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If you are trying to find confidence intervals, how does $\alpha$ for Tukey and Bonferroni differ? I understand that for Bonferroni the $\alpha$ is divided by the number of groups; however, does the $\alpha$ change when using Tukey?

The Pointer
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rabito
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1 Answers1

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The Tukey honest significant difference test keeps the desired family-wise error rate (FWER) at the desired value $\alpha$ by adjusting the distribution against which test statistics are compared. Instead of comparing test statistics against a t-distribution, the comparisons are against a Studentized range distribution that takes into account the number of pairwise comparisons being made.

The Bonferroni correction, in contrast, uses standard t-tests and then adjusts $\alpha$ for the individual tests to correct for multiple comparisons. See this page for discussion and links on when each of these approaches might be preferred. (Don't forget that the Holm modification to the Bonferroni correction provides the same FWER control with potentially greater power.)

EdM
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  • Yes, you can find the implicit $\alpha$ for the Tukey comparisons by equating the Tukey critical value (chosen as the one that multiplies the s.e. of the estimated parameter) to $t_{1-\alpha/2}$, then solving for $\alpha$. The resulting value will not be as small as the Bonferroni $\alpha/k$. – BigBendRegion May 26 '21 at 21:12