Post Hoc Tests and Data Analyses

 A post hoc test is a statistical test used to determine if a pair of values are significantly different from each other after the primary analysis has been completed.

The term post hoc is a Latin phrase meaning after the event.

A common use of post hoc tests is the comparison of group means after an F-test in an ANOVA has revealed significant differences among the groups. The reason to test for differences after an overall test like ANOVA is to reduce the risk of finding a significant difference by chance. That is, if researchers perform a large number of tests on a sample, they may find one or more tests significant by chance.

There are many post hoc tests. Following are some examples of tests that compare the means of two groups.

Bonferroni Test

This is a popular test. By dividing the significance level by the number of comparisons, the risk of finding a significant difference by chance is reduced. This procedure is called the Bonferroni Correction.

Tukey's Honest Significant Difference Test (HSD)

The Tukey HSD is a commonly used test, which adjusts for the number of comparisons.

Scheffés Test

Scheffés Test is similar to the Tukey HSD but it is slightly more conservative.

More post hoc tests

Additional post hoc tests are available. I will list them so you can recognize the test as one that evaluates a pair of means for significant differences after an overall test (such as an ANOVA).

Duncan's New Multiple Range Test (MRT)

Dunn's Multiple Comparison Test

Fisher's Least Significant Difference (LSD)

Holm-Bonferroni Procedure


Rodger's Method

Dunnett's correction

Benjamin-Hochberg (BH) procedure

Cite this post

Sutton, G. (2022, July 24). Post hoc tests and data analyses. Assessment, Statistics, and Research. Retrieved from 

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