1. ## Tukey's HSD formulas

I am analyzing real-world temperature data which came out significantly different in the ANOVAs. There seem to be two formulas for the Tukey's HSD test floating around, and I am trying to find out the difference. Here are the two versions I have found, both taken from lectures posted online by instructors at different universities:

HSD = q(α,k,N-k)(√(MSw/n))
HSD = q(√(MSw/n)

The first test appears to give extremely conservative results when applied to my data. The middle term is the one I'm having trouble with. Why the addition of alpha, k, and N-k? My best guess is that it is supposed to correct for differences in sample size. However, wouldn't using the second formula with the harmonic mean for n correct for differences in sample sizes between groups?

Any help would be appreciated!

2. ## Re: Tukey's HSD formulas

These both are equal. Actually the terms which you see after q , these are in subscripts and are used to find the values of q statistic from table, just like when you use chi square and write alpha and degress of freedom value within parenthesis in subscript.

3. ## Re: Tukey's HSD formulas

Thank you for clearing that up! I think the lecture I found the formula in had a few errors in calculation that threw me off.

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