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

Newman-Keuls

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 https://statistics.suttong.com/2022/07/post-hoc-tests-and-data-analyses.html

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