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<body>

<h1 id="probability-of-direction-pd">Probability of Direction (pd)</h1>
<ul>
<li><a href="#what-is-the-pd">What is the <em>pd?</em></a></li>
<li><a href="#relationship-with-the-p-value">Relationship with the <em>p</em>-value</a></li>
<li><a href="#methods-of-computation">Methods of computation</a></li>
<li><a href="#methods-comparison">Methods comparison</a>
<ul>
<li><a href="#correlation">Correlation</a></li>
<li><a href="#accuracy">Accuracy</a></li>
</ul></li>
</ul>
<p>This vignette can be referred to by citing the package:</p>
<ul>
<li>Makowski, D., Ben-Shachar M. S. &amp; Lüdecke, D. (2019). <em>Understand and Describe Bayesian Models and Posterior Distributions using bayestestR</em>. Available from <a href="https://github.com/easystats/bayestestR">https://github.com/easystats/bayestestR</a>. DOI: <a href="https://zenodo.org/record/2556486">10.5281/zenodo.2556486</a>.</li>
</ul>
<hr />
<h1 id="what-is-the-pd">What is the <em>pd?</em></h1>
<p>The <strong>Probability of Direction (pd)</strong> is an index of <strong>effect existence</strong>, ranging from 50% to 100%, representing the certainty with which an effect goes in a particular direction (<em>i.e.</em>, is positive or negative).</p>
<p>Beyond its <strong>simplicity of interpretation, understanding and computation</strong>, this index also presents other interesting properties:</p>
<ul>
<li>It is <strong>independent from the model</strong>: It is solely based on the posterior distributions and does not require any additional information from the data or the model.</li>
<li>It is <strong>robust</strong> to the scale of both the response variable and the predictors.</li>
<li>It is strongly correlated with the frequentist <strong><em>p</em>-value</strong>, and can thus be used to draw parallels and give some reference to readers non-familiar with Bayesian statistics.</li>
</ul>
<p>However, this index is not relevant to assess the magnitude and importance of an effect (the meaning of “significance”), which is better achieved through other indices such as the <a href="https://easystats.github.io/bayestestR/articles/region_of_practical_equivalence.html">ROPE percentage</a>. In fact, indices of significance and existence are totally independent. You can have an effect with a <em>pd</em> of <strong>99.99%</strong>, for which the whole posterior distribution is concentrated in the <code>[0.0001, 0.002]</code> range. In this case, the effect is <strong>positive with a high certainty</strong>, but also <strong>not significant</strong> (<em>i.e.</em>, very small).</p>
<p>Indices of effect existence, such as the <em>pd</em>, are particularly useful in exploratory research or clinical studies, for which the focus is to make sure that the effect of interest is not in the opposite direction (for clinical studies, that a treatment is not harmful). However, once the effect’s direction is confirmed, the focus should shift toward its significance, including a precise estimation of its magnitude, relevance and importance.</p>
<h1 id="relationship-with-the-p-value">Relationship with the <em>p</em>-value</h1>
