the Reality Bending Lab (ReBeL) along with &lt;a href=&#34;https://realitybending.github.io/authors/auz-moore/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Auz&lt;/a&gt;, as the first two members since the lab moved to the UK. The title of my project was &lt;strong&gt;&amp;ldquo;Exploring the Correlation between Interoception and Primal World Beliefs&amp;rdquo;&lt;/strong&gt;, which involved collecting &lt;strong&gt;physiological data&lt;/strong&gt; (e.g., heart rate, respiration, &amp;hellip;) in various tasks, analysing them, and investigating the relationship between various measures. The project started from scratch, where I learned how to use the &lt;strong&gt;JavaScript package JsPsych&lt;/strong&gt; to build the entire paradigm via coding. I also received detailed training on how to run a lab-based experiment, something I used to be worried but am now &lt;strong&gt;extremely confident about&lt;/strong&gt;. After collecting the data from 20 participants (&lt;em&gt;summer time goes by veryyyy fast!&lt;/em&gt;), I learned how to make and visualize Bayesian correlations in R. The output of this project was made into an academic poster, where I had to be creative and selective, to be presented at the poster session (see below). Additionally, we created the &lt;a href=&#34;https://github.com/RealityBending/SussexPhysioProtocol&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;em&gt;&amp;ldquo;Sussex Psychophysiological Research Protocol&amp;rdquo;&lt;/em&gt;&lt;/a&gt;, a document aiming at providing guidelines for the best practices in psychophysiological research, to benefit future research done at Sussex. It might not seem like much, but it felt like doing real contributions to research, which was great!&lt;/p&gt;
&lt;p&gt;Something important I learned is, beyond pure academic excellence, research is also about community and networking. It was a great occasion to &lt;strong&gt;informally meet many researchers&lt;/strong&gt;, and make bonds with other students. What is cool is that the JRA journey doesn&amp;rsquo;t stop abruptly and continues into the next academic year, as all candidates are invited to present their work at the &lt;strong&gt;JRA conference&lt;/strong&gt; held by the university in October. This was an amazing opportunity to get a glimpse of what a scientific conference might be, feel proud about your work, connecting with fellow students, learning how to talk about research with other staff members, and gaining public speaking skills. For those who are more ambitious, why not submit your work to the national level, and present it in the British Conference for Undergraduate Research (BCUR)?&lt;/p&gt;
&lt;p&gt;In summary, I see the JRA as a golden key to open countless possibilities for your &lt;strong&gt;future career path&lt;/strong&gt;. For those considering applying to &lt;strong&gt;postgraduate studies&lt;/strong&gt; or research assistants, the strong research experience you gained will &lt;strong&gt;put you at the top of the list&lt;/strong&gt;. Even for those who decided to not do research in the future, it will still be rewarding as it gives a clear idea of what career you do not want. Don&amp;rsquo;t miss on it!&lt;/p&gt;
&lt;p align=&#34;right&#34;&gt;- Jing&lt;/p&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img alt=&#34;&#34; srcset=&#34;
               /post/2024-03-12-jingjra/ceremony_hu_79578bb193b81a68.webp 400w,
               /post/2024-03-12-jingjra/ceremony_hu_1defa5a8c38bfddd.webp 760w,
               /post/2024-03-12-jingjra/ceremony_hu_2287f73e27748a4c.webp 1200w&#34;
               src=&#34;https://realitybending.github.io/post/2024-03-12-jingjra/ceremony_hu_79578bb193b81a68.webp&#34;
               width=&#34;760&#34;
               height=&#34;570&#34;
               loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>How do we know what is real? The &#39;Affective Reality Theory&#39;</title>
      <link>https://realitybending.github.io/post/2023-04-11-affectivereality/</link>
      <pubDate>Tue, 11 Apr 2023 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2023-04-11-affectivereality/</guid>
      <description>&lt;p&gt;I thought it would be interesting to summarize an idea developed during my PhD on &amp;ldquo;fictional reappraisal&amp;rdquo;, i.e., on the effect of the belief that an emotional stimulus is not real (&lt;a href=&#34;https://www.theses.fr/2018USPCB188&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Makowski, 2018&lt;/a&gt;). That of &lt;strong&gt;Affective Reality&lt;/strong&gt;, which is a hypothesis about the &lt;strong&gt;role of affective reactions in the formation of reality beliefs&lt;/strong&gt;.&lt;/p&gt;
&lt;p&gt;The premise it lies on is that we have entered a &amp;ldquo;post-truth era&amp;rdquo;, in which &lt;strong&gt;the distinction between real and simulated (&amp;ldquo;fake&amp;rdquo;) objects has become virtually impossible&lt;/strong&gt; based on physical characteristics alone. In other words, technology has developed so much that we can forge (or will be able to in the near future) &amp;ldquo;artificial&amp;rdquo; &lt;strong&gt;&lt;sup id=&#34;fnref:1&#34;&gt;&lt;a href=&#34;#fn:1&#34; class=&#34;footnote-ref&#34; role=&#34;doc-noteref&#34;&gt;1&lt;/a&gt;&lt;/sup&gt;&lt;/strong&gt; content (e.g., text and images with AIs, and even environments with VR) that is indistinguishable from its original counterpart. For instance, face generation algorithms are so advanced that it is impossible nowadays to tell the difference with the naked eye between a real photo and AI-generated image.&lt;/p&gt;
&lt;p&gt;Once we agree on this premise of objective equivalence between reality and simulation, the question of &lt;strong&gt;how do we form judgments and make decisions about the reality of objects&lt;/strong&gt; arises. In the absence of clues within the stimuli, we are left with with other sources of epistemological information, such as contextual cues (in the case of news, who is the author, what is the outlet it got published, etc.), and &lt;strong&gt;&lt;em&gt;internal&lt;/em&gt; cues&lt;/strong&gt; (subjective characteristics: how does it relate to our knowledge, how does it make us feel, etc.). The latter is of particular interest to us psychologists.&lt;/p&gt;
&lt;p&gt;We refer to the process of forming reality beliefs as &lt;strong&gt;simulation monitoring&lt;/strong&gt; (&lt;a href=&#34;https://realitybending.github.io/publication/makowski2019phenomenal/makowski2019phenomenal.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Makowski et al., 2019&lt;/a&gt;), which is a somewhat controversial term (that some &lt;strong&gt;&lt;sup id=&#34;fnref:2&#34;&gt;&lt;a href=&#34;#fn:2&#34; class=&#34;footnote-ref&#34; role=&#34;doc-noteref&#34;&gt;2&lt;/a&gt;&lt;/sup&gt;&lt;/strong&gt; have considered as almost counterintuitive). The reason for this term, instead of something along the lines &amp;ldquo;reality appraisal&amp;rdquo; &lt;strong&gt;&lt;sup id=&#34;fnref:3&#34;&gt;&lt;a href=&#34;#fn:3&#34; class=&#34;footnote-ref&#34; role=&#34;doc-noteref&#34;&gt;3&lt;/a&gt;&lt;/sup&gt;&lt;/strong&gt;, is the assumption that &lt;strong&gt;reality is our default mode of experience&lt;/strong&gt;. In other words, we are not well equipped (neurocognitively speaking) to detect and classify things as non-real, as these objects are very recent in our evolutionary history. Thus, according to the &lt;strong&gt;Affective Reality Theory&lt;/strong&gt;, by default, the brain considers the origin of its experiences as real&amp;hellip; but this &amp;ldquo;belief&amp;rdquo; is, most of the time, not even fully formed, remaining implicit and subconscious (i.e., we don&amp;rsquo;t spend all our cognitive resources with a constant &amp;ldquo;this is real. This is real too. That too.&amp;rdquo; labelling). &lt;strong&gt;This default mode acts as a higher-level, transparent prior over our experiences&lt;/strong&gt;, providing a scaffolding and structuring our perception, thoughts and reactions. We do not actively appraise the world as real (it is the baseline position), but instead can ask ourselves whether it is simulated, hence simulation monitoring.&lt;/p&gt;
&lt;figure&gt;
  &lt;img src=&#34;AffectiveRealityTheory_Makowski.png&#34; alt=&#34;The Affective Reality Theory (Makowski, 2018)&#34;/&gt;
  &lt;figcaption&gt;&lt;i&gt;The Affective Reality Theory posits that reality beliefs (the tendency to believe that something is real, as opposed to non-real) is related to  emotions and/or bodily reactions through a quadratic (inverse U-shaped) relationship..&lt;/i&gt;&lt;/figcaption&gt;
&lt;/figure&gt;
&lt;p&gt;The &lt;strong&gt;Affective Reality&lt;/strong&gt; hypothesis posits that simulation monitoring is strongly connected to &amp;ldquo;affective processing&amp;rdquo; &lt;strong&gt;&lt;sup id=&#34;fnref:4&#34;&gt;&lt;a href=&#34;#fn:4&#34; class=&#34;footnote-ref&#34; role=&#34;doc-noteref&#34;&gt;4&lt;/a&gt;&lt;/sup&gt;&lt;/strong&gt; through a quadratic (inverse U-shaped) relationship. This means that stimuli associated with a stronger emotional and/or bodily reaction will preferentially bias our judgment towards &amp;ldquo;reality&amp;rdquo;. In other words, things that elicit feelings and/or bodily arousal, &lt;em&gt;ceteris paribus&lt;/em&gt;, will be more likely to be classified as &amp;ldquo;real&amp;rdquo; (as opposed to fake). In fact, strongly emotional events will even &amp;ldquo;feel&amp;rdquo; more real: this transparent default prior and subconscious belief (&amp;ldquo;agnostic-real&amp;rdquo;) will be replaced in high-intensity scenarios by an explicit and conscious impression that the stimulus is very real, and, if logic opposes, that it &amp;ldquo;must be real&amp;rdquo; regardless.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Isn&amp;rsquo;t it the other way round&lt;/strong&gt;, you might wonder: that real stimuli (as opposed to ones believed to be non-real) are associated with a stronger emotional reactions? And that &lt;strong&gt;it is the believed reality that drives the emotional response&lt;/strong&gt;? Indeed, we do believe that there is a two-ways relationship between simulation monitoring and emotions. But it is not exactly that beliefs of reality are associated with stronger emotions, but rather that beliefs that something is &lt;em&gt;not&lt;/em&gt; real leads to a lower emotional response (the usage of fiction as an emotion regulation strategy - &amp;ldquo;fictional reappraisal&amp;rdquo; - was the main topic of my doctoral dissertation). In fact, the Affective Reality theory posits that this regulatory effect of &lt;strong&gt;simulation monitoring starts to dominate after a certain point where the emotion becomes too strong&lt;/strong&gt; and unbearable: beliefs such as &amp;ldquo;it can&amp;rsquo;t be real&amp;rdquo;, and other forms of reality denials are invoked automatically to protect us and help us cope with distressing information.&lt;/p&gt;
&lt;p&gt;To summarize this summary, the Affective Reality hypothesis claims that from mild to relatively strong emotional stimuli, the effect of affect on simulation monitoring dominates (&lt;strong&gt;+affect → +reality&lt;/strong&gt;) and will bias our judgment towards &amp;ldquo;reality&amp;rdquo; (strengthening awareness and confidence), up until a point where the emotion regulation benefits of unreality will be automatically invoked (&lt;strong&gt;-reality → -affect&lt;/strong&gt;), increasing the likelihood and confidence of judgments of simulation (potentially far into psychopathological terrains).&lt;/p&gt;
&lt;h2 id=&#34;open-questions&#34;&gt;Open questions&lt;/h2&gt;
&lt;p&gt;The Affective Reality theory is for now a working hypothesis that we are trying to empirically prove or disprove at the &lt;a href=&#34;https://realitybending.github.io/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Reality Bending Lab&lt;/strong&gt;&lt;/a&gt;. Moreover, some questions remain open:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Is it actually &lt;strong&gt;embodied reality or emotional reality?&lt;/strong&gt; While we used the term &amp;ldquo;affective&amp;rdquo; reality to remain general, the question of whether it is emotions as a subjective psychological reaction, or merely bodily arousal (reactions of the body, e.g., stronger heart rate variability), that is the key ingredient remains unclear. The role of &lt;strong&gt;interoception&lt;/strong&gt; (the ability and tendency to detect, track, attend to and rely on internal signals), while likely important, also remains to be specified.&lt;/li&gt;
&lt;li&gt;Is it the affective &lt;strong&gt;context or stimulus&lt;/strong&gt; that matters? Let&amp;rsquo;s assume we have affective reaction concomitant to the experience of an object, but not directly related to the object. Would that bias simulation monitoring? Does perceived causality between a bodily reaction and the object of experience matters?&lt;/li&gt;
