All Pairwise Comparisons among Means: Fisher's LSD Procedure (1 of 2)

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An approach suggested by the statistician R. A. Fisher (called the "least significant difference method" or Fisher's LSD) is to first test the null hypothesis that all the population means are equal (the omnibus null hypothesis) with an analysis of variance. If the analysis of variance is not significant, then neither the omnibus null hypothesis nor any other null hypothesis about differences among means can be rejected. If the analysis of variance is significant, then each mean is compared with each other mean using a t-test. The advantage of this approach is that there is some control over the EER. If the omnibus null hypothesis is true, then the EER is equal to whatever significance level was used in the analysis of variance. In the example with the six groups of subjects given in the section on t-tests, if the 0.01 level were used in the analysis of variance, then the EER would be 0.01. The problem with this approach is that it can lead to a high EER if most population means are equal but one or two are different.