If you’ve ever run a one-way analysis of variance (ANOVA), you’re familiar with post-hoc tests. The ANOVA omnibus test only tells you whether any groups differ in their means. But if you want to explore which specific group mean is different from which, you need to follow up with a post-hoc test. (more…)
When you need to compare a numeric outcome for two groups, what analysis do you think of first? Chances are, it’s the independent samples t-test. But that’s not the only, or always, the best option. In many situations, the Mann-Whitney U test is a better option.
The non-parametric Mann-Whitney U test is also called the Mann-Whitney-Wilcoxon test, or the Wilcoxon rank sum test. Non-parametric means that the hypothesis it’s testing is not about the parameter of a particular distribution.
It is part of a subgroup of non-parametric tests that are rank based. That means that the specific values of the outcomes are not important, only their order. In other words, we will be ranking the outcomes.
Like the t-test, this analysis tests whether two independent groups have similar typical outcomes. You can use it with numeric data, but unlike the t-test, it also works with ordinal data. Like the t-test, it is designed for comparisons, and not for estimation or prediction.
The biggest difference from the t-test is that it does not compare means. The Mann-Whitney U test determines whether a random observation from one group tends to be higher (or lower) than a random observation from the other group. Imagine choosing two observations, one from each group, over and over again. This test will determine whether one group is more likely to have the higher values.
It has many advantages: It is a straightforward comparison of means. There are versions for similar and different variances in the two groups. Many people are familiar with it.
There are not a lot of statistical methods designed just to analyze ordinal variables.
But that doesn’t mean that you’re stuck with few options. There are more than you’d think.
Some are better than others, but it depends on the situation and research questions.
Here are five options when your dependent variable is ordinal.