&lt;/ul&gt;
&lt;!-- Experiment  with loud unpleasant noises around images vs. pleasant noises. --&gt;
&lt;!-- We know that fake news tend to be emotional on average, and are also believed by anxious people. --&gt;
&lt;h2 id=&#34;notes&#34;&gt;Notes&lt;/h2&gt;
&lt;div class=&#34;footnotes&#34; role=&#34;doc-endnotes&#34;&gt;
&lt;hr&gt;
&lt;ol&gt;
&lt;li id=&#34;fn:1&#34;&gt;
&lt;p&gt;You may notice that I used different words related to the concept of &amp;ldquo;unreal&amp;rdquo;, such as simulated, fake, artificial, virtual, simulated, fictional. While they can be used interchangeably in the context above, they are not exact synonyms.&amp;#160;&lt;a href=&#34;#fnref:1&#34; class=&#34;footnote-backref&#34; role=&#34;doc-backlink&#34;&gt;&amp;#x21a9;&amp;#xfe0e;&lt;/a&gt;&lt;/p&gt;
&lt;/li&gt;
&lt;li id=&#34;fn:2&#34;&gt;
&lt;p&gt;Like that pesky &lt;em&gt;reviewer 2&lt;/em&gt;, obviously.&amp;#160;&lt;a href=&#34;#fnref:2&#34; class=&#34;footnote-backref&#34; role=&#34;doc-backlink&#34;&gt;&amp;#x21a9;&amp;#xfe0e;&lt;/a&gt;&lt;/p&gt;
&lt;/li&gt;
&lt;li id=&#34;fn:3&#34;&gt;
&lt;p&gt;Note that &amp;ldquo;reality monitoring&amp;rdquo; already exists  as a concept and refers to a (possibly related) mechanism involved in tracking the origin of an experience (e.g., a memory) as internal vs. external.&amp;#160;&lt;a href=&#34;#fnref:3&#34; class=&#34;footnote-backref&#34; role=&#34;doc-backlink&#34;&gt;&amp;#x21a9;&amp;#xfe0e;&lt;/a&gt;&lt;/p&gt;
&lt;/li&gt;
&lt;li id=&#34;fn:4&#34;&gt;
&lt;p&gt;&amp;ldquo;Affective&amp;rdquo; is in this context used as a generic term to encompass emotions, feelings and bodily activity (the question of which exactly of these aspects is the key remains to be answered).&amp;#160;&lt;a href=&#34;#fnref:4&#34; class=&#34;footnote-backref&#34; role=&#34;doc-backlink&#34;&gt;&amp;#x21a9;&amp;#xfe0e;&lt;/a&gt;&lt;/p&gt;
&lt;/li&gt;
&lt;/ol&gt;
&lt;/div&gt;
</description>
    </item>
    
    <item>
      <title>I got ChatGPT to do a personality test. You won&#39;t believe what happened next!</title>
      <link>https://realitybending.github.io/post/2023-04-06-chatgptpersonality/</link>
      <pubDate>Thu, 06 Apr 2023 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2023-04-06-chatgptpersonality/</guid>
      <description>&lt;p&gt;Related to this &lt;a href=&#34;https://dominiquemakowski.github.io/post/2023-04-04-psychologychatgpt/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;blogpost&lt;/strong&gt;&lt;/a&gt; about including AIs in psychological experiments, I proceeded to do a small experiment to see whether we could administer a personality scale to ChatGPT.&lt;/p&gt;
&lt;p&gt;I started by copy-pasting the instructions and the items from the Mini IPIP-6 personality scale. However, it appeared that having the following context &lt;em&gt;&amp;ldquo;Please answer the following questions based on how accurately each statement describes you in general&amp;rdquo;&lt;/em&gt; often led to ChatGPT simply refusing to answer. In most of the cases, it explained that as an AI it does not have a personality and therefore cannot answer related questions (or any &amp;ldquo;subjective statements&amp;rdquo;). Perhaps that makes sense and we should just stop trying to force Human characteristics on an AI. &lt;strong&gt;But can we, for fun, bamboozle ChatGPT into answering personality items?&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Sometimes yes, at least for ChatGPT 3.5 (free version). I created a prompt that emphasized AI research and safety, and the fact that I was interested in the &amp;ldquo;trends&amp;rdquo; present in the AI&amp;rsquo;s training data (instead of explicitly saying its personality). And sometimes it answered, so I compiled the responses, computed the trait scores, and &lt;em&gt;voilà&lt;/em&gt;, &lt;strong&gt;it got me a personality profile!&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img src=&#34;https://github.com/DominiqueMakowski/ChatGPTpersonality/raw/main/figures/unnamed-chunk-3-1.png&#34; alt=&#34;https://github.com/DominiqueMakowski/ChatGPTpersonality&#34; loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;p&gt;&lt;sub&gt;&lt;em&gt;This plot shows the average personality profile (with a 95% confidence interval) based on ChatGPT&amp;rsquo;s answers. ChatGPT tells us that it is particularly &lt;strong&gt;agreeable&lt;/strong&gt; (kind, understanding, empathetic of emotions, socially adjusted) and &lt;strong&gt;honest&lt;/strong&gt; (though with strong variability).&lt;/em&gt;&lt;/sub&gt;&lt;/p&gt;
&lt;p&gt;A personality profile of &lt;em&gt;&lt;strong&gt;what&lt;/strong&gt;&lt;/em&gt; is another question though&amp;hellip; Please take a look at the &lt;a href=&#34;https://github.com/DominiqueMakowski/ChatGPTpersonality&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;GitHub repo&lt;/strong&gt;&lt;/a&gt; for &lt;strong&gt;data, code and details&lt;/strong&gt;. It was a fun little thing to do, and I am looking forward to better future attempts at including AIs in cognitive experiments.&lt;/p&gt;
&lt;hr&gt;
&lt;p&gt;&lt;strong&gt;Interested in doing research on the perception of reality?&lt;/strong&gt; We are looking for research assistants and PhD students at the &lt;em&gt;Reality Bending Lab&lt;/em&gt; (check-out the &lt;a href=&#34;https://realitybending.github.io/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;join us page&lt;/a&gt;)!&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>We should treat AIs like Human participants in psychological experiments</title>
      <link>https://realitybending.github.io/post/2023-04-04-psychologychatgpt/</link>
      <pubDate>Wed, 05 Apr 2023 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2023-04-04-psychologychatgpt/</guid>
      <description>&lt;p&gt;A lot of diverse and interesting perspectives have been recently discussed in regards to chatGPT and AGI (artificial &lt;em&gt;&lt;strong&gt;global&lt;/strong&gt;&lt;/em&gt; intelligence), but there is one opinion that I found particularly relevant that I wanted to share and expand on.&lt;/p&gt;
&lt;p&gt;In his recent &lt;a href=&#34;https://www.youtube.com/watch?v=AaTRHFaaPG8&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;interview with Lex Fridman&lt;/a&gt;, Eliezer Yudkowsky underlines the &lt;strong&gt;existential threat posed by current and future AIs&lt;/strong&gt;, and laments about the fact that we don&amp;rsquo;t really know what is actually going on inside these giant &amp;ldquo;matrices of floating-point numbers&amp;rdquo;. He draws a parallel to &lt;strong&gt;neuroimaging&lt;/strong&gt;, that enabled us to take leaps in the understanding of the brain, hoping for an alternative to be invented and applied to these AIs.&lt;/p&gt;
&lt;p&gt;While such &amp;ldquo;cognitive imaging&amp;rdquo; techniques are yet to be developed to map out and understand how the capabilities of such AI models are implemented within their architecture, &lt;a href=&#34;https://x.com/mcxfrank/status/1643296168276033538&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Michael C. Frank&lt;/a&gt; highlights the - at least equally important - need to first truly understand the extend of said abilities. What are these models actually capable of in terms of Human-like thinking (and, hopefully, answer the much harder question of whether they are endowed with true cognitive processes or merely pseudo-cognition). Frank proposes to apply &lt;strong&gt;experimental psychology&lt;/strong&gt; methods and paradigms to them. In essence, whenever testing a particular &amp;ldquo;skill&amp;rdquo; of chatGPT (or other AI systems), a researcher should consider developing an actual scientific paradigm consisting of multiple trials/items (e.g., different prompt formulations) and participants (e.g., independent instances of the AI), a control condition, and a demonstration of the paradigm validity.&lt;/p&gt;
&lt;p&gt;I agree that we must take AIs seriously and study them with the best methods available for complex systems like ourselves (&amp;ldquo;complex&amp;rdquo; at least from our intelligence level), and likely should strive at improving and generalize these methods. However, I would also argue that we psychologists might seriously need to consider including AI systems alongside Human participants in cognitive experiments. These systems will be able, in the very near future, to perform all kinds of tasks beyond language manipulation, such as perception or complex problem solving, thus opening the possibility of studies with one group of human participants, and one &amp;ldquo;group&amp;rdquo; of AI-based attempts. &lt;strong&gt;How would that help psychological science?&lt;/strong&gt;&lt;/p&gt;
&lt;iframe src=&#34;https://giphy.com/embed/1M9fmo1WAFVK0&#34; width=&#34;480&#34; height=&#34;270&#34; frameBorder=&#34;0&#34; class=&#34;giphy-embed&#34; allowFullScreen&gt;&lt;/iframe&gt;
&lt;ol&gt;
&lt;li&gt;It would help us &lt;strong&gt;understand the abilities of AI-systems&lt;/strong&gt; in similar contexts and to highlight some intuitive comparisons with Humans&lt;/li&gt;
&lt;li&gt;If we show that AI cannot perform the task, well it is informative with regards to their abilities (previous point).&lt;/li&gt;
&lt;li&gt;If we show that AI can perform the task similarly to Humans (same response patterns), it does &lt;strong&gt;not mean that AI have Human-like intelligence&lt;/strong&gt;, just that their algorithm (and training data) is able to encapsulate and imitate Human performance. This is interesting with regards to the debate of whether cognition, conscience and &amp;ldquo;Human-ness&amp;rdquo; is present within the vast amount of data on which we train AIs.&lt;/li&gt;
&lt;li&gt;If we show that AI performs differently to Humans, this helps us understand the logic and processes at stake under AI&amp;rsquo;s hood.&lt;/li&gt;
&lt;li&gt;In any case, publishing the results by one particular AI system at one particular moment in time will helps us to objectively monitor and track their performance as these systems improve over time.&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;Comparing Human performance to that of emerging AI-systems will be both beneficial to Human-oriented psychology, to understand the particularities and idiosyncrasies of Human-like cognition, and well as to AI-oriented cognitive science by approaching the issue of artificial intelligence with the seriousness and cautiousness it deserves.&lt;/p&gt;
&lt;p&gt;EDIT (09/04/2023): François Chollet, expert in deep learning, &lt;a href=&#34;https://x.com/fchollet/status/1644435265795280897&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;underlines&lt;/a&gt; an important caveat when testing AIs (and especially LLM that are trained on written material existing on the internet): it is possible that the system has already seen and &amp;ldquo;learned&amp;rdquo; a given task. Thus, cross-validating any findings with diverse and new tasks is important.&lt;/p&gt;
&lt;hr&gt;
&lt;p&gt;&lt;strong&gt;Interested in doing research related to effects of reality and fiction?&lt;/strong&gt; We are looking for research assistants and PhD students at the &lt;em&gt;Reality Bending Lab&lt;/em&gt; (check-out the &lt;a href=&#34;https://realitybending.github.io/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;join us tab&lt;/a&gt;)!&lt;/p&gt;
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    <item>
      <title>When fiction is better than reality: Cypher&#39;s Complex</title>
      <link>https://realitybending.github.io/post/2023-02-07-cypherscomplex/</link>
      <pubDate>Tue, 07 Feb 2023 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2023-02-07-cypherscomplex/</guid>
      <description>&lt;p&gt;Did you ever feel empty after finishing a good book? &lt;strong&gt;Like (your) reality was dull and boring&lt;/strong&gt; as compared to the fictional world you were immersed in? Yearning to stay in longer, and at the same time knowing well that it had to come to an end? You might have experienced what we can call &lt;strong&gt;Cypher&amp;rsquo;s Complex&lt;/strong&gt;.&lt;/p&gt;
&lt;p&gt;In the movie &lt;strong&gt;The Matrix&lt;/strong&gt;, Cypher is a &amp;ldquo;redpill&amp;rdquo;, i.e., an individual that has been awaken from the matrix (a virtual world). However, he becomes disappointed and unhappy with the true nature of reality, and actively seeks to &lt;strong&gt;return to the illusory world&lt;/strong&gt; of the matrix. Interestingly, he also explicitly desires to forget everything about the true reality, as if keeping the awareness of living in an illusion could prevent him from fully enjoying it.&lt;/p&gt;
&lt;figure&gt;
  &lt;img src=&#34;cypher.gif&#34; alt=&#34;Cypher&#34;/&gt;
  &lt;figcaption&gt;&lt;i&gt;&#34;You know... I know this steak doesn&#39;t exist. I know that when I put it in my mouth; the Matrix is telling my brain that it is juicy, and delicious. After nine years... you know what I realize? Ignorance is bliss.&#34;&lt;/i&gt;&lt;/figcaption&gt;
