Pairwise comparisons (post hoc: Tukey, Games-Howell, Bonferroni)

The analysis of variance only says that at least two groups differ. Pairwise comparisons test each pair on its own and adjust the p values, because many comparisons together more easily "find" something by chance. Games-Howell (the default in Statable) does not need equal spread in the groups, Tukey assumes it. Bonferroni is strict and simple: each p times the number of pairs.

Example: Three doses: Games-Howell shows that 0.5 and 1 mg differ by 9.1 points (95% CI [5.7, 12.6], p < .001), and so do the other pairs.

Caution: The interval (CI) of the difference shows how precisely it is known. A pair without a clear difference does not mean "equal", only "no clear evidence". With many groups there are many pairs, and each difference is harder to detect.