<p>In most cases, it seems that the <em>pd</em> has a direct correspondance with the frequentist <strong>one-sided <em>p</em>-value</strong> through the formula: [p_{one sided} = 1-p_d/100] Similarly, the <strong>two-sided <em>p</em>-value</strong> (the most commonly reported one) is equivalent through the formula: [p_{two sided} = 2*(1-p_d/100)] Thus, the two-sided <em>p</em>-value of respectively <strong>.1</strong>, <strong>.05</strong>, <strong>.01</strong> and <strong>.001</strong> would correspond approximately to a <em>pd</em> of <strong>95%</strong>, <strong>97.5%</strong>, <strong>99.5%</strong> and <strong>99.95%</strong> .</p>
<img 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DxxcrIG8T7zNudhgk0DHk+Y8pkQSTrGY+fA4+kSKHKvVUI2eFPrIdg04PF0UYuM5bWvtguw2GEBwaYBjydMJm08gzpKx3jsJng8aZKJ064c20SwacDj6eL72UIma1ZCrIdg04DHkyVyeM6payMBjydLnI5tHmWC2uDxdJF1ac8To8a47Dh4PGVEQv6LvyiPI1sMwaYBjydIvDIiDBcLf7746qvTpZwB4oLIBJuG4oM53Nq6d/jOlxuUALajku8yslfsartYiH0/XEnIBJuGwoN58c6ff3DvzdMb7UsAq4nzrky/p6dS5GzyhwsaE2w68g/m9Qf3ov/CV29/3rYEsBox8VJMvRTTMU9lbdrPTovAY5fB4wkhJ1CrXbfk19yGttSrnabwYA5Fvfr1B7fblwBWk8qa7meLx+Og+GBebUU005hH6wRFSVN/c9MxXdAYdDDuNAkK2TY/rxrGAR5PgrzHaDxCiv1cWxL6ucZHKR0bvJONINg0rD6Y19/+eMMSwG7c1Zhg01HxYF41m9DFo7WVUs9VfOiLF7jcpUWwaajymHr1KMjaxHI+tZy25XsRJ7bvwqWHYNNQ8WBekI+dp3BAUzx5Wh6fGHl8cHJyYuEJbPUg2DRU9HO9pWkfXz6abR+r66vdnaoSwA6Sw16yV8EyPvRFJWSjd7cBBJuG+g9GqHt0V704muGxxZSGi3NnsIWyiUy9emzUfzCXT/bDi/v78vrin/4bPLaZimGm/AEw7ooM1aQWJoPH2vHjiwfH4eXj5+Ly6rP/FNerb0bgsd1UDBfj8eiob+HZdurx0UPax+5QMVyMxmOjvoVZPo6u8BhMQLBpKDyY81tr6tVZ+/hoJnhYVQJAnxBsGvIP5s3T22+eyq0EqrjafZj1V5OPHWMkNWmCTUNpP5DwxW3tvMx4/DhOyXhsG+tFHUvPFsGmoezx4Q3mZbqITlTRyRX9weORU9wvU0rccONbHq0NBNWbXvoK6tUjp/BgogZy+EI7L7NOCWCGVON00la2AZfL643LEGwa2A9kDCT+ptvJK3fjjW3HozHowOMxEG9JHWQixx6PpVUM11Ls52q4VeZKCWAIqXG+aq3SMR5PhOL+1VtbW9WDx3VLAGNkdev8e6bupicINg3lB/NCv/64ZglgiNFJWwHBpqFqPxDGj11l9CoTbBoq8nEzjXm05lGdXBNoDxNsGorzQBpXqsslwPAkR6Hi8YQpz8vcrAQYHnWIojtnGG8CwaaB8WPXCQLvJEir1iOHYNNQfjANJ1dXlAAD43kMFk8ePHaedA4mHk8XPHaT/JxpdV3UGKknBR47ybVrmEaanQk2DfRzOQkeQ4HigxETrJvOsObRDkhq77VrEUepMcGmo7hOQkzlarrqiUc7HBVpeFqLiwk2DRXzQNify1pWPa449WXMEGwa8NgpKtLxpAadCDYNhQfzSsyupl7tFEk6xuNJU3H+sf5IiWtLAFNMQ2PQwbiTU2S6Ii7kwGOXyKrPU6lIW8/rb4uVvi8arxR883Qrar+ev7e24ht96G/Kz2VofgKPXWLyHlsQbD//eeHlq+8KzZp7HPt4jcfRt8ufwOMxMPV6tflg+/nPCyK/+YMf/sMvI4+/K+dPvYp7ll5/IL6cf/PfyTejV299rN4TyKvszR//yq+9/eNITiHo6oe2xNYe6m3xMz/8oLrvCo/BIcwHW8nj829+KXLxi3e+jDx8/Z3PxQFp4rDD6Mv5LXnm4Zun98SX+D1BfBRimo/Pb92TDos/hQ+JIuJ8HL+IC/rf1+djxo9tZZrJtwILgq1Yrz6MpLwR16tf3IvbyrLJHCmt5IyFVe+Jq+jv6FXmsXJY/DuQfSgtInt7bU0cjx0gPS5i8tgWbG+exoO0//Vj6fL5LVVbFrXhxONvihWE6r0wFvHNH1R7nH4oKyJ7Oy7oWo8P08HjG43+p9j2aEeIPOxlsVjZZn562BZs0q1I4Og/Ue2NiKrMcUoNi/n4O4l+6/Jx4UPpt3PlNcnHDbHt0Y6RSN5FRDjZfuoE24LtUBgTVaxfyLZs5LDwONcCjv4Iv6Mv8XviZ8rt4/ek13KRUsWHVPtYNbTP3/sx/dXOIk9eWyzEDMzlctIeW8abf6sasy++K+vDL9L+6ujVedYJHVe21Z7Sqjdb+vjmqeyrFpXhv/Gdz4sfiovISoi/RD9xbX91lJBfa/q19eBx38SHKMbrIZany/gtw/cEdlHch/6GyO6HtI/tIkj2mRfpeLkMJ1+7hhVK7eM3T2/QX20d6lTjKCOLPefDCXtMsGkoeSwWLeo8vnw02z6WV0ez2ez9/YoSoA/iI1/ipcbK34lqTLDpyD+YN09vixXIL6rr1Ve7O+HRXXn5ckdTAvRAknyv3VtvAhBsGgoP5vzW1g0xxazyk5dP9sOL+yILX332XFcCdE9aiRYaTzURKwg2DfUfzMWD4/DysTA4qmDPZjIl34zg0fZCTtjC5bRFJtg01H8wZ9uJxxfff57LyTzaPtAIi8dQSfpg4rHjNZv6ZPlYkraRebR9oBN22hoTbDrqP5isfSzB436ZuLDQjPrrna52H6r+alHDvvoTxp16ptQ7LV/SYw2VNFi3GI8fi5R8NJvdSSvYeNwPpWEm+ZKhJ6iGdYu2UnDW9/FYQLBpYN2ijcjG8arG1KsJNg2sW7SQlc7qyefhBNuC7fyWqMA2O4AlR3eb35bnczU8TKJcAnTB6qATGsdYEGzf+EbuhRRKbcvVgu42vy3Or27WMl4tAbqBQScN5oPtG9/IiyyFevP03vmv/JrcplakQCOb39I+BocwH2wVHp//8sdi81q1Pa2ZzW+L+RiPjZM2hcnJFVgQbMV6tWyJxg6q7WnNbH5bPDe14ZY+qyXAJsiRpfl8Uicau00ilKoPy11rjWx+W3VuKv1cZhAG5z1eIrLtFDxOd601sPkt407WEBk8FwlZ7m8rttQjI1tP3mPV5jWz+S0eW4NIxWGuQk3NehXbgq3gsdqe1sjmt8UHE5V071CzH4gO2x6tU6itt2LiDq6oPr3MvgkFCDYNxX1v3/nzeMvM1iVAIwJF4U22mtdDsGlY2S/zHvve9kFuQlZpm54Vj6lP6yHYNODxIOQmSBc09byK6jMaayHYNBQezKGoV4strFuXANVoPM7ext1aEGwaig/mVYvVGzzaOlTXq5XHxco1Sush2DQw7mQSf55O+UjtpXkMzcFjUyQnvaymYzyGpjAv0xDxUajJkHHxO2buCBxm1cKmq6LxuBXJCYrQBIJNQ8WDedVsQhePth36tIvdWgg2DVUeU68ejCqZ2YxLD8GmoeLB6A5crF8CVLPi52IRxMeSFz+FxzoINg0V/Vxv0T7ujIKhK4L6i0jk1R5qNNZCsGlg3KlPioaueuwvvq7wGLQQbBrwuE9Khq4kWn8RFFYuwjUQbBqqxo+bDSHzaNdwnaGkYuiE4j578YYDrJPomcLKRYP3AaOhwXmLNUqAdSTOBrJ369qPAdQGjwcjrUMvFmorvfUfg1UINg3F9cfx/mDUq3shFdRfLOLlEes/BqsQbBpW9tmTp9G0LwH0yP3zhKRiFxC9r2ish2DTwLjTYEhxsx25yLstINg04PFglDwm77aAYNPA/tV9klc1sXcZYHBrCDYN7F/dI1nV2feTa6rTm0CwaWDf2x7Jeqh938Nj6I8GHl8+mm0fy6ur3dmd51UlQJFEWc8TCbn4HkB31N+/+mp3Jzy6Ky9f7oRnSmk8rkEQyJEmgL6ov3/15ZP98OL+vrrSlQBlVCe16dsYBwSbhvoP5uLBcXj5+Lm8+lNVr74ZwaOtJKtGB3RQdwbBpiH/YMQZyXpETVp5/OGOtHq1BEhIx4iD5RKJO4Ng01CxTkJDPh8nV+USIEGeERFrjMfdQbBpKPVzrZkCkmsf/z4e61F1aHnUS/HEF9gYgk1D/fMkrnYf5vqrqVdrSPu0koYxGncIwaahwYOJx49FSo6u3k+7rHm0BbK+aQTuHoJNA+skNmNVVtZAwPCkFq7v5KpTwhTRLF1iwBiGpehxw6nVxRKmSLqU2PNX3wYYCjzeDJWOxQRq+Vru+UG9ui+mHWxrwOMuiNJx7PEyAon7g2DTgMfdkKbj5ZJKdX8QbBrwuBOSE1+C0yXHrvUIwaYh53GbQ2FCHq0gOYEtmY1Z9T3oAIJNA+PHXZB5LKrV1d+DDiDYNOBxY6pav2m9umI6NRp3x+SCrS543JT13VgBq5vAAHjclLUe01cNRsDjxqxNx3gMJsDjbkHjXiHYNOBxFwh7q7qzsLpjCDYNeNwBojYdDy8VxaWW3TUEmwY87oDU45K4eNw1BJsGPG5JSdi4Xl0WF407ZqLBdj143I7ydraqdYy4/TLNYKsBHrdDLlDMyE2+ROUemWaw1QCPWyB2wSzm48xj2sRgADxuSrwtdTnt5tIxHsPg4HFD0q3ldbqiMQwPHjdEpWO5RNH0vUyPiQVbffD4Olb3tI2/cHCTAcYebK3B42vQtnfVjgGsLh6SkQdbe/D4GjQ7zSdvsdvHoIw82NqDx9eRnGOcilwQF48HZezB1ho8rkXO45K5aDwkkwi2NuBxPfLpGHWNMY1gawEeN2axMH0HACXwuClM2AL7wOMa5MW9ZjYXgAnwOIdGznwGjk+MICkbYkTB1i14nKGTs+RxeRwKhmM8wdYxeJyh9Tg/ATOZlonGJhhPsHUMHueonrkllxrjrRWMKNi6pcGDuXw02z4WF0czwU7zEuwnWc2Uf0edacyqCAsYVbB1Sf0Hc7W7Ex7dTV6dxUo3KsF+0sXFuXe8k1jjlYMUYXjGFGydUv/BXD7ZDy/u76sXj583L8F+KtKxFxFUH6QIgzOmYOuU+g/m4sFxpq9KzDcjRvVoV131PLkvNT1bYDP1LRQ16cTjXDoe1z+RFdtP+3OfUSawnHb5OGsdj8rjUuU51tf3fQ+PwW7atY9fPmxTgu2UO7NijxcL32fQ2BLGE2wd06S/+mHSLL76LKtWj+jRRtqeFvbOC+TAcbq+ieq1ccYTbB3TePxYpOR883hMj3Z10KnQgY3HxhlRsHUL87nyVJ2XmHsHjU0zpmDrFDwuUDIVcS1jVMHWJXi8Cvv2WMv4gq0j8HgF3/MQ2VJGF2xdgcdlghPPO0BkcAo8LhEEy5MDT26KSesYXAGPS4ilTVFC3vP9BcNM4Ap4XEYMNR0c/GyOxxYytmDrDDxeIdLXizKyR73aPkYXbF2BxwnJHBA5g8tjaYSVjCXYOgePFekiieSYcjy2kJEEW/fgsSJb7JT/G+xiJMHWPRP3uDB5GnWtx+lg65Npe5zUoXNvGLwbuBaXg61X8Di/WJGcDG4ybY+luLlNQPAY3GTSHquO6SX1anCc0XusO3pN/iW27EFdh7A82Mwxdo+z2R2r70YaL/zCu4PeGjTH7mAzyEQ8Xt2wx/PD4KtFfssAGsf2Y3ewGWTsHofZZMv0rfk8jDQWu1J7xXSMx7ZjebCZY/QeKxJFowQ8j6jcXR6NrceNYDPAVDxWiP0BpMeyXo23ruFUsA3J+D0u2Cr3+RAal3a0BTewPdiMMXqPS61e1bElViZyojGMhql5nCRhz/NOTk7wGMbB6D2uHDkWedk7ODnxycgwCsbvcZE0Pftim2p2/XAMt4JtQEbvcflwiJy4PgeUu4blwWaOsXssO6j1oLFb2B1sBpmsxxzi5CJ2B5tBxu5x4mtZ22vyNNiJ5cFmjtF7HLNyzgseO4kTwWaC6Xg8P1kWRTZ3N9AWJ4LNBGPzOLdFT+F9f+6dnCzp1YJxMjKP04GklREl3/NOliZuCaB/JuNxJDLZGMZKAwsvH822j+XVxYez9/dblDAA6aZ5VSPDpc2qwTnsCjaLqP9grnZ3wqO74ury8fPwSClt26Nd2Vm+9D1mcDmNXcFmEfUfzOWT/fDivkjDFw+O5aumJQyBWlhcKSseO49dwWYR9R+MtDfKxPl8fDPCskcrNvoQK4urxpWoV7uOZcFmD/UfzNl24nGupdyohEGQG28tl+WJH7rxKHAKy4LNHtrk44vvPw/P3rezXp1soOd5hdVMa/qxwSEsCzZ7aNM+zmXmRiX0TVyVlnlYiBzi8eiwJ9gso0l/9UPVX21pPs5Pma44EDUVefg7A+iZxuPHIiWfzWZ3knRsp8erupKIYcSMaD6XP9dvSc3WHzBqxuPxYiFkXVbOoRapGo1HgC3BZh2j8VgenhhpXLmmidXGI8GSYLMPRzxem0xzhxlHGudFTn8MjccBHmtww+O1jdv0aFT5Ypn7KG3isYHHGkbjcfKB/GkveDw28FiDGx5fX69OlC32dKHxyMBjDY54fC2Jx1k6xuERYkewWchYPA7L6ZjTFGFCjMbjmGz6pWYECmCMjMzjMKtVV88IARgjjnucHIJaeFm+hNFgV9KwCLc9jqvR/nzu517CeMFjDU57LCZ9fL0I5xHpumNzdwP9g8caXPY4snb5tZhWLfKxOJecyvTYwWMNjnssVkcsZPvYO/HYaH704LEGlz2W6VesjpCXJydk49GDxxpc9jjvrahjo/HowWMNDntc7NUiGcOEGY3HABPGYY9JwQAKtzzG3IlD+1iDUx6v1KSjl+zYMyXwWINzHudnVIvxY3bQmxJ4rMENj7NVTGpGdWxv0Yf2W+IAAAmcSURBVGMq3eMHjzU44fHKQU3JaYpxvTrZQgCRRw8ea3DI4/w2XPlFEel+mXg8evBYgxMepwrnXQ2SDT+yLfYGuBMwCh5rcMPjuA6t8RiBYfK44bHw1/c0J6ECTB4XPBbGLk9WBpjQGEDhgMdS46XnMVAMtI81WOVxdYZV7WKPk08BjzXY5LGuxSs6uZZBuPx6gcgTB481uOCxSslff/31orPfBU6Cxxps8riqXu37cTYWUzC//poW8sTBYw1WebyK2AVTWCyGioMFGk8dPNZgtcdiQ1vPW54yUgwxeKyhwYO5fDTbPpZXFx/O3t9vUUJDfLHBvL9cimyMyQB66lt4tbsTHt0VV5ePoiuldN8eq/UQTN4CWEN9Cy+f7IcX90UavnhwHF4+ft64hMb483iVMZMwAdZS38LM3uzqZkTnHsfrild38AGgfayh/oM5207slfXqO33lY7mjPH1bUAUea2iTj0U/169/1qfHy+Vp9B8iQwk81tCmfZy8alpCTUQ6Xganp0sOeoESeKyhSX/1w6S/OsrK8VWzEmqi1kUs8RjK4LGGxuPHIiWfzWbpsFN3jzZZl5jst4XGUAaPNdgzn8v3M5E7KhLGBh5rsMpjDiIHaIU9HoeRxulOtl2VCTAJTHucV3a5ZEd5gDYY9riwkW2wXCbHveAxVEH7WINxj5fL7DrwfM8LqVeDDjzWYM7jWNakLh2/E2lMXxfowWMNxjyuPpUp0hiPQQseaxje4+LpaqxrggbgsYbBPQ6uG1xiu3nQgscazHmcvi5+3185/wUgAY81GKlXrzttDY8BGmOin6s4aLyakDe+JYCJMbzHYmf5QkLe+A4Aps7gHot6c+qu9jwngCpoH2sw4nFyXT0Bk2mZoAOPNZioV6eXOWOr3wUogMcazMznSoaQ5bFN4rrQS43GoAGPNRjxOD8nM75mtAnqgMcaLPGY0SaoAx5rGMDjCkXzUzMrp1kDVIHHGvr3OK0yr0u59G0BbMBwHq9tAuMxwAYMV69e35WFxgDtGbCfi64s2BTaxxpM75cJ0ACCTYOhcaeNfytMEjzWMLDHVXtyAdQFjzUM63FsMB5DS/BYgwmPxQa39HlBC/BYQ/8eF3KvesF0amgFHmvo3ePKSjQeA3SJGY/FWDImA3TFgPXqos+kZIDOGK6fq5SY8RiaQ/tYgzGPqVdDc/BYw0AeBwGzuGBz8FhDowdzcX9ffr18NNs+blICMz+gE/BYQ5MHczZ7X3p8tbsTHt1tUgIeQyfgsYYGD+blnR/F+fjyyX6amhvUqwE2BY81tKlXXzw4Di8fP4+ubkbwaGEwCDYNbTw+2048blwCAPTAZvm4cQkA0ANtPG7RPgaAHmnj8dXuw4b91QCdQLBpaOyx+NN4/BigEwg2DeyzBw5BsGnAY3AIgk0DHoNDEGwa8BgcgmDTgMfgEASbBjwGcB88BnAfPAZwHzwGhyDYNOAxOATBpgGPwSEINg14DA5BsGnAY3AIgk0DHoNDEGwa8BgcgmDT0IHHa7i57psDwT3EWHAPm9/CACV0IJUB+r3tm72WXg/uIcaCe9j8FmwowUrweAi4h45uwYYSrASPh4B76OgWbCjBShxtDgBADjwGcB88BnAfPAZwHzwGcJ++PD6azcRpyYUd64fmand253lo9B7EY5jNdsw+h4sP5cHVJu9h81tQJai4avHz97Pfb/T/jX7oy+OXO+Lv4onnQxPdw9n2sdl7CEPj9yCO1Dsyew+Xj3Y2vAVVgoqr5pwJ+9XvNx4RPdCTx1efyeMYiye6DYz45abvIYw1MnoP8njMJ/sm70Gd0LnBLagSVFw15uWdH4nzjOLfbzoi+qAnj6Oai6hOFk9YHZiLB38q6tVG7yFC/Mtv9B5UPjZ5D+p3b3ALyb8EcVy1KUCcTbbxbVhLTx5ffP+5yMnFE88H5uJD+Q+J0XuILQrN3kPcHDR5D7JWfGeTcFAlqLhqUYDwWP1+wxHRC332V7/cMZyPbfjXVwSN4XpJFPtn7++bvYcPZ7/+2Ub/V8QlyMtWbWTycWte7phtH//+po2yLnj5MDTcRlfpx3SrcPMmuurwaO8x7eOmiNi5+pP94onnQ/NS1qvN3kNcCTR6Dyofm7wH2US/u8ljUCWouGpRgBBX/X6zEdEPPY4fmx67Fb/c9LhpUn8zeg9n5v+/iG5hw4FbVYKKq+YwfgwAloPHAO6DxwDug8cA7oPHAO6DxwDug8cA7oPHAO6DxwDug8cA7oPHAO6DxwDug8cA7oPHAO6DxwDug8cA7oPHAO6DxwDug8cA7oPHAO6DxwDug8cA7oPHAO6Dx13z5umW4K2Pi2+f//LHla+jr/F/4f/9b5XlHcZFqWJvVBSVEpWg/d6bp/cKr1+9/fnrb2s+C86Bx13z5ult8eXw7c8Lb+s8Ti81Br7+4F6u2DdP3/lS+5u1Dsv7uVF8HXkcvlpTGDgFHneN8jjxL6Gtx8nbmmLX/Yo8K7lXeFzO0eAseNw1mXDn7/3h1tufiwrxDSHZD7a2RP47vxVVj2+nr5N69b+P3r79QiRNlTnjnxOfvpErVnxXfD4tWqT97KO3hcvpbxRlKlMP5a9St/D6g623fiB+kIQ8FvC4a5RwL97+/PzWDfHyhvxzfuudL8VXmVAPxTfj12n7WBiYS5LpzxXzsVBPfDgpWgiaFCs+Gv3J/8akei9/+vyWUF989nb0R3xjbU0cHAKPu0Z1SEWanN+6F9dfxV/yReTN/xMZUJp4LyxILJySNr4nzUt/ruyxfCsrWuT9rMtM/Cn/RvEt+a9H8ob8wKH6YROPCDoHj7smEU45JKuusiacePNK9mYnrwsei1qzqlanP1edj+WH5T8YW7dfqS61xOP8TxY8FtfR1aH8wHuf5+8V3AaPu+Yaj19/8NbH+ddFj8/f+++q70nn8Ysb6buHqnWLx4DHXVP2WIz+JvXjxLLozeR10eM3T/9RXK0u/lxY6K9OPvzqraw+nXwVv6H0G5MfU/Xq9z5PKt7Uq8cDHndNyeNyP5ew7PxW5HG5nyt26nDrRlJMVT+XHD/OpI9eROUlH1WOF34y+fEXhX6uG/RzjQw87pqSx2F+3Ek4+iJqHf9Q1Kd/oN5PkvEL+fLWvbSc5PvpSzlglatti/fe+jj9qCihMO6U8/hVMu4kPpeOOx0y7jQS8NguVG9154h5ICvZl3kgowGP7eKwr46nwxurHjMNZDTgsU3IqRv9EOXesseskxgPeAzgPngM4D54DOA+eAzgPngM4D54DOA+eAzgPv8fPihe7WjJcAUAAAAASUVORK5CYII=" title="Correlation between the frequentist p-value and the probability of direction (pd)" alt="Correlation between the frequentist p-value and the probability of direction (pd)" style="display: block; margin: auto;" />

<blockquote>
<p><strong>But if it’s like the <em>p</em>-value, it must be bad because the <em>p</em>-value is bad [<em>insert reference to the reproducibility crisis</em>].</strong></p>
</blockquote>
<p>In fact, this aspect of the reproducibility crisis might have been misunderstood. Indeed, it is not that the <em>p</em>-value is an intrinsically bad or wrong index. Rather, it is its <strong>misuse</strong>, <strong>misunderstanding</strong> and <strong>misinterpretation</strong> that fuels the decay of the situation. For instance, the fact that the <strong>pd</strong> is highly correlated with the <em>p</em>-value suggests that the latter is more an index of effect <em>existence</em> than <em>significance</em> (<em>i.e.</em>, “worth of interest”). The Bayesian version, the <strong>pd</strong>, has an intuitive meaning and makes obvious the fact that <strong>all thresholds are arbitrary</strong>. Nevertheless, the <strong>mathematical and interpretative transparency</strong> of the <strong>pd</strong>, and its reconceptualisation as an index of effect existence, offers a valuable insight into the characterization of Bayesian results. Moreover, its concomittant proximity with the frequentist <em>p</em>-value makes it a perfect metric to ease the transition of psychological research into the adoption of the Bayesian framework.</p>
<h1 id="methods-of-computation">Methods of computation</h1>
<p>The most <strong>simple and direct</strong> way to compute the <strong>pd</strong> is to 1) look at the median’s sign, 2) select the portion of the posterior of the same sign and 3) compute the percentage that this portion represents. This “simple” method is the most straigtfoward, but its precision is directly tied to the number of posterior draws.</p>
<p>The second approach relies on <a href="https://easystats.github.io/bayestestR/reference/estimate_density.html"><strong>density estimation</strong></a>. It starts by estimating the density function (for which many methods are available), and then computing the <a href="https://easystats.github.io/bayestestR/reference/area_under_curve.html"><strong>area under the curve</strong></a> (AUC) of the density curve on the other side of 0. The density-based method could hypothetically be considered as more precise, but strongly depends on the method used to estimate the density function.</p>
<h1 id="methods-comparison">Methods comparison</h1>
<p>Let’s compare the 4 available methods, the <strong>direct</strong> method and 3 <strong>density-based</strong> methods differing by their density estimation algorithm (see <a href="https://easystats.github.io/bayestestR/reference/estimate_density.html"><code>estimate_density</code></a>).</p>
