Which post hoc test is commonly used to examine differences between independent groups without increasing the multiplicity problem?

The Tukey HSD (Honestly Significant Difference) test is a widely used post hoc test specifically designed for comparing all possible pairs of means after an ANOVA when there are three or more independent groups. It is particularly effective in controlling the type I error rate that can arise from making multiple comparisons.

One of the key strengths of the Tukey HSD test is that it adjusts for the number of comparisons being made without overly conservative adjustments, which helps maintain a balance between detecting true differences and controlling for false positives. This characteristic makes it ideal for situations where researchers want to identify significant differences while avoiding the multiplicity issue inherent in performing multiple tests.

In contrast, while the Scheffe test is also used for post hoc analysis, it is more conservative and less powerful than Tukey HSD, which means it can miss some significant differences. The Bonferroni correction, on the other hand, adjusts the significance level downward to control for type I error but can be overly stringent, particularly when the number of comparisons increases. The Wilcoxon test is a non-parametric test typically used for comparing two related samples or matched samples, rather than for independent group comparisons, making it less relevant in this context.

Thus, the Tukey HSD