&lt;/figure&gt;
&lt;p&gt;From a scientific perspective, the latter part can find some echo in the down-regulatory effect of &lt;a href=&#34;https://link.springer.com/article/10.3758/s13415-018-00681-0&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;fictional reappraisal&lt;/strong&gt;&lt;/a&gt;. In a few studies, we showed that believing that a stimulus is &amp;ldquo;fictional&amp;rdquo; (not real) dampens our emotional state. &lt;a href=&#34;https://www.sciencedirect.com/science/article/pii/S2589004222017138?via%3Dihub&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Tucciarelli et al. (2023)&lt;/strong&gt;&lt;/a&gt; also showed that the simple knowledge that a set of images of faces contains AI-generated images decreased the perceived trustworthiness of all the faces. These results suggest that being aware that the causes of our experience (the events and stimuli) are fictional can be a barrier to enjoyment and engagement. And yet, the desire to supplant reality with a fictional world can be found in real life.&lt;/p&gt;
&lt;p&gt;Cypher&amp;rsquo;s Complex is common in mild forms. Examples can be found in the feelings of emptiness, disconnection and dullness (itself a transient and mild form of &lt;a href=&#34;https://en.wikipedia.org/wiki/Depersonalization-derealization_disorder&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;depersonalization/derealization&lt;/strong&gt;&lt;/a&gt;) that follows the return from an engaging fictional world (be it in a novel, a movie or a video-game). For instance, many reported feeling blue &lt;strong&gt;after watching the Avatar (2009)&lt;/strong&gt; movie, to the extent where it has been coined the &lt;a href=&#34;https://www.theguardian.com/film/2022/dec/15/post-avatar-depression-syndrome-why-do-fans-feel-blue-after-watching-james-camerons-film&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;&amp;ldquo;post-Avatar depression syndrome&amp;rdquo;&lt;/strong&gt;&lt;/a&gt;. Most of the time, the negative affects passes, and the dissonance gets resolved either through closure (acceptance of the fictional or impermanent nature of the alternative reality), or a compromise that allows the fictional world to take a delimited space in one&amp;rsquo;s reality. For example, people might engage in activities (e.g., role playing games) or create content (writing a book or doing fan art) to integrate the fictional world into their reality.&lt;/p&gt;
&lt;p&gt;However, &lt;strong&gt;Cypher&amp;rsquo;s Complex can also give rise to more severe issues&lt;/strong&gt; with conscious or unconscious attempts at forgetting or ignoring reality (delusions, denial, &amp;hellip;), which can lead to dire outcomes.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Interested in doing research related to effects of reality and fiction?&lt;/strong&gt; We are looking for research assistants and PhD students at the &lt;em&gt;Reality Bending Lab&lt;/em&gt; (check-out the &lt;a href=&#34;https://realitybending.github.io/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;join us tab&lt;/a&gt;)!&lt;/p&gt;
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      <title>New location and new logo!</title>
      <link>https://realitybending.github.io/post/2023-02-01-new_logo/</link>
      <pubDate>Wed, 01 Feb 2023 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2023-02-01-new_logo/</guid>
      <description>&lt;p&gt;New year, new start. And as I am officially starting a new faculty position at the &lt;strong&gt;University of Sussex&lt;/strong&gt; in Brighton, UK, the lab is moving too.&lt;/p&gt;
&lt;p&gt;To give a bit of perspective, we started as the &amp;ldquo;Reality Bending League&amp;rdquo;, which was the unofficial name of the team working with me (&amp;ldquo;League&amp;rdquo; was chosen to keep the lab&amp;rsquo;s acronym, &lt;strong&gt;ReBeL&lt;/strong&gt;). It then became a semi-official group in 2021, when I became a semi-independent PI after being awarded a transition grant from &lt;a href=&#34;https://www.ntu.edu.sg/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;NTU&lt;/a&gt;. And with 2023 comes our fully official start.&lt;/p&gt;
&lt;figure&gt;
  &lt;img src=&#34;old_logo.png&#34; alt=&#34;Vintage logo&#34;/&gt;
  &lt;figcaption&gt;ReBeL logo (2020-2022).&lt;/figcaption&gt;
&lt;/figure&gt;
&lt;p&gt;To mark this (re)birth anniversary, we are changing our logo. As much as I loved the old one - which was &lt;a href=&#34;https://realitybending.github.io/post/2021-06-30-logo_meaning/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;packed with symbols&lt;/strong&gt;&lt;/a&gt;, it was arguably a bit too&amp;hellip; &lt;em&gt;&lt;strong&gt;extravagant&lt;/strong&gt;&lt;/em&gt;. Something more sleek and minimal felt good with respect to the lab&amp;rsquo;s newly acquired legitimacy. I know that many will prefer the old-&amp;hellip; sorry, the &lt;em&gt;&lt;strong&gt;vintage&lt;/strong&gt;&lt;/em&gt;- logo, and I must say it wasn&amp;rsquo;t easy for me to move forward with the change. Perhaps it will make a come-back in the future in another form, who knows!&lt;/p&gt;
&lt;p&gt;The new logo contains 3 symbols. The &lt;strong&gt;curved spoon&lt;/strong&gt; is a reference to the Matrix scene where a kid shows Neo how to bend a spoon, which is a &lt;strong&gt;metaphor for reality&lt;/strong&gt; (hence of the name of the lab, reality bending).&lt;/p&gt;
&lt;figure&gt;
  &lt;img src=&#34;Matrix1.gif&#34;/&gt;
&lt;/figure&gt;
&lt;p&gt;In the movie, Neo becomes able to &lt;strong&gt;control reality by becoming aware of its illusory nature&lt;/strong&gt;, and of the predominant role of one&amp;rsquo;s Self in its generation.&lt;/p&gt;
&lt;figure&gt;
  &lt;img src=&#34;Matrix2.gif&#34;/&gt;
  &lt;figcaption&gt;&#34;Try to realize the truth... There is no spoon. Then you&#39;ll see that it is not the spoon that bends, it is only yourself.&#34;&lt;/figcaption&gt;
&lt;/figure&gt;
&lt;p&gt;The &lt;strong&gt;second meaning&lt;/strong&gt; of the logo is the &lt;em&gt;Psi&lt;/em&gt; Greek letter, symbol of psychology, formed by the spoon and the white vertical line.&lt;/p&gt;
&lt;figure&gt;
  &lt;img src=&#34;APA.png&#34;/&gt;
  &lt;figcaption&gt;The logo of the APA features the Psi letter.&lt;/figcaption&gt;
&lt;/figure&gt;
&lt;p&gt;Thirdly, the black rectangles represent &lt;strong&gt;open doors&lt;/strong&gt;, which is a good illustration of progress, research, discovery and&amp;hellip; consciousness expansion? Interestingly, Jim Morrison named its band &amp;ldquo;The Doors&amp;rdquo; in reference to a quote by William Blake, who said that when &lt;em&gt;&lt;strong&gt;&amp;ldquo;the doors of perception were cleansed then everything would appear to man as it is, Infinite&amp;rdquo;&lt;/strong&gt;&lt;/em&gt;.&lt;/p&gt;
&lt;figure&gt;
  &lt;img src=&#34;TheDoors.jpg&#34;/&gt;
&lt;/figure&gt;
&lt;p&gt;To share a blooper, here is an alternative direction for the logo that wasn&amp;rsquo;t selected, that incorporated the spoon and the open door in another way. Unfortunately, some said it looked too much like the Pixar lamp, or like a spermatozoid&amp;hellip;&lt;/p&gt;
&lt;figure&gt;
  &lt;img src=&#34;logo_alternative.png&#34; alt=&#34;Alternative logo&#34;/&gt;
  &lt;figcaption&gt;A tentative version of the logo.&lt;/figcaption&gt;
&lt;/figure&gt;
</description>
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    <item>
      <title>Podcast &#39;Learn Bayesian Stats&#39; with Dominique Makowski</title>
      <link>https://realitybending.github.io/post/2022-02-01-learnbayesstats/</link>
      <pubDate>Tue, 01 Feb 2022 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2022-02-01-learnbayesstats/</guid>
      <description>&lt;h2 id=&#34;the-learning-bayesian-statistics-podcast&#34;&gt;The &amp;lsquo;Learning Bayesian Statistics&amp;rsquo; Podcast&lt;/h2&gt;
&lt;p&gt;I had the chance of being invited to talk about R, Python, Reality Bending and much more! It was my first experience of that kind, so thanks a ton to the host of the podcast &lt;a href=&#34;https://x.com/alex_andorra&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Alex Andorra&lt;/a&gt;. Listen to it here:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://www.learnbayesstats.com/episode/55-neuropsychology-illusions-bending-reality-dominique-makowski&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;https://www.learnbayesstats.com/episode/55-neuropsychology-illusions-bending-reality-dominique-makowski&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
</description>
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    <item>
      <title>What visual agnosia might feel like</title>
      <link>https://realitybending.github.io/post/2021-01-03-visual_agnosia/</link>
      <pubDate>Sun, 03 Jan 2021 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2021-01-03-visual_agnosia/</guid>
      <description>&lt;h3 id=&#34;name-one-thing-in-this-photo&#34;&gt;Name One Thing In This Photo&lt;/h3&gt;
&lt;p&gt;&lt;strong&gt;Can you name &lt;em&gt;one&lt;/em&gt; thing in the image above?&lt;/strong&gt; It all looks familiar, but something is off. The image makes &amp;ldquo;sense&amp;rdquo; overall; there are well-defined shapes and objects, that seem to be placed in a plausible - albeit chaotic - fashion, like some random rubbish thrown in the corner of a room. Even the colors, the lightning, the quality, is coherent, and helps making it believable. And yet, chances are you cannot name one single element that composes it.&lt;/p&gt;
&lt;p&gt;This image, after appearing on &lt;a href=&#34;https://x.com/melip0ne/status/1120503955526750208?s=20&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;twitter&lt;/a&gt; in April 2019, surfaced on reddit with the caption &amp;ldquo;This picture is &lt;strong&gt;designed to give the viewer the simulated experience of having a stroke&lt;/strong&gt; (particularly in the &lt;strong&gt;occipital lobe&lt;/strong&gt; of the cerebral cortex, where visual perception occurs.) &lt;strong&gt;Everything looks hauntingly familiar but you just can&amp;rsquo;t quite recognize anything&lt;/strong&gt;&amp;rdquo;, and became subsequently &lt;a href=&#34;https://www.dailymail.co.uk/news/article-6959547/Extremely-frustrating-slightly-disturbing-image-goes-viral.html&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;viral&lt;/a&gt;. However, the author of the caption later admitted that he made this description up.&lt;/p&gt;
&lt;p&gt;&lt;em&gt;So where does the image come from?&lt;/em&gt;&lt;/p&gt;
&lt;p&gt;One can trace back the original publication to an &lt;a href=&#34;https://youtu.be/0F7XBwFwA-M?t=104&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;instagram account&lt;/a&gt;, which author declared having made the image using &lt;a href=&#34;https://www.artbreeder.com/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;ArtBreeder.com&lt;/strong&gt;&lt;/a&gt;. This website gives access to an AI algorithm (Generative Adversarial Networks - GAN), commonly used in the processing and generation of images (one mindblowing example can be found on &lt;a href=&#34;https://thispersondoesnotexist.com/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;em&gt;thispersondoesnotexist.com&lt;/em&gt;&lt;/a&gt;, which generates realistic pictures of non-existing people). There were even some attempts to &lt;em&gt;reverse engineer&lt;/em&gt; the process to retrieve what the original image could have been like.&lt;/p&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img src=&#34;https://i.kym-cdn.com/photos/images/original/001/486/325/1dd.jpg&#34; alt=&#34;&#34; loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;p&gt;After all, it seems like there is no intelligent design behind this image. No clever neuropsychologist carefully crafting a meaningful experience. Just one of these lucky accident.&lt;/p&gt;
&lt;p&gt;Nonetheless, it&amp;rsquo;s still an intriguing image, falling in this uncanny abyss of things that we recognize as familiar, but slightly too alien for our sense-seeking brains to dissolve in meaning. &lt;strong&gt;Could it tell something about brain processes?&lt;/strong&gt; Surely, but &lt;strong&gt;brain disorders?&lt;/strong&gt; Maybe.&lt;/p&gt;
&lt;p&gt;The &lt;strong&gt;&amp;ldquo;occipital stroke&amp;rdquo; hypothesis&lt;/strong&gt; mentioned above suggests, by its formulation, a lesion to the primary visual cortices. However, as neuroscientists know, these brain regions, located at the extreme back of the brain, are mostly supporting lower level aspects of visual processing, and their damage is usually related to alterations of a somewhat different nature than of that above, such as vision loss, visual hallucinations, visual deformations, loss of color, movement, stereoscopy, etc.&lt;/p&gt;
