The Bonferroni correction

We therefore require an alternative approach while conducting multiple tests that will account for an increased probability of discovering a significant effect through repeated trials. The Bonferroni correction is a very simple adjustment that ensures we are unlikely to make Type I errors. It does this by adjusting the alpha for our tests.

The adjustment is a simple one—the Bonferroni correction simply divides our desired alpha by the number of tests we are performing. For example, if we had k site designs to test and an experimental alpha of 0.05, the Bonferroni correction is expressed as:

This is a safe way to mitigate the increased probability of making a Type I error in multiple testing. The following example is identical to ex-2-22, except the alpha value has been divided by the number of groups:

(defn ex-2-23 []
  (let [data (->> (load-data "multiple-sites.tsv")
                  (:rows)
                  (group-by :site)
                  (map-vals (partial...