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    <p>You'll have to read about each multiple testing correction technique, whether it be <code>False Discovery Rate (FDR)</code> or <code>Family-Wise Error Rate (FWER</code>). (Thanks to @thelatemail for pointing out to expand the abbreviations).</p> <p>Bonferroni correction controls the <code>FWER</code> by setting the significance level <code>alpha</code> to <code>alpha/n</code> where <code>n</code> is the number of hypotheses tested in a typical multiple comparison (here <code>n=3</code>).</p> <p>Let's say you are testing at 5% alpha. Meaning if your p-value is &lt; 0.05, then you reject your NULL. For <code>n=3</code>, then, for Bonferroni correction, you could then divide <code>alpha</code> by 3 = 0.05/3 ~ 0.0167 and then check if your p-values are &lt; 0.0167. </p> <p>Equivalently (which is directly evident), instead of checking <code>pval &lt; alpha/n</code>, you could take the <code>n</code> to the other side <code>pval * n &lt; alpha</code>. So that the <code>alpha</code> remains the same value. So, your p-values get multiplied by <code>3</code> and then would be checked if they are &lt; alpha = 0.05 for example.</p> <p>Therefore, the output you obtain is the <code>FWER controlled p-value</code> and if this is &lt; alpha (5% say), then you would reject the NULL, else you'd accept the NULL hypothesis.</p> <p>For each tests, there are different procedures to control the false-positives due to multiple testing. Wikipedia might be a good start point to learn about other tests as to how they correct for controlling false-positives.</p> <p>However, your output of <code>p.adjust</code>, gives in general <code>multiple-testing corrected p-value</code>. In case of Bonferroni, it is FWER controlled p-value. In case of BH method, it is FDR corrected p-value (or also otherwise called q-value).</p> <p>Hope this helps a bit.</p>
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    1. POMultiple testing methods
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    1. COFor those not in the know, FDR = False Discovery Rate
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    2. CO@thelatemail, Thanks for filling the gaps! Feel free to edit the post to add the info.
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