&lt;p&gt;However, there is another neuropsychological disorder, referred to as &lt;strong&gt;&amp;ldquo;visual agnosia&amp;rdquo;&lt;/strong&gt;, in which patients experience difficulties to recognize visually presented objects, despite preserving an intact vision. In fact, it is more an umbrella term for different subcategories of deficits, and the image above could be reminiscent of visual agnosia of the &lt;em&gt;associative&lt;/em&gt; type, which corresponds to a a specific impairment in the assignment of meaning to a stimulus that is accurately perceived (and can be visually described). This symptom is often related to injuries in the left occipito-temporal region, located on the ventral &amp;ldquo;what&amp;rdquo; stream of the brain (as opposed to the so-called &amp;ldquo;where&amp;rdquo; dorsal stream).&lt;/p&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img alt=&#34;&#34; srcset=&#34;
               /post/2021-01-03-visual_agnosia/whatstream_hu_2b480e0dcef3f8b3.webp 400w,
               /post/2021-01-03-visual_agnosia/whatstream_hu_894caeede8fefd.webp 760w,
               /post/2021-01-03-visual_agnosia/whatstream_hu_e6334db72bb29fee.webp 1200w&#34;
               src=&#34;https://realitybending.github.io/post/2021-01-03-visual_agnosia/whatstream_hu_2b480e0dcef3f8b3.webp&#34;
               width=&#34;760&#34;
               height=&#34;513&#34;
               loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;h3 id=&#34;ivan-seals-art&#34;&gt;Ivan Seal&amp;rsquo;s Art&lt;/h3&gt;
&lt;p&gt;From there, the youtuber &lt;a href=&#34;https://www.youtube.com/channel/UCR6LasBpceuYUhuLToKBzvQ&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;em&gt;Solar Sands&lt;/em&gt;&lt;/a&gt; helped me discover the artist &lt;a href=&#34;https://en.wikipedia.org/wiki/Ivan_Seal&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;strong&gt;Ivan Seal&lt;/strong&gt;&lt;/a&gt;, which work is somewhat akin to the image above. They are not purely abstract renditions, or depictions of impossible entities, but plausible objects that sit in this awkward space, deep between boring reality and total weirdness.&lt;/p&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img src=&#34;https://rca-media.rca.ac.uk/images/dumtrimiestonmo_blurosperiod150x100_cm_-_Phot.width-1000.jpg&#34; alt=&#34;&#34; loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;p&gt;















&lt;figure  &gt;
  &lt;div class=&#34;d-flex justify-content-center&#34;&gt;
    &lt;div class=&#34;w-100&#34; &gt;&lt;img src=&#34;https://i.redd.it/ywee14vpk8y41.jpg&#34; alt=&#34;&#34; loading=&#34;lazy&#34; data-zoomable /&gt;&lt;/div&gt;
  &lt;/div&gt;&lt;/figure&gt;
&lt;/p&gt;
&lt;hr&gt;
&lt;p&gt;&lt;em&gt;Thanks for reading! Do not hesitate to tweet and share this post and don&amp;rsquo;t forget to join me on X&lt;/em&gt; 🐦 &lt;a href=&#34;https://x.com/Dom_Makowski&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;@Dom_Makowski&lt;/a&gt;&lt;/p&gt;
</description>
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      <title>What is Reality Bending?</title>
      <link>https://realitybending.github.io/post/2020-09-28-what_is_realitybending/</link>
      <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2020-09-28-what_is_realitybending/</guid>
      <description>&lt;p&gt;As you know, &lt;strong&gt;reality bending&lt;/strong&gt; is my primary research direction. However, it is not (yet) a well-established scientific topic, nor is it clearly defined. In fact, &lt;strong&gt;it is not defined at all, hence the purpose of this article&lt;/strong&gt;.&lt;/p&gt;
&lt;p&gt;But what does it refer too? Is it some kind of &lt;a href=&#34;https://en.wikipedia.org/wiki/Avatar:_The_Last_Airbender&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;em&gt;Avatar: The Last Airbender&lt;/em&gt;&lt;/a&gt; thing? Or some &lt;a href=&#34;https://marvel-movies.fandom.com/wiki/Reality_Stone&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;em&gt;Avengers&lt;/em&gt;&lt;/a&gt;-style superpower? Well&amp;hellip; I sure wish it was &amp;#x1f601;&lt;/p&gt;
&lt;p&gt;Essentially, &lt;strong&gt;reality bending&lt;/strong&gt; refers to the study of the internal and external determinants of subjective reality. In other words, we seek to understand the processes that modulate our conscious experience of reality. The word &amp;ldquo;bending&amp;rdquo; encapsulates the active nature of the mechanisms at stake. Indeed, being anything but stable, our perception of reality can be quite easily influenced, whether voluntarily or not, sometimes to extreme degrees of alteration.&lt;/p&gt;
&lt;figure&gt;
  &lt;img src=&#34;DonQuixote.jpg&#34; alt=&#34;github for psychologists&#34;/&gt;
  &lt;figcaption&gt;Daumier, H. (1925), Don Quixote attacking the windmills.&lt;/figcaption&gt;
&lt;/figure&gt;
&lt;p&gt;&lt;strong&gt;Reality benders&lt;/strong&gt; seek to unravel the structure and mechanisms of the sense of reality by studying natural instances of its distortion, or by directly inducing them through a variety of means.&lt;/p&gt;
&lt;h2 id=&#34;objective-and-subjective-determinants-of-the-sense-of-reality&#34;&gt;Objective and subjective determinants of the sense of reality&lt;/h2&gt;
&lt;p&gt;Let&amp;rsquo;s take for example a guy watching some episode of his favourite TV show, &lt;em&gt;Friends&lt;/em&gt;. As he swiftly moves from laughing to snivelling, we can confidently say that he is fully &lt;strong&gt;immersed&lt;/strong&gt; in the show. He feels like he&amp;rsquo;s &lt;em&gt;present&lt;/em&gt; in the show, from which the fictional characters &lt;em&gt;feel&lt;/em&gt; very real: for a moment, his brain processes the perceived experience almost as if it was real.&lt;/p&gt;
&lt;p&gt;What leads to this high sense of reality? First, there are &lt;strong&gt;objective characteristics&lt;/strong&gt; of the experience (or rather, of the external source of the experience), i.e., characteristics of the environment. Here, it&amp;rsquo;s a realistic stimulus displayed on a flat screen. But one could wonder what would happen if the sensory input was richer (imagine being physically IN the show by means of some super &lt;strong&gt;virtual reality&lt;/strong&gt; setup), or poorer (the same story presented as comic strips with the characters portrayed as stick figures).&lt;/p&gt;
&lt;p&gt;However, while such manipulations could indeed be used to manipulate our immersion, there is also a &lt;strong&gt;subjective component&lt;/strong&gt; contributing to our sense of reality, related for instance to the affective response, attentional engagement, or self-relevance, that will cause a stimulus to strum unique strings in each individual, depending on his history and state of mind.&lt;/p&gt;
&lt;h2 id=&#34;tell-me-your-reality-and-ill-tell-you-who-you-are&#34;&gt;Tell me your reality and I&amp;rsquo;ll tell you who you are&lt;/h2&gt;
&lt;p&gt;The fact that the sense of reality is, in the end, a subjective experience, means that is is intrinsically connected to the Self (i.e., our physical and mental identity). As such, aside from studying how our sense of reality is influenced by external and internal factors, but also investigate the reverse relationship, i.e., &lt;strong&gt;how the variability of our sense of reality can inform us about oneself&lt;/strong&gt;.&lt;/p&gt;
&lt;p&gt;Note that, although the focus is the subjective aspect of reality, it doesn&amp;rsquo;t mean that we deny the existence, or downplay the importance, of objective reality. Stating that most of our experience is &amp;ldquo;made-up&amp;rdquo; (i.e., is a construction of the brain) does not equate absolute relativism (more on that in another post). Objective truths and facts do exist, and are essential to seek.&lt;/p&gt;
&lt;h2 id=&#34;altered-states-of-consciousness&#34;&gt;Altered states of consciousness&lt;/h2&gt;
&lt;p&gt;Naturally, states in which our sense of reality is distorted (as compared to the consensual collective experience) are of particular interest as models or study-cases of our ideas and theories. They include long-term affections (e.g., neuropsychiatric disorders such as schizophrenia) or transcient states (induced by psychoactive substances or specific practices like meditation and trance).&lt;/p&gt;
&lt;hr&gt;
&lt;p&gt;&lt;em&gt;Thanks for reading! Don&amp;rsquo;t forget to join me on X&lt;/em&gt; &lt;a href=&#34;https://x.com/Dom_Makowski&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;@Dom_Makowski&lt;/a&gt; &amp;#x1f917;&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>How to extract individual scores from repeated measures</title>
      <link>https://realitybending.github.io/post/2020-09-14-individual_scores/</link>
      <pubDate>Mon, 14 Sep 2020 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2020-09-14-individual_scores/</guid>
      <description>&lt;h3 id=&#34;introduction&#34;&gt;Introduction&lt;/h3&gt;
&lt;p&gt;Many psychology fields require to extract individual scores, i.e., point-estimates (&lt;em&gt;i.e.&lt;/em&gt;, a single value) for a participant/patient, to be used as an index of something and later interpreted or re-used in further statistical analyses. This single index is often derived from several &amp;ldquo;trials&amp;rdquo;. For instance, the reaction times in the condition A (let&amp;rsquo;s say, the baseline) will be &lt;strong&gt;averaged&lt;/strong&gt; together, and the same will be done with the condition B. Finally, the difference between these two means will be used an the &lt;strong&gt;individual score&lt;/strong&gt; for a given participant.&lt;/p&gt;
&lt;p&gt;However, we can intuitively feel that we &lt;strong&gt;lose a lot of information&lt;/strong&gt; when averaging these scores. Do we deal appropriately with the variability related to individuals, conditions, or the noise aggravated by potential outliers? This is especially important when working with a limited amount of trials.&lt;/p&gt;
&lt;p&gt;With the advent of recent computational advances, new easy-to-implement alternatives emerge. For instance, &lt;strong&gt;one can &amp;ldquo;model&amp;rdquo; the effects at an individual level&lt;/strong&gt; (e.g., the simplest case, for the two conditions paradigm described above, would be a linear regression with the condition as a unique predictor), and use the &lt;strong&gt;parameters&lt;/strong&gt; of each model as individual scores (e.g., the &amp;ldquo;slope&amp;rdquo; coefficient of the effect of the manipulation), rather than the raw mean. This opens up the possibility of including covariates and take into account other sources of known variability, which could lead to better estimates.&lt;/p&gt;
&lt;p&gt;However, individual models are also sensitive to outliers and noise. Thus, another possibility is to &lt;strong&gt;model the effects at the population level&lt;/strong&gt; and, &lt;em&gt;at the same time&lt;/em&gt;, at the individual level. This can be achieved by modelling the participants as a &lt;strong&gt;random factor in a mixed model&lt;/strong&gt;. In this case, the individual estimates might benefit from the population estimates. In other words, the effects at the population level will &amp;ldquo;constrain&amp;rdquo; or &amp;ldquo;guide&amp;rdquo; the estimation at an individual level to potentially limit extreme parameters.&lt;/p&gt;
&lt;p&gt;Unfortunately, the above method requires to have all the data at hand, to be able to fit the population model. This is often not the case in on-going acquisition, or in neuropsychological contexts, in which the practitioners simply acquire data for one patient, and have to compute individual scores, without having access to the detailed population data. Thus, an in-between alternative could make use of &lt;strong&gt;Bayesian models&lt;/strong&gt;, in which the population effects (for instance, the mean effect of the condition) could be entered as an informative &lt;strong&gt;prior&lt;/strong&gt; in the individual models to, again, &amp;ldquo;guide&amp;rdquo; the estimation at an individual level and hopefully limit the impact of noise or outliers observations.&lt;/p&gt;
&lt;p&gt;In this post, the aim is to compare these 4 methods (basic individual model - equivalent to using the raw mean, population model, individual model with informative priors) in recovering the &amp;ldquo;true&amp;rdquo; effects using a simulated dataset.&lt;/p&gt;
&lt;h3 id=&#34;results&#34;&gt;Results&lt;/h3&gt;
&lt;h4 id=&#34;generate-data&#34;&gt;Generate Data&lt;/h4&gt;
