﻿ The Bonferroni method

# The Bonferroni method

## How the Bonferroni test works

The Bonferroni method is a simple method for correcting for multiple comparisons. It can be used to correct any set of P values for multiple comparisons, and is not restricted to use as a followup test to ANOVA.

It works like this:

 1 Compute a P value for each comparison. Do no corrections for multiple comparisons when you do this calculation.
 2 Define the familywise significance threshold. Often this value is kept set to the traditional value of 0.05.
 3 Divide the value you chose in step 2 by the number of comparisons you are making in this family of comparisons. If you use the traditional 0.05 definition of significance, and are making 20 comparisons, then the new threshold is 0.05/20, or 0.0025.
 4 Call each comparison "statistically significant" if the P value from step 1 is less than or equal to the value computed in step 3. Otherwise, declare that comparison to not be statistically significant.

The advantages of this method are that it is simple to understand and is very versatile. When you are making only a few comparisons at once, the method works pretty well. If you are making lots of comparisons, the power of this method is low.

## Bonferroni tests in Prism

Prism can perform Bonferroni multiple comparisons tests as part of several analyses:

 • Following one-way ANOVA. This makes sense when you are comparing selected pairs of means, with the selection based on experimental design. Prism also lets you choose Bonferroni tests when comparing every mean with every other mean. We don't recommend this. Instead, choose theTukey test if you want to compute confidence intervals for every comparison or the Holm-Šídák test if you don't.
 • Following two-way ANOVA. If you have three or more columns, and wish to compare means within each row (or three or more rows, and wish to compare means within each column), the situation is much like one-way ANOVA. The Bonferroni test is offered because it is easy to understand, but we don't recommend it. If you enter data into two columns, and wish to compare the two values at each row, then we recommend the Bonferroni method, because it can compute confidence intervals for each comparison. The alternative is the Holm-Šídák method, which has more power, but doesn't compute confidence intervals.
 • As part of the new analysis to perform many t tests at once.