<h2 id="correlation">Correlation</h2>
<p>Let’s start by testing the proximity and similarity of the results obtained by different methods.</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" title="1"><span class="kw">library</span>(bayestestR)</a>
<a class="sourceLine" id="cb1-2" title="2"><span class="kw">library</span>(logspline)</a>
<a class="sourceLine" id="cb1-3" title="3"><span class="kw">library</span>(KernSmooth)</a>
<a class="sourceLine" id="cb1-4" title="4"></a>
<a class="sourceLine" id="cb1-5" title="5"><span class="co"># Compute the correlations</span></a>
<a class="sourceLine" id="cb1-6" title="6">data &lt;-<span class="st"> </span><span class="kw">data.frame</span>()</a>
<a class="sourceLine" id="cb1-7" title="7"><span class="cf">for</span>(the_mean <span class="cf">in</span> <span class="kw">runif</span>(<span class="dv">25</span>, <span class="dv">0</span>, <span class="dv">4</span>)){</a>
<a class="sourceLine" id="cb1-8" title="8">  <span class="cf">for</span>(the_sd <span class="cf">in</span> <span class="kw">runif</span>(<span class="dv">25</span>, <span class="fl">0.5</span>, <span class="dv">4</span>)){</a>
<a class="sourceLine" id="cb1-9" title="9">    x &lt;-<span class="st"> </span><span class="kw">rnorm</span>(<span class="dv">100</span>, the_mean, <span class="kw">abs</span>(the_sd))</a>
<a class="sourceLine" id="cb1-10" title="10">    data &lt;-<span class="st"> </span><span class="kw">rbind</span>(data,</a>
<a class="sourceLine" id="cb1-11" title="11">      <span class="kw">data.frame</span>(<span class="st">&quot;direct&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x),</a>
<a class="sourceLine" id="cb1-12" title="12">                 <span class="st">&quot;kernel&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x, <span class="dt">method=</span><span class="st">&quot;kernel&quot;</span>),</a>
<a class="sourceLine" id="cb1-13" title="13">                 <span class="st">&quot;logspline&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x, <span class="dt">method=</span><span class="st">&quot;logspline&quot;</span>),</a>
<a class="sourceLine" id="cb1-14" title="14">                 <span class="st">&quot;KernSmooth&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x, <span class="dt">method=</span><span class="st">&quot;KernSmooth&quot;</span>)</a>
<a class="sourceLine" id="cb1-15" title="15">                 ))</a>
<a class="sourceLine" id="cb1-16" title="16">  }</a>
<a class="sourceLine" id="cb1-17" title="17">}</a>
<a class="sourceLine" id="cb1-18" title="18">data &lt;-<span class="st"> </span><span class="kw">as.data.frame</span>(<span class="kw">sapply</span>(data, as.numeric))</a>
<a class="sourceLine" id="cb1-19" title="19"></a>
<a class="sourceLine" id="cb1-20" title="20"><span class="co"># Visualize the correlations</span></a>
<a class="sourceLine" id="cb1-21" title="21"><span class="kw">library</span>(ggplot2)</a>
<a class="sourceLine" id="cb1-22" title="22"><span class="kw">library</span>(GGally)</a>
<a class="sourceLine" id="cb1-23" title="23"></a>
<a class="sourceLine" id="cb1-24" title="24">GGally<span class="op">::</span><span class="kw">ggpairs</span>(data) <span class="op">+</span></a>
