What is a post hoc test used for in statistical analysis?

A post hoc test is utilized in statistical analysis specifically after conducting an ANOVA (Analysis of Variance) to determine whether there are significant differences between the means of various groups. When an ANOVA indicates that at least one group mean is different from the others, it does not specify exactly which means differ from each other. A post hoc test is then employed to perform pairwise comparisons between group means while controlling for the overall Type I error rate.

This makes it a crucial step in understanding the specific relationships between groups after finding an overall effect in an ANOVA. Common post hoc tests include Tukey's HSD, Bonferroni correction, and Scheffé’s test, among others, each designed to handle multiple comparisons appropriately.

The other options do not accurately describe the purpose of a post hoc test. Initial hypothesis formulation is part of the study design phase and not specifically related to post hoc testing. Estimating effect sizes can be done during or after analysis, but it is not the primary function of a post hoc test. Similarly, calculating correlation coefficients involves assessing the relationship between two continuous variables but is fundamentally different from examining differences among group means following an ANOVA.