What is the Dunn-Bonferroni test?

The Dunn-Bonferroni post-hoc test is a statistical procedure used to compare multiple pairs of means (averages) in a group of data. It is often used after conducting a statistical test that compares means, such as an analysis of variance (ANOVA). The purpose of the Dunn-Bonferroni test is to identify which pairs of means are significantly different from each other.

The Dunn-Bonferroni test works by adjusting the alpha level (the level of statistical significance) to account for the number of pairs of means being compared. This is necessary because the more pairs of means that are compared, the greater the chance that a difference between means will be found simply by chance. By adjusting the alpha level, the Dunn-Bonferroni test helps to control for this problem, known as the "multiple comparisons problem."

How to perform a Dunn-Bonferroni test?

To use the Dunn-Bonferroni test, you need to have data that are organized into groups and have at least two groups with at least two measurements in each group. You would then run an ANOVA to test for significant differences between the groups. If the ANOVA indicates that there are significant differences between the groups, you can use the Dunn-Bonferroni test to identify which pairs of means are significantly different from each other.

1. Open the menu "Statistics" and click on "Test variables"
2. Select a Numeric variable
3. Select a List variable. This variable should be composed of at least 3 modalities
4. Open the panel "Compare values of ... (ANOVA)"
5. If the p-value of the test is below the significance threshold (usually p<0.05), the Dunn-Bonferroni test is performed automatically

The Dunn-Bonferroni test is not performed, why?

There are several reasons why the Dunn-Bonferroni test would not be performed:

1. The p-value of the ANOVA is not below the significance threshold (p>0.05). In this case, it is not recommended to perform a Dunn-Bonferroni test
2. An ANOVA has not been performed because the conditions were not met. For example, a Kruskal-Wallis test may have been performed instead of an ANOVA. In this case, the post-hoc test is usually a non-parametric test like the Nemenyi's method.
3. The variables you have chosen are not appropriate for an ANOVA. Indeed, 2 variables are required for an ANOVA: a Numeric variable and a List variable with at least 3 modalities
4. You do not have enough data to perform these kinds of tests