What is the purpose of a tukey test?
Why can't we compare all the posible pairs of group means using the two-sample t-test?
The Tukey HSD test looks at the probability of making one or more Type I errors (rejecting a true null hypothesis) in comparing population means and is sensitive to treatment errors. Could we use 2-sample t-tests? No. Multiple t-tests increase the probability of making a Type I error.
I hope this helps.
The purpose of a Tukey test is to compare the means of multiple groups simultaneously in order to determine if there is a significant difference between any pair of groups. It is a post-hoc test typically used in analysis of variance (ANOVA) to account for multiple comparisons.
When we have more than two groups, comparing all possible pairs using the two-sample t-test would result in an increased chance of making a Type I error (rejecting the null hypothesis when it is true). The more comparisons we make, the higher the probability of obtaining a significant result by chance alone, even if there is no true difference between the groups.
The Tukey test, on the other hand, controls the family-wise error rate (or overall Type I error rate) by adjusting the significance level for each pairwise comparison. It takes into account the number of groups and the sample size to determine the critical value for each comparison. By using this method, the Tukey test allows for a fair and accurate comparison between groups, avoiding the problem of multiple comparisons.