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

In the example, if a seventh treatment condition were included and the population mean for the seventh condition were very different from the other six population means, an analysis of variance would be likely to reject the omnibus null hypothesis. So far, so good, since the omnibus null hypothesis is false. However, the probability of a Type I error in one or more of the 15 t-tests computed among the six treatments with equal population means is about 0.10. Therefore, the LSD method provides only minimal protection against a high EER.

Homogeneity of variance is typically assumed for Fisher's LSD procedure. Therefore, MSE, the estimate of variance, is based on all the data, not just on the data for the two groups being compared. In order to make the relationship between Fisher's LSD and other methods of computing pairwise comparisons clear, the formula for the studentized t (ts) rather then the usual formula for t is used. This makes no difference in the outcome since, for Fisher's LSD procedure, the critical value of t is computed as if their were only two means in the experiment, a situation in which t and ts result in identical probability values. although ts will be 1.414 times t, the critical value of ts will also be 1.414 times the critical value of t. It makes no difference in the results.