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<h1 id="reporting-guidelines">Reporting Guidelines</h1>
<ul>
<li><a href="#reporting-guidelines">Reporting Guidelines</a>
<ul>
<li><a href="#interpretation-rules-of-thumb">Interpretation Rules of Thumb</a></li>
<li><a href="#template-sentence">Template Sentence</a></li>
</ul></li>
</ul>
<p>These guidelines can be referred to by citing the package:</p>
<ul>
<li>Makowski, D. &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>
<h1 id="reporting-guidelines-1">Reporting Guidelines</h1>
<p>Based on the previous <a href="https://easystats.github.io/bayestestR/articles/indicesEstimationComparison.html"><strong>comparison of point-estimates</strong></a> and <a href="https://easystats.github.io/bayestestR/articles/indicesExistenceComparison.html"><strong>indices of effect existence</strong></a>, we can conclude that:</p>
<ul>
<li>For simple models and normally distributed posteriors, the <strong>MAP estimate</strong> seems to be more biased than the mean and the median of the posterior distribution.</li>
<li>Aside from being more robust, the <strong>median</strong> makes more sense than the <strong>mean</strong> in a probabilistic framework (<em>e.g.</em>, there is 50% chance that the true effect is either higher or lower than the median).</li>
<li>The <strong>traditional ROPE</strong> (using a 90% HDI) is not sensitive to delineate highly “significant” effects. The full ROPE (100% HDI) does not present the same flaw.</li>
<li>The <strong>Probability of Direction (<em>p</em>d)</strong> is the closest index to the frequentist <em>p</em> value.</li>
</ul>
<p>Thus, to minimally <strong>describe the posterior distribution</strong> of a parameter, we suggest reporting the <strong>median</strong> and the <strong>90% CI</strong> (using HDI rather than quantiles) for parameter characterisation and, in the context of null-hypothesis testing, the <strong>Probability of Direction (<em>p</em>d)</strong> for effect existence and, especially in the context of confirmatory analyses, the <strong>ROPE percentage (full)</strong> with an explicitly specified range for effect significance.</p>
<h2 id="interpretation-rules-of-thumb">Interpretation Rules of Thumb</h2>
<p><strong>The following thresholds are presented as landmarks only, and any use of such “labels” should be explicitly justified. Please consider with caution.</strong></p>
<ul>
<li><p><strong>Probability of Direction (<em>p</em>d)</strong>: In most cases, it seems that the <em>pd</em> corresponds to the frequentist one-sided <em>p</em> value through the formula <code>p value = (1-pd/100)</code> and to the two-sided <em>p</em> value (the most commonly reported) through the formula <code>p value = 2*(1-pd/100)</code>. Thus, a <code>pd</code> of <code>95%</code>, <code>97.5%</code> <code>99.5%</code> and <code>99.95%</code> corresponds approximately to a two-sided <em>p</em> value of respectively <code>.1</code>, <code>.05</code>, <code>.01</code> and <code>.001</code>. Thus, for convience, we recommend using the following reference values:</p>
<ul>
<li><em>p</em>d <strong>&lt;= 95%</strong> ~ <em>p</em> &gt; .1: uncertain</li>
<li><em>p</em>d <strong>&gt; 95%</strong> ~ <em>p</em> &lt; .1: possibly existing</li>
<li><em>p</em>d <strong>&gt; 97%</strong>: likely existing</li>
<li><em>p</em>d <strong>&gt; 99%</strong>: probably existing</li>
<li><em>p</em>d <strong>&gt; 99.9%</strong>: certainly existing</li>
</ul></li>
<li><p><strong>ROPE (full)</strong>: Extra caution is required as its interpretation highly depends on other parameters such as sample size and ROPE range.</p>
<ul>
<li><strong>&gt; 99%</strong> in ROPE: negligible (we can accept the null hypothesis)</li>
<li><strong>&gt; 97.5%</strong> in ROPE: probably negligible</li>
<li><strong>&lt;= 97.5%</strong> &amp; <strong>&gt;= 2.5%</strong> in ROPE: not significant</li>
<li><strong>&lt; 2.5%</strong> in ROPE: probably significant</li>
<li><strong>&lt; 1%</strong> in ROPE: significant (we can reject the null hypothesis)</li>
</ul></li>
</ul>
<p><em>Note: If you have any advice, opinion or such, we encourage you to let us know by opening an <a href="https://github.com/easystats/bayestestR/issues">discussion thread</a> or making a pull request.</em></p>
<h2 id="template-sentence">Template Sentence</h2>
<p>Based on these suggestions, a template sentence for minimal reporting of a parameter based on its posterior distribution could be:</p>
<ul>
<li>“the effect of <em>X</em> has a probability of <strong><em>p</em>d</strong> of being <em>negative</em> (Median = <em><strong>median</strong></em>, 90% CI [***…***, ***…***]) and can be considered as <em>significant</em> (<em><strong>ROPE</strong></em>% in ROPE).”</li>
</ul>

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