Some Comments on “The Unit of Analysis: Group Means Versus Individual Observations”
Hopkins (1982) has criticized the use of means as the unit of analysis in situations where intact groups (e.g. classes) rather than individuals have been randomly assigned to various treatment conditions. Instead Hopkins advocates the use of certain ANOVA models which, insofar as tests for treatment effects are concerned, yield results that are equivalent to those that would be obtained if class means were employed as the unit of analysis. This paper points out that, because of the nonrobustness of the sample mean as an estimator of location, use of the class mean as the unit of analysis or of the ANOVA models advocated by Hopkins can lead to larger than necessary Type II error rates in tests of significance for treatment effects. This paper also shows how, in the nonnormal population situation, use of summary statistics other than the mean (e.g. members of the family of trimmed means) can lead to significant increases in the power of tests for treatment effects. It is also suggested here that the pooling options offered by Hopkins should be viewed with caution.