Understanding Tukey’s q & p

For a planned SINGLE comparison, the CI of \mu_2-\mu_1 can be interpreted as (M_2-M_1)\pm qt_{1-\frac{\alpha}{2},df}\times SE , in which SE=s\times \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}. The df and s should be defined according to the denominator of F.

For post hoc multiple comparisons, the CI of \mu_2-\mu_1 can still be interpreted as (M_2-M_1)\pm \frac{qtukey_{1-\alpha,nmeans,df}}{\sqrt{2}}\times SE , wherein nmeans indicates the number of sub-groups whose means are compared. Note that qtukey(...) and ptukey(...) is defined with a two-tailed probability while qt(...) and pt(...) with a single-tailed one.

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