I am analysing data on levels of proteins in the brain, there are 4 groups, I did a one way anova followed by Fishers LSD. I also carried out individual unpaired ttests comparing each group to the control. For some of the groups I got a more significant p-value from the ttests than the Fishers LSD, which should I use?
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It is good to lay out the key underlying question and the principles involved in analytic choices. Without knowing your ultimate intentions I'd say that you are at risk for making choices not based on statistical principles, and recommend either sticking with the overall ANOVA result (which has a perfect multiplicity adjustment built-in) or use simultaneous confidence intervals that also build-in all possible multiplicity adjustments. – Frank Harrell Dec 21 '21 at 14:01
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@FrankHarrell Thanks for your reply! As a general principle would it be wrong to display a p value from a t-test and a p value from a Fishers LSD on the same graph? – Emma Dec 21 '21 at 14:34
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Not necessarily wrong, but somewhat arbitrary and confusing, not to mention emphasizing testing too much over estimation and interval estimation. There is no principle in frequentist statistics that leads to a logical choice of a unique multiplicity adjustment other than perhaps simultaneous confidence intervals (which are more concordant with the overall ANOVA F test). – Frank Harrell Dec 22 '21 at 13:53
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Great thanks for your help! @FrankHarrell – Emma Dec 23 '21 at 17:08