Tukey honestly significant difference test

n. A test of differences between group means in an analysis of variance which takes into account the increase in obtaining a false positive result when making multiple comparisons. The Tukey test is calculated as

$ Dmin = t(\sqrt{MSError} / \sqrt{SampleSize} ) $

where \(Dmin\) is the minimal difference between group means needed to infer a population difference, \(t\) is the critical value of Student's t statistic with appropriate degrees of freedom and alpha level, MSError is the mean square of the within-group errors, and Sample Size is the sample size per cell. It is more conservative than Fisher's LSD test but less conservative than the Scheffe procedure.