A post-hoc test is an additional analysis conducted after an ANOVA if the null hypothesis is rejected, indicating that at least one group's mean differs significantly from others. It is necessary because ANOVA only tells us that there is a difference somewhere between the groups but does not specify which groups differ. Post-hoc tests, such as Turkey's HSD or Bonferroni correction, compare all the pairs of group means to identify where these specific differences lie. For example, if you were a researcher studying the effectiveness of three teaching methods, Method A, Method B, and Method C on a student's test scores, an ANOVA might reveal a significant difference among methods. Running a post-hoc test would then allow you to pinpoint whether Method outruns B, C, or both. This assures that the conclusions are precise, detailing methods that significantly impact student performance