Question

Why would Tukey's fixed range test NOT be an appropriate mean comparison test?

Answer 1

Tukey's range test, also known as the Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, is a single-step multiple comparison procedure and statistical test.

Assumption :-

The observations being tested are independent within and among the groups.

The groups associated with each mean in the test are normally distributed.

There is equal within-group variance across the groups associated with each mean in the test

The Tukey method however deals with all possible pairwise comparisons, while a the same time correcting for the increase in type 1 error that you would otherwise have when doing multiple contrasts.

This leads to Tukeys fixed range test not be an appropriate mean comparison test.