![]() Where \(Y_ $$Įntering the values that were found earlier into the equation yields the same intervals as was found from the TukeyHSD() output. \(q\) can be found similarly to the t-statistic: The test statistic used in Tukey’s test is denoted \(q\) and is essentially a modified t-statistic that corrects for multiple comparisons. Tukey’s test compares the means of all treatments to the mean of every other treatment and is considered the best available method in cases when confidence intervals are desired or if sample sizes are unequal ( Wikipedia). The test is known by several different names. One common and popular method of post-hoc analysis is Tukey’s Test. This step after analysis is referred to as ‘post-hoc analysis’ and is a major step in hypothesis testing. Although ANOVA is a powerful and useful parametric approach to analyzing approximately normally distributed data with more than two groups (referred to as ‘treatments’), it does not provide any deeper insights into patterns or comparisons between specific groups.Īfter a multivariate test, it is often desired to know more about the specific groups to find out if they are significantly different or similar. In a previous example, ANOVA (Analysis of Variance) was performed to test a hypothesis concerning more than two groups.
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