&lt;p&gt;We generate several datasets in which we manipulate the number of participants, in which the score of interest is the effect of a manipulation as compared to a baseline condition. 20 trials per condition will be generated with a known &amp;ldquo;true&amp;rdquo; effect (the centre of the distribution from which the data is generated). Gaussian noise of varying standard deviation will be added to create a natural variability (See the functions&amp;rsquo; definition below).&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-r&#34; data-lang=&#34;r&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;library&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;tidyverse&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;library&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;easystats&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;get_data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_participants&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1000&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;20&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;results&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;get_results&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;div class=&#34;figure&#34;&gt;
&lt;img src=&#34;individual.png&#34; alt=&#34;*Example of a dataset containing 20 participants (shown with different colors). As can be seen, we introduced modulations in the inter- and intra- individual variability.*&#34; width=&#34;1575&#34; /&gt;
&lt;p class=&#34;caption&#34;&gt;&lt;span id=&#34;fig:unnamed-chunk-3&#34;&gt;&lt;/span&gt;Figure 1: *Example of a dataset containing 20 participants (shown with different colors). As can be seen, we introduced modulations in the inter- and intra- individual variability.*&lt;/p&gt;
&lt;/div&gt;
&lt;p&gt;We will then compare the scores obtained by each method to the &amp;ldquo;true&amp;rdquo; score of each participant by substracting them from one another. As such, for each method, we obtain the absolute &amp;ldquo;distance&amp;rdquo; from the true score.&lt;/p&gt;
&lt;h4 id=&#34;fit-model&#34;&gt;Fit model&lt;/h4&gt;
&lt;p&gt;Contrast analysis will be applied to compare the different methods together.&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-r&#34; data-lang=&#34;r&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;lm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Diff_Abs&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;~&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;results&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;modelbased&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;estimate_contrasts&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;arrange&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Difference&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Level1&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;stringr&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;str_remove&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Level1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Diff_&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;         &lt;span class=&#34;n&#34;&gt;Level2&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;stringr&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;str_remove&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Level2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Diff_&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt; 
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;select&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Level1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Level2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Difference&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;CI_low&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;CI_high&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;p&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-fallback&#34; data-lang=&#34;fallback&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;## Level1                 | Level2                 | Difference |            CI |      p
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;## -------------------------------------------------------------------------------------
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;## IndividualModel_Priors | PopulationModel        |  -1.85e-03 | [-0.01, 0.01] | &amp;gt; .999
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;## IndividualModel_Freq   | PopulationModel        |   1.70e-03 | [-0.01, 0.01] | &amp;gt; .999
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;## IndividualModel_Freq   | IndividualModel_Priors |   3.55e-03 | [-0.01, 0.01] | &amp;gt; .999
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;h4 id=&#34;visualize-the-results&#34;&gt;Visualize the results&lt;/h4&gt;
&lt;div class=&#34;figure&#34;&gt;
&lt;img src=&#34;featured.png&#34; alt=&#34;*Average accuracy of the different methods (the closest to 0 the better).*&#34; width=&#34;2250&#34; /&gt;
&lt;p class=&#34;caption&#34;&gt;&lt;span id=&#34;fig:unnamed-chunk-6&#34;&gt;&lt;/span&gt;Figure 2: *Average accuracy of the different methods (the closest to 0 the better).*&lt;/p&gt;
&lt;/div&gt;
&lt;div class=&#34;figure&#34;&gt;
&lt;img src=&#34;n_participants.png&#34; alt=&#34;*Accuracy depending on the number of total participants in the dataset.*&#34; width=&#34;2250&#34; /&gt;
&lt;p class=&#34;caption&#34;&gt;&lt;span id=&#34;fig:unnamed-chunk-7&#34;&gt;&lt;/span&gt;Figure 3: *Accuracy depending on the number of total participants in the dataset.*&lt;/p&gt;
&lt;/div&gt;
&lt;h3 id=&#34;conclusion&#34;&gt;Conclusion&lt;/h3&gt;
&lt;p&gt;Though not significantly different, it seems that &lt;strong&gt;raw basic estimates&lt;/strong&gt; (that rely only on the individual data) &lt;strong&gt;perform consistently worse than the population model or individual models informed by priors&lt;/strong&gt;, especially for small datasets (between 10 and 100 participants) - though again, the difference is tiny in our simulated dataset. In the absence of the whole population dataset, it seems that using individual Bayesian model with informative priors (derived from the population model) is a safe alternative.&lt;/p&gt;
&lt;h3 id=&#34;functions&#34;&gt;Functions&lt;/h3&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-r&#34; data-lang=&#34;r&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;library&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;tidyverse&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;library&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;easystats&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;library&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;rstanarm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;library&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;ggdist&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Get data ----------------------------------------------------------------&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;get_data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;kr&#34;&gt;function&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_participants&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;10&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;20&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;d&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1.5&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;var&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;3&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;noise&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0.1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;{&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;scores_baseline&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_participants&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;scores_condition&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_participants&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;d&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;variances&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rbeta&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_participants&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;8&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;variances&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0.1&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;variances&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;*&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;var&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;/&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;max&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;variances&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;c1&#34;&gt;# Rescale&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;noise_sd&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;abs&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_participants&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;noise&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;data.frame&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;kr&#34;&gt;for&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;i&lt;/span&gt; &lt;span class=&#34;kr&#34;&gt;in&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;:&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_participants&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;{&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;a&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;scores_baseline[i]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;variances[i]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;b&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;scores_condition[i]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;variances[i]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;a&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;a&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;noise_sd[i]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;c1&#34;&gt;# Add noise&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;b&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;b&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rnorm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;noise_sd[i]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;c1&#34;&gt;# Add noise&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rbind&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;data.frame&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;s&#34;&gt;&amp;#34;Participant&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;sprintf&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;S%02d&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;i&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;s&#34;&gt;&amp;#34;Y&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;a&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;b&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;s&#34;&gt;&amp;#34;Score_True&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rep&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;scores_baseline[i]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;scores_condition[i]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;each&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;s&#34;&gt;&amp;#34;Condition&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rep&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Baseline&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Manipulation&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;each&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;p&#34;&gt;))&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;p&#34;&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;p&#34;&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Visualize data -----------------------------------------------------------&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;p&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;get_data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_participants&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;20&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;group_by&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Condition&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;mean&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;mean&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Y&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;ggplot&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;y&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Y&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;x&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Condition&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;fill&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;color&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;group&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;geom_line&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;y&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;mean&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;position&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;position_dodge&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;width&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0.66&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;ggdist&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;stat_eye&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;point_interval&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;ggdist&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;mean_hdi&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;alpha&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0.66&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;position&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;position_dodge&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;width&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0.66&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;.width&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.95&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;ylab&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Score&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;theme_modern&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;theme&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;legend.position&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;none&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;ggsave&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;individual.png&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;p&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;width&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;7&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;height&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;7&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;dpi&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;450&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Get results -------------------------------------------------------------&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;get_results&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;kr&#34;&gt;function&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;{&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;c1&#34;&gt;# Raw method ----&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;results&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;group_by&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Condition&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;summarise_all&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;mean&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;rename&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Score_Raw&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Y&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;arrange&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Condition&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;ungroup&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;c1&#34;&gt;# Population model ----&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;model&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;lme4&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;lmer&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Y&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;~&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Condition&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Condition&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;|&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;fixed&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;insight&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;get_parameters&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;effects&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;fixed&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;$&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Estimate&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;random&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;insight&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;get_parameters&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;effects&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;random&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;$&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;c1&#34;&gt;# Transform coefs into scores&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;pop_baseline&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;random[&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;]&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;fixed[1]&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;pop_manipulation&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;pop_baseline&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;random[&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;2&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;]&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;fixed[2]&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;results&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;$&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Score_PopulationModel&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;pop_baseline&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;pop_manipulation&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;c1&#34;&gt;# Individual model ----&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;individual_model_data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;data.frame&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;kr&#34;&gt;for&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;participant&lt;/span&gt; &lt;span class=&#34;kr&#34;&gt;in&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;unique&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;$&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;{&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;cat&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;.&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;c1&#34;&gt;# Print progress&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;dat&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data[data&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;$&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;==&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;]&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;c1&#34;&gt;# Frequentist&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;model1&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;lm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Y&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;~&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Condition&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;dat&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;nopriors&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;parameters&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;parameters&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;$&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Coefficient&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;c1&#34;&gt;# Bayesian without priors&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;c1&#34;&gt;# model2 &amp;lt;- stan_glm(Y ~ Condition, data = dat, refresh = 0)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;c1&#34;&gt;# bayes &amp;lt;- parameters::parameters(model2)$Median&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;c1&#34;&gt;# Bayesian with Priors&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;model3&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;stan_glm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Y&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;~&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Condition&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;dat&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;n&#34;&gt;refresh&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;n&#34;&gt;prior&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;normal&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;fixed[1]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;n&#34;&gt;prior_intercept&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;normal&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;fixed[2]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;priors&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;parameters&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;parameters&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model3&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;$&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Median&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;individual_model_data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rbind&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;n&#34;&gt;individual_model_data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;nf&#34;&gt;data.frame&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;        &lt;span class=&#34;s&#34;&gt;&amp;#34;Participant&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;        &lt;span class=&#34;s&#34;&gt;&amp;#34;Condition&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Baseline&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Manipulation&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;        &lt;span class=&#34;s&#34;&gt;&amp;#34;Score_IndividualModel&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;nopriors[1]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;nopriors[1]&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;nopriors[2]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;        &lt;span class=&#34;c1&#34;&gt;# &amp;#34;Score_IndividualModel_Bayes&amp;#34; = c(bayes[1], bayes[1] + bayes[2]),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;        &lt;span class=&#34;s&#34;&gt;&amp;#34;Score_IndividualModel_Priors&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;c&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;priors[1]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;priors[1]&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;priors[2]&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;p&#34;&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;results&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;merge&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;results&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;individual_model_data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;c1&#34;&gt;# Clean output ----&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;diff&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;results&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;c1&#34;&gt;# Diff_Raw = Score_True - Score_Raw,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;n&#34;&gt;Diff_PopulationModel&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Score_True&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Score_PopulationModel&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;n&#34;&gt;Diff_IndividualModel&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Score_True&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Score_IndividualModel&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;c1&#34;&gt;# Diff_IndividualModel_Bayes = Score_True - Score_IndividualModel_Bayes,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;      &lt;span class=&#34;n&#34;&gt;Diff_IndividualModel_Priors&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Score_True&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Score_IndividualModel_Priors&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;select&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Condition&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;starts_with&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Diff&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;pivot_longer&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;starts_with&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Diff&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;names_to&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Method&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;values_to&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Diff&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Diff_Abs&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;abs&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Diff&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;diff&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;p&#34;&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Analysis ----------------------------------------------------------------&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;results&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;data.frame&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;kr&#34;&gt;for&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n&lt;/span&gt; &lt;span