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When conducting an ANOVA test, multiple treatment conditions or populations are sampled and compared. This allows for a comprehensive analysis of the difference between the sample means to detect significant treatment effects. However, when there are several treatment conditions it is not possible to tell which treatment conditions produced the most differences. Therefore, post-hoc tests are used to provide more information.

One of the post-hoc tests available is the Honestly Significant Difference (HSD) tests. The HSD difference is computed using a q value, and the MS within and n to produce the HSD value (Gravetter et al., 2021). The differences between each sample mean are then calculated and compared with the HSD; any difference that is higher in value than the HSD is considered significant (Gravetter et al., 2021).

Another post-hoc test that can be used is the Scheffe test, which uses the same F-ratio and is considered to be the safest test to use post-hoc because it has the smallest risk of Type I error (Gravetter et al., 2021). The Scheffe test simply compares the mean difference between each pair of samples but uses the degrees of freedom for the entire set of samples. This essentially makes it more difficult to get a significant effect, therefore any significant F-ratio value is considered valid.