<a class="sourceLine" id="cb1-25" title="25"><span class="st">  </span><span class="kw">theme_classic</span>()</a></code></pre></div>
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style="display: block; margin: auto;" />

<p>All methods give are highly correlated and give very similar results. That means that the method choice is not a drastic game changer and cannot be used to tweak the results too much.</p>
<h2 id="accuracy">Accuracy</h2>
<p>To test the accuracy of each methods, we will start by computing the <strong>direct <em>pd</em></strong> from a very dense distribution (with a large amount of observations). This will be our baseline, or “true” <em>pd</em>. Then, we will iteratively draw smaller samples from this parent distribution, and we will compute the <em>pd</em> with different methods. The closer this estimate is from the reference one, the better.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" title="1">data &lt;-<span class="st"> </span><span class="kw">data.frame</span>()</a>
<a class="sourceLine" id="cb2-2" title="2"><span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="dv">25</span>){</a>
<a class="sourceLine" id="cb2-3" title="3">  the_mean &lt;-<span class="st"> </span><span class="kw">runif</span>(<span class="dv">1</span>, <span class="dv">0</span>, <span class="dv">4</span>)</a>
<a class="sourceLine" id="cb2-4" title="4">  the_sd &lt;-<span class="st"> </span><span class="kw">abs</span>(<span class="kw">runif</span>(<span class="dv">1</span>, <span class="fl">0.5</span>, <span class="dv">4</span>))</a>
<a class="sourceLine" id="cb2-5" title="5">  parent_distribution &lt;-<span class="st"> </span><span class="kw">rnorm</span>(<span class="dv">100000</span>, the_mean, the_sd)</a>
<a class="sourceLine" id="cb2-6" title="6">  true_pd &lt;-<span class="st"> </span><span class="kw">pd</span>(parent_distribution)</a>
<a class="sourceLine" id="cb2-7" title="7">  </a>
<a class="sourceLine" id="cb2-8" title="8">  <span class="cf">for</span>(j <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="dv">25</span>){</a>
<a class="sourceLine" id="cb2-9" title="9">    sample_size &lt;-<span class="st"> </span><span class="kw">round</span>(<span class="kw">runif</span>(<span class="dv">1</span>, <span class="dv">25</span>, <span class="dv">5000</span>))</a>
<a class="sourceLine" id="cb2-10" title="10">    subsample &lt;-<span class="st"> </span><span class="kw">sample</span>(parent_distribution, sample_size)</a>
<a class="sourceLine" id="cb2-11" title="11">    data &lt;-<span class="st"> </span><span class="kw">rbind</span>(data,</a>
<a class="sourceLine" id="cb2-12" title="12">      <span class="kw">data.frame</span>(<span class="st">&quot;sample_size&quot;</span> =<span class="st"> </span>sample_size, </a>
<a class="sourceLine" id="cb2-13" title="13">                 <span class="st">&quot;true&quot;</span> =<span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-14" title="14">                 <span class="st">&quot;direct&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample) <span class="op">-</span><span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-15" title="15">                 <span class="st">&quot;kernel&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample, <span class="dt">method=</span><span