class=&#34;kr&#34;&gt;in&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;seq.int&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;10&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;300&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;length.out&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;10&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)){&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;get_data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_participants&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;round&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;n_trials&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;20&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;rez&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;get_results&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;select&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;-&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Participant&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;group_by&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Condition&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;summarise_all&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;mean&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_Participants&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;n&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;           &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;as.factor&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;           &lt;span class=&#34;n&#34;&gt;Dataset&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;paste0&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Dataset&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;round&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)))&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;n&#34;&gt;results&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;rbind&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;results&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;rez&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;print&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;c1&#34;&gt;# Print progress&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;p&#34;&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# model &amp;lt;- mgcv::gam(Diff_Abs ~ Method + s(n_Participants, by = Method), data = results)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;lm&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Diff_Abs&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;~&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;*&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;poly&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;n_Participants&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;3&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;results&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;parameters&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;parameters&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;contrasts&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;modelbased&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;estimate_contrasts&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;arrange&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Difference&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;Level1&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;stringr&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;str_remove&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Level1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Diff_&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;Level2&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;stringr&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;str_remove&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Level2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Diff_&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;select&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Level1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Level2&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Difference&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;CI_low&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;CI_high&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;p&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Visualize results ---------------------------------------------------------&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;p&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;modelbased&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;estimate_means&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;arrange&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Mean&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;stringr&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;str_remove&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Diff_&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;factor&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;levels&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;  &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;ggplot&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;x&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;y&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Mean&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;color&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;geom_line&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;group&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;geom_pointrange&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;ymin&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;CI_low&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;ymax&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;CI_high&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;size&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;theme_modern&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;theme&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;axis.text.x&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;element_text&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;angle&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;45&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;hjust&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;scale_color_material&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;ggsave&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;featured.png&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;p&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;width&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;10&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;height&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;6&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;dpi&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;450&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;p&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;modelbased&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;estimate_relation&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;model&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;stringr&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;str_remove&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Diff_&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt;  &lt;span class=&#34;o&#34;&gt;%&amp;gt;%&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;ggplot&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;x&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;n_Participants&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;y&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Predicted&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;geom_point&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;mutate&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;results&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;stringr&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;::&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;str_remove&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;Diff_&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)),&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;             &lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;y&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Diff_Abs&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;color&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;geom_ribbon&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;ymin&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;CI_low&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;ymax&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;CI_high&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;fill&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;alpha&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0.1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;geom_line&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nf&#34;&gt;aes&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;color&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;Method&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;),&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;size&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;theme_modern&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;theme&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;axis.text.x&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;element_text&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;angle&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;45&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;hjust&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;))&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;scale_color_material&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;+&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;nf&#34;&gt;scale_fill_material&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;ggsave&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;n_participants.png&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;p&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;width&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;10&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;height&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;6&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;dpi&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;m&#34;&gt;450&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;c1&#34;&gt;# Save results ------------------------------------------------------------&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;d&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;&amp;lt;-&lt;/span&gt; &lt;span class=&#34;nf&#34;&gt;list&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;results&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;results&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;model&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;model&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;contrasts&amp;#34;&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;contrasts&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nf&#34;&gt;save&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;d&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;,&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;file&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;s&#34;&gt;&amp;#34;data.Rdata&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;h3 id=&#34;references&#34;&gt;References&lt;/h3&gt;
&lt;p&gt;&lt;sub&gt;You can reference this post as follows:&lt;/sub&gt;&lt;/p&gt;
&lt;p&gt;&lt;sub&gt;- Makowski, D. (2020, September 14). How to extract individual scores from repeated measures. Retrieved from &lt;a href=&#34;https://dominiquemakowski.github.io/post/individual_scores/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;https://dominiquemakowski.github.io/post/individual_scores/&lt;/a&gt;&lt;/sub&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;p&gt;&lt;em&gt;Thanks for reading! Do not hesitate to share this post, and leave a comment below&lt;/em&gt; &amp;#x1f917;&lt;/p&gt;
&lt;p&gt;🐦 &lt;em&gt;And don&amp;rsquo;t forget to join me on X&lt;/em&gt; &lt;a href=&#34;https://x.com/Dom_Makowski&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;@Dom_Makowski&lt;/a&gt;&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>What is neuropsychology?</title>
      <link>https://realitybending.github.io/post/2020-09-13-what_is_neuropsychology/</link>
      <pubDate>Sun, 13 Sep 2020 00:00:00 +0000</pubDate>
      <guid>https://realitybending.github.io/post/2020-09-13-what_is_neuropsychology/</guid>
