Final answer:
If Mauchy's assumption is violated at a significance level of <0.05, the Greenhouse-Geisser correction is the appropriate method to use.
Step-by-step explanation:
If Mauchy's assumption of sphericity is violated at a significance level of 0.05, the Greenhouse-Geisser correction can be used to adjust the degrees of freedom for the F-distribution, which helps in maintaining the Type I error rate.
The Bonferroni correction is used when conducting multiple pairwise comparisons to reduce the chance of Type I errors. Holm's method is a stepwise version of the Bonferroni correction. Tukey's HSD (Honestly Significant Difference) is another post-hoc test that is used to find means that are significantly different from each other after an ANOVA.