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What is a Post Hoc Test in Statistics?


A post hoc test in statistics means a test that is conducted after some test for significance (like ANOVA) has been carried out for more than two populations.

In the post hoc test, we consider populations two at a time to understand where the statistically significant difference is truly coming from.

Let us understand this by means of an example. Suppose you want to test the effect of five different teaching methods on the marks obtained by students in a standardized test.

We use the one-way ANOVA technique for this. If the null hypothesis is accepted and there is no difference between any of the five teaching methods then we are done.

But if the null hypothesis is rejected then we conclude that there is a difference between the five teaching methods. In such a case we are interested in knowing things like: Are the 1st and 2nd methods different?

Is the difference between the 3rd and the 4th test statistically significant?  These kinds of questions can be answered by doing pairwise testing for equality of means using T-test.

Examples of Post Hoc Tests:

By far the most famous example of a post hoc test is the Tukey test. This test is conducted after the one-way ANOVA procedure to test for pairwise differences of means as explained in the above example.

Other examples of post hoc tests that are applied after the ANOVA procedure are Scheffe’s test and Fisher’s LSD test.

Scheffe’s test is used to compare all pairs of means simultaneously. Fisher’s LSD test tells us the lowest significant value of the difference between the two means.

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