Dunn's test is a post-hoc statistical procedure used to make pairwise comparisons between groups after a Kruskal-Wallis test has indicated a significant difference between at least two groups.
Understanding Dunn's Test
After performing a Kruskal-Wallis test, which is a non-parametric alternative to the one-way ANOVA, you might find that there's a statistically significant difference amongst your groups. But the Kruskal-Wallis test doesn't tell you which groups are significantly different from each other. This is where Dunn's test comes into play.
Why Use Dunn's Test?
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Post-Hoc Analysis: Dunn's test is used to perform multiple pairwise comparisons after an omnibus test, like the Kruskal-Wallis test, finds an overall significant effect. As referenced, performing multiple comparisons without adjustment redefines the significance level, alpha (α).
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Non-Parametric Data: Dunn's test is designed for non-parametric data, meaning data that doesn't follow a normal distribution.
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Multiple Comparisons: It corrects for the increased risk of making a Type I error (false positive) that arises when performing multiple comparisons.
How Dunn's Test Works
Dunn's test compares each pair of groups and assesses whether their difference is statistically significant.
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Rank-Based Comparisons: Like the Kruskal-Wallis test, it uses the ranks of the data rather than the original values.
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Multiple Testing Correction: It applies adjustments, such as the Bonferroni correction, to control the overall family-wise error rate when testing multiple hypotheses.
- This helps ensure that the chance of incorrectly rejecting the null hypothesis (that two groups are not significantly different) is not inflated.
Practical Insights
- When to Apply: Always use Dunn's test after a significant result in a Kruskal-Wallis test. This will allow you to identify which specific groups differ from one another.
- Alternatives: While Dunn’s test is a popular choice, other non-parametric post-hoc tests exist for pairwise comparisons after a Kruskal-Wallis test, such as the Conover-Iman test.
Example
Let's say you are comparing the customer satisfaction scores of three different versions of a website. Your satisfaction data is not normally distributed, and the Kruskal-Wallis test showed a significant difference. To determine which versions specifically vary in scores, you would use Dunn’s test.
Summary
| Feature | Description |
|---|---|
| Type | Post-hoc test |
| Usage | Used after a significant Kruskal-Wallis test to make pairwise comparisons. |
| Data Type | Non-parametric data |
| Primary Function | Controls the family-wise error rate when doing multiple pairwise comparisons. |
| Key Characteristic | Rank based comparisons and provides a method to evaluate individual significant differences between groups. |
| Objective | Identifies which groups differ significantly from each other. |
