Tukey’s HSD for ANCOVA

Following a significant ANCOVA, we can use the usual approach to Tukey’s HSD and the Tukey-Kramer follow up test, as described in Unplanned Comparisons, except that we need to modify the value of MSW as follows:

Modified MSW

where SSB(x) and SSW(x) are the sum of squares between and within the covariance groups (based on one-way Anova on the covariate data), i.e.

SST(x)SSB(x)SSW(x)

The standard error can then be calculated as

Standard Error ANCOVA

if all the group sizes are equal (to m). This is the Tukey HSD test. If the group sizes are unequal, the standard error is (i.e. the Tukey-Kramer test)

Standard error unequal samples

Example 1: Repeat Example 1 of Contrasts for ANCOVA using the Tukey-Kramer test.

The results are shown in Figure 1.

Tukey-Kramer for ANCOVA

Figure 1 – Tukey-Kramer for ANCOVA

Note that some of the formulas in column Q reference cells in Figure 1 of ANOVA Approach to ANCOVA, although the formula for MSW in cell Q9 references Figure 3 of ANOVA Approach to ANCOVA.

See ANCOVA Analysis Tools for information about how to conduct Tukey’s HSD or Tukey-Kramer using the Real Statistics ANCOVA data analysis tool.

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