Tukey’s Honestly Significant Differences (also known as Tukey’s Whole Significant Differences). The test statistic is:
- and are the means of the two groups being compared and is the mean of the of groups,
- when applying the test to Repeated Measures, each respondent’s average is initially subtracted from their data and it is this corrected data that constitutes of ,
- is the number of observations in the th of groups,
- is the Calibrated Weight for the th observation in the group,
- is the Effective Sample Size for the group,
- for Repeated Measures and otherwise.
- is evaluated using a Tukey’s Studentized Range distribution with degrees of freedom for groups.
Circumstances when this test is applied
- Computing either:
- This test has been selected in the Statistical Assumptions setting of Multiple comparison correction > Column comparisons