Comparing Treatment Means: A Compendium1

Abstract

The equality of the true average responses of several treatments (cultivars, insecticides, concentrations, temperatures, etc.) is usually tested statistically by means of the F-test or the analysis of variance. If the F-test rejects the hypothesis that the treatment means are all equal, it does not necessarily follow that these means are all unequal. The next stage in the data analysis is to determine which treatment means are different. Repeated application of the Student's t-test to all possible pairs of treatment means is usually discouraged, since this procedure gives a large probability of declaring one or more pairs of treatment means to be different, when they are in fact equal. Special techniques called multiple comparison procedures are available for this purpose.