Statistical Power with Group Mean as the Unit of Analysis

In 1940 Lindquist presented a discussion of an analysis of variance using the group mean as the unit of analysis. Unfortunately, most modern writers on statistical methodology have ignored this important topic and some of the best text-book book writers make the error of using the individual as the unit of analysis when the group mean would be more appropriate. The reluctance to use group mean as the unit of analysis is due in part to the belief that the resultant drop in the number of observations per treatment greatly reduces the probability of detecting a treatment effect. This concern is put in perspective in this paper and equations are presented to facilitate power estimates when the group mean is the unit of analysis.