Effect size

In this chapter, we focused on statistical significance—the methods employed by statisticians to ensure a difference is discovered, which cannot be easily explained as chance variation. We must always remember that finding a significant effect isn't the same as finding a large effect. With very large samples, even a tiny difference in sample means will count as significant. To get a better sense of whether our discovery is both significant and important, we should state the effect size as well.

Cohen's d

Cohen's d is an adjustment that can be applied to see whether the difference we have observed is not just statistically significant, but actually large. Like the Bonferroni correction, the adjustment is a straightforward one:

Here, S_ab is the pooled standard deviation (not the pooled standard error) of the samples. It can be calculated in a way similar to the pooled standard error:

(defn pooled-standard-deviation [a b]
  (i/sqrt (+ (i/sq (standard-deviation a))
             (i/sq...