class="st">&quot;kernel&quot;</span>)<span class="op">-</span><span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-16" title="16">                 <span class="st">&quot;logspline&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample, <span class="dt">method=</span><span class="st">&quot;logspline&quot;</span>) <span class="op">-</span><span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-17" title="17">                 <span class="st">&quot;KernSmooth&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample, <span class="dt">method=</span><span class="st">&quot;KernSmooth&quot;</span>) <span class="op">-</span><span class="st"> </span>true_pd</a>
<a class="sourceLine" id="cb2-18" title="18">                 ))</a>
<a class="sourceLine" id="cb2-19" title="19">  }</a>
<a class="sourceLine" id="cb2-20" title="20">}</a>
<a class="sourceLine" id="cb2-21" title="21">data &lt;-<span class="st"> </span><span class="kw">as.data.frame</span>(<span class="kw">sapply</span>(data, as.numeric))</a></code></pre></div>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb3-1" title="1"><span class="kw">library</span>(tidyr)</a>
<a class="sourceLine" id="cb3-2" title="2"><span class="kw">library</span>(dplyr)</a>
<a class="sourceLine" id="cb3-3" title="3"></a>
<a class="sourceLine" id="cb3-4" title="4">data <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb3-5" title="5"><span class="st">  </span>tidyr<span class="op">::</span><span class="kw">gather</span>(Method, Distance, <span class="op">-</span>sample_size, <span class="op">-</span>true) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb3-6" title="6"><span class="st">  </span><span class="kw">ggplot</span>(<span class="kw">aes</span>(<span class="dt">x=</span>sample_size, <span class="dt">y =</span> Distance, <span class="dt">color =</span> Method, <span class="dt">fill=</span> Method)) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-7" title="7"><span class="st">  </span><span class="kw">geom_point</span>(<span class="dt">alpha=</span><span class="fl">0.3</span>, <span class="dt">stroke=</span><span class="dv">0</span>, <span class="dt">shape=</span><span class="dv">16</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-8" title="8"><span class="st">  </span><span class="kw">geom_smooth</span>(<span class="dt">alpha=</span><span class="fl">0.2</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-9" title="9"><span class="st">  </span><span class="kw">geom_hline</span>(<span class="dt">yintercept=</span><span class="dv">0</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-10" title="10"><span class="st">  </span><span class="kw">theme_classic</span>() <span class="op">+</span></a>
<a class="sourceLine" id="cb3-11" title="11"><span class="st">  </span><span class="kw">xlab</span>(<span class="st">&quot;</span><span class="ch">\n</span><span class="st">Distribution Size&quot;</span>)</a></code></pre></div>
<img 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" 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<p>The “Kernel” based density methods seems to consistently underestimate the <em>pd</em>. Interestingly, the “direct” method appears as being the more reliable, even in the case of small number of posterior draws.</p>

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