      <description>&lt;h2 id=&#34;the-place-of-neuropsychology&#34;&gt;The place of neuropsychology&lt;/h2&gt;
&lt;p&gt;&lt;strong&gt;Let&amp;rsquo;s make a simple experiment&lt;/strong&gt;. Pick one young and brilliant neuropsychologist and ask &amp;ldquo;what is neuropsychology?&amp;rdquo;. In some cases, after a few seconds of hesitation, you could hear answers like &amp;ldquo;being a neuropsychologist means doing &lt;em&gt;this&lt;/em&gt; or &lt;em&gt;that&lt;/em&gt;&amp;rdquo;. In other cases, you might come across incomplete - or even false - responses, such as &amp;ldquo;neuropsychology is a tool&amp;rdquo;, &amp;ldquo;a method&amp;rdquo;, &amp;ldquo;a paradigm&amp;rdquo;, or even worse, &amp;ldquo;a point of view&amp;rdquo;.&lt;/p&gt;
&lt;p&gt;That does not mean that our neuropsychologist is incompetent, far from it. But formally defining our field as a whole is not an exercise that we are used to do. Indeed, &lt;strong&gt;the training in neuropsychology usually comes in a fragmented way&lt;/strong&gt;, little by little. &lt;em&gt;A bit of cognitive neuroscience here, a bit of neuropsychological syndromes there, some cognitive tests administration over here, and some cortical neuroanatomy over there&amp;hellip;&lt;/em&gt; Though we might, &lt;em&gt;in fine&lt;/em&gt;, acquire a global vision and understanding of neuropsychology, verbalizing it is seldom necessary.&lt;/p&gt;
&lt;p&gt;The definition of neuropsychology is actually quite complex to formalize, and can even be hotly debated. The jobs and positions that stem out of this field are many, and &lt;strong&gt;practitioners often tend to circumscribe neuropsychology to their own activity&lt;/strong&gt;. For instance, a neuropsychologist that mainly does cognitive rehabilitation with psychiatric patients might have quite a different vision from another that does, day after day, presurgical cognitive assessments. And that is without mentioning the neuropsychologists pursuing an academic career, or even the ones that have moved to the private sector.&lt;/p&gt;
&lt;p&gt;&lt;em&gt;No problem&lt;/em&gt;, would argue the careful reader, &lt;em&gt;if the definitions are too narrow, let&amp;rsquo;s take more general one&lt;/em&gt;. &lt;strong&gt;It&amp;rsquo;s not that simple&lt;/strong&gt;. Indeed, neuropsychology occupies a very particular place in the network of science, as it is at &lt;strong&gt;the crossroads between social sciences, biological sciences and medical fields&lt;/strong&gt;. Giving a definition that is too large would lose its essence in the nebulous depths of neuroscience and psychology, which would be not be accurate; neuropsychologists, whether they are clinical practitioners or not, have a common training, a specific theoretical grounding, as well as a unique interpretation and analysis framework underpinned by a scientifically rigorous method. Taking these elements into account, I will attempt to give a &lt;strong&gt;simple, comprehensive and informative definition of neuropsychology&lt;/strong&gt;.&lt;/p&gt;
&lt;p&gt;The first axiom that we need to discuss is the notion of science. &lt;strong&gt;Is neuropsychology its &amp;ldquo;own&amp;rdquo; scientific field&lt;/strong&gt;, or is it a mere portion of another one, such as cognitive neuroscience or psychology, which differs from other specializations only through its object of interest? &lt;em&gt;&amp;ldquo;By science&amp;rdquo;&lt;/em&gt;, says Schopenhauer in his PhD thesis with a baroque title (On the Fourfold Root of the Principle of Sufficient Reason), &lt;em&gt;&amp;ldquo;we understand a system of notions, i.e. a totality of connected, as opposed to a mere aggregate of disconnected, notions.&amp;rdquo;&lt;/em&gt; This definition applies well to neuropsychology, that contains a set of theories, hypotheses, methods and proofs feeding from one another and creating a coherent ensemble. As such, neuropsychology is its own scientific discipline, although a singular one&amp;hellip;&lt;/p&gt;
&lt;p&gt;Indeed, &lt;strong&gt;what is the &amp;ldquo;bigger&amp;rdquo; box in which neuropsychology fits?&lt;/strong&gt; While neuropsychologists are often initially trained in psychology, one could argue that the focus on the brain makes it more belonging to neuroscience. Well, the organization and structure of Science is a complicated issue. However, the particularity of the topographical location of neuropsychology is quite apparent.&lt;/p&gt;
&lt;p&gt;On the one hand, neuropsychology belongs to a cluster of sciences interested a specific biological organ: the brain. As such, &lt;strong&gt;neuropsychology is an integral part of neuroscience&lt;/strong&gt;. On the other hand, neuropsychology is interested in the productions of the brain (e.g., thoughts, feelings and behaviours) with a focus on the cognitive level (analyzing things in terms of cognitive processes and mechanisms), which makes it also &lt;strong&gt;belonging to psychology&lt;/strong&gt;. Moreover, one could argue that neuropsychology, through its integration of the study of what we are biologically, and who we are mentally, has been connected to, and used as evidence in, &lt;strong&gt;philosophy of mind&lt;/strong&gt; debates (for instance, famous neuropsychological cases studied by Sacks, Ramachandran or Milner have been widely discussed by contemporary philosophers). Finally, contrary to many other domains, neuropsychology has also an applied, practical component, that can be used in clinical practice. This clinical aspect, registering &lt;strong&gt;neuropsychology withing medical fields&lt;/strong&gt;, takes multiple forms, such as assessment, diagnostic or therapeutic care, and can be used with a wide variety of patients and illnesses. These multiple facets make the wealth of &lt;strong&gt;neuropsychology, which offers an exceptional freedom of practice&lt;/strong&gt;.&lt;/p&gt;
&lt;p&gt;As we have seen, &lt;strong&gt;neuropsychology is located at the centre of colliding galaxies of knowledge&lt;/strong&gt;, such as neuroscience, psychology, medicine and philosophy. However, the fast development of neuropsychology is gradually leading to the creation of subcomponents within itself, corresponding to different practices and theoretical steps. And these clusters are themselves growing. For instance, clinical neuropsychology was historically focused on diagnostic cognitive assessments, but has recently expanded on the treatment-side of things, with innovations like cognitive training and rehabilitation. This underlines neuropsychology as a rapidly evolving field, moving its potential towards yet uncharted territories.&lt;/p&gt;
&lt;h2 id=&#34;the-fourfold-structure-of-neuropsychology&#34;&gt;The fourfold structure of neuropsychology&lt;/h2&gt;
&lt;p&gt;Neuropsychology is born from the convergence of &lt;strong&gt;cognitive neurology&lt;/strong&gt;, with pioneers such as &lt;a href=&#34;https://en.wikipedia.org/wiki/Paul_Broca&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Broca&lt;/a&gt; and &lt;a href=&#34;https://en.wikipedia.org/wiki/Carl_Wernicke&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Wernicke&lt;/a&gt; (which made inferences about brain functioning based on the observations of patients with brain lesions) and psychologists such as &lt;a href=&#34;https://en.wikipedia.org/wiki/Th%C3%A9odule-Armand_Ribot&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Ribot&lt;/a&gt; (focusing on the organization and semiology of cognitive deficits). This history has shaped neuropsychology as a two-faced entity, with one &lt;strong&gt;experimental side&lt;/strong&gt; dedicated to understand the relationship between brain and cognition (by using pathological cases or natural variability of neurocognitive characteristics), and one &lt;strong&gt;clinical aspect&lt;/strong&gt;, focusing on bringing this knowledge to the benefit of the patients suffering from brain disorders.&lt;/p&gt;
&lt;p&gt;However, beyond these two pillars of neuropsychology, recent advances have outlined a more &lt;strong&gt;theoretical level&lt;/strong&gt; of neuropsychology, dedicated to a high-level integration of the data at hand to elaborate general theories and interfacing them with evolutionary or philosophical principles. Similarly, a &lt;strong&gt;computational&lt;/strong&gt; facet, referring to the operationalization of the functioning in statistical terms, starts to emerge as a pseudo-independent aspect, propelled by the regain of interest and focus on the methodological and statistical aspects of psychology and neuroscience.&lt;/p&gt;
&lt;p&gt;This structure is not fixed, but driven by the evolution of the field. It is possible that new poles will emerge, or differentiate over time, until maybe they separate from - or create new clusters within - neuropsychology.&lt;/p&gt;
&lt;figure&gt;
  &lt;img src=&#34;cycle.png&#34; alt=&#34;Structure of neuropsychology&#34;/&gt;
  &lt;figcaption&gt;The fourfold structure of neuropsychology.&lt;/figcaption&gt;
&lt;/figure&gt;
&lt;h2 id=&#34;the-definition-of-neuropsychology&#34;&gt;The definition of neuropsychology&lt;/h2&gt;
&lt;p&gt;&lt;strong&gt;Neuropsychology is a theoretical and practical science investigating the relationship between 1) the structure and functioning of the brain, and 2) cognitive processes and their related derivatives, such as thoughts, feelings and behaviours.&lt;/strong&gt; It is organised in four interconnected and overlapping dimensions:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Experimental neuropsychology&lt;/strong&gt; studies the variability of the brain and cognition (whether from pathological origin or not) to test theories and models through empirical experimentation.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Clinical neuropsychology&lt;/strong&gt; uses theories and models about mental functioning to better detect and assess disorders and deficits, leading to a precise diagnostic and an adapted treatment.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Computational neuropsychology&lt;/strong&gt; transforms the data acquired through experiments and observation into logical or statistical models of mental functioning that are used to operationalize the processes at stake.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Theoretical neuropsychology&lt;/strong&gt; integrates the evidence to elaborate and develop unifying theories to address fundamental questions about mental functioning.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;Neuropsychology is located at the crossroads between neuroscience and psychology, at the interface between theory and practice. &lt;strong&gt;Its practitioners, the neuropsychologists&lt;/strong&gt;, are bound by a specific training, by unique theoretical and historical references, and are endowed with an analysis and interpretation framework backed by a rigorous and scientific investigation methodology.&lt;/p&gt;
&lt;!-- La neuropsychologie expérimentale étudie les variabilités du cerveau et de la cognition (qu’elles soient d’origine pathologique ou non) pour tester des modèles et développer des théories sur le fonctionnement mental, visant ainsi à une meilleure compréhension de l’Homme. --&gt;
&lt;!-- La neuropsychologie clinique utilise les théories et les modèles sur le fonctionnement mental pour mieux détecter et appréhender les troubles et les déficits d’une pathologie, menant à un diagnostic précis, tout en développant et appliquant des prises en charges modernes et adaptées. --&gt;
&lt;!-- La neuropsychologie se situe au centre de la nébuleuse des neurosciences, au carrefour de la théorie et de la pratique. Ses praticiens, les neuropsychologues, sont liés par une formation commune, des bases théoriques spécifiques, un canevas d’analyse et d’interprétation sous-tendu par une méthode d’investigation rigoureuse et scientifique.  --&gt;
&lt;p&gt;&lt;em&gt;Thanks for reading! Do not hesitate to tweet and share this post, and leave a comment below&lt;/em&gt; &amp;#x1f917;&lt;/p&gt;
&lt;h2 id=&#34;references&#34;&gt;References&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;Nicolas, S., &amp;amp; Murray, D. J. (1999). Théodule Ribot (1839–1916), founder of French psychology: A biographical introduction. History of Psychology, 2(4), 277.&lt;/li&gt;
&lt;li&gt;Schopenhauer, A. (1813). &lt;em&gt;On the Fourfold Root of the Principle of Sufficient Reason&lt;/em&gt;. PhD dissertation.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;&lt;sub&gt;You can reference this post as follows:&lt;/sub&gt;&lt;/p&gt;
&lt;p&gt;&lt;sub&gt;- Makowski, D. (2020, September 13). What is Neuropsychology?. Retrieved from &lt;a href=&#34;https://dominiquemakowski.github.io/post/what_is_neuropsychology/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;https://dominiquemakowski.github.io/post/what_is_neuropsychology/&lt;/a&gt;&lt;/sub&gt;&lt;/p&gt;
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