Familywise Error Rate - Example

Example

Consider a randomized clinical trial for a new antidepressant drug using three groups:

• Existing drug
• New drug
• Placebo

In such a design, the researcher might be interested in whether depressive symptoms (measured, for example, by a Beck Depression Inventory score) decreased to a greater extent for those using the new drug compared to the old drug. Further, one might be interested in whether any side effects (e.g., hypersomnia, decreased sex drive, and dry mouth) were observed. In such a case, two families would likely be identified:

1. Effect of drug on depressive symptoms
2. Occurrence of any side effects.

The researcher would assign an acceptable Type I error rate, (usually 0.05) to each family, and control for family-wise error using appropriate multiple comparison procedures:

• For the first family, effect of antidepressant on depressive symptoms, pairwise comparisons among groups might be jointly controlled using techniques such as Tukey's range test. Bonferroni correction might also suffice here since there are only three tests (three comparisons of depressive symptoms).
• In terms of the side effect profile, since we have three comparisons for each side effect, allowing each side effect its own alpha would result in a 37% chance of making at least one Type I error (i.e.,(1 - (0.95)^9 = 1 - 0.63 = 0.37). Having a total of 9 hypotheses, the Bonferroni correction might be too conservative in this case; a more powerful tool such as Tukey's range test or the Holm-Bonferroni method will probably be more suitable: for example, the researcher may divide by three (0.05/3 = 0.0167) and allocate .0167 to each side effect multiple comparison procedure. In the case of Tukey's range test, the critical value of q, the studentized range statistic, would thus be based on an value of 0.0167.