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I am wondering why max-t methods use the maximum of the t-values to generate the distribution. Does this not make it overly conservative compared to other methods, since the critical value will be decided by the 0.05 quantile of only the maximum of the generated sample? This question also encompasses the analog of the minimum p-value estimation techniques.

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Math is your friend:

$P_{null}$(Make at least one type I error)

=$P_{null}$(any p-values less than the critical)

=$P_{null}$(min p-values less than the critical)

=$F_{minP}$(critical)

Clearly you can see why you need to compare your p-values with the critical value from the min P distribution. I'll not be surprised if the minP and sidak correction methods give you the same result when the data are independent.

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