It can be difficult to interpret the test outcome when there are several mean differences. An F-ratio can indicate that there is a significant difference but it does not necessarily tell where. This is where the post hoc test comes in and is necessary when rejecting the null hypothesis because it can “determine exactly which mean differences are significant and which are not” (Gravetter et al., 2021, pg. 416). One example provided of an ANOVA test done is comparing three strategies used to find which is best for test prep. Three mean differences are calculated but the researcher is not sure which differences between each mean are significant. The researcher could then use Tukey’s HSD test to compare two treatments at a time and identify the value the shows the minimum difference needed for there to be a significant difference.
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