The assumptions that went into the derivation see, for example,the books at this link. The better ones will help you: https://www.amazon.com/s?k=Multiple+statistical+comparisons&i=stripbooks&ref=nb_sb_noss
Best, David Booth
Tukey’s test was developed in reaction to the LSD test and studies have
shown the procedure accurately maintains alpha levels at their intended values as long as statistical model assumptions are met (i.e., normality, homogeneity, independence). Tukey’s HSD was designed for a situation with equal sample sizes per group, but can be adapted to unequal sample sizes as well
Other post hoc procedures. A number of other post hoc procedures are available. There is aTukey-Kramer procedure designed for the situation in which n-sizes are not equal. Brown-Forsythe’s post hoc procedure is a modification of the Scheffe test for situations withheterogeneity of variance. Duncan’s Multiple Range test and the Newman-Keuls test providedifferent critical difference values for particular comparisons of means depending on how adjacentthe means are. Both tests have been criticized for not providing sufficient protection against alpha
slippage and should probably be avoided. Further information on these tests and related issues incontrast or multiple comparison tests is available from Kirk (1982)
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