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In R, we can use the following options for POST HOC, with Bonferroni P value

summary(glht(fit, linfct=mcp(variable="Tukey")),test=adjusted("Bonferroni"))

Based on my understanding the Bonferroni correction is alpha divided by the number of comparisons. It means we can use

summary(glht(fit, linfct=mcp(variable="Tukey")),test=adjusted("none"))

and compare the nonadjusted p value with alpha/number of test.

Now I was wondering how the first function adjusts the values as for correction we have to divide the alpha to the number of the test? Also are the two ways of analysis provide the same result?

Jeremy Miles
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user178953
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  • I think an appropriate answer would be the Bonferroni adjusted p-value equals 1 - (1 - p) ^ n_tests. It is as it is since alpha divided by the number of comparisons is just an approximation of the Bernoulli trials. – Alexey Burnakov Oct 27 '17 at 16:32
  • @AlexeyBurnakov That's Šidák adjustment – Firebug Oct 27 '17 at 18:41
  • Isn't it the same procedure as the Bonferroni one? – Alexey Burnakov Oct 27 '17 at 19:33
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    @AlexeyBurnakov It's not. Bonferroni procedure is the approximation you mentioned, which results in $p_\text{ADJ}= n \cdot p$ – Firebug Nov 01 '17 at 12:37
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    @Firebug, thank you, I have read about it. They are VERY close and differ in only that Bonferroni is usually approximated as n*p or alpha/n. Interesting information, thanks. – Alexey Burnakov Nov 01 '17 at 12:43

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