All Pairwise Comparisons among Means: Fisher's LSD
Procedure (2 of 2)
Next section: Tukey's HSD
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 (t
s)
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 t
s result in identical
probability values. although t
s
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.
Next section: Tukey's HSD