Honestly Significant Difference (HSD) Test

When an analysis of variance (ANOVA) gives a significant result, this indicates that at least one group differs from the other groups. Yet, the omnibus test does not inform on the pattern of differences between the means. To analyze the pattern of difference between means, the ANOVA is often followed by specific comparisons, and the most commonly used involves comparing two means (the so-called pairwise comparisons).

An easy and frequently used pairwise comparison technique was developed by John Tukey under the name of the honestly significant difference (HSD) test. The main idea of the HSD is to compute the honestly significant difference (i.e., the HSD) between two means using a statistical distribution defined by Student and called the q distribution. This distribution gives the exact sampling ...