Mann-Whitney-Wilcoxon test: overview
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|One categorical with 2 independent groups|
|One categorical of ordinal level|
|Group 1 sample is a simple random sample (SRS) from population 1, group 2 sample is an independent SRS from population 2. That is, within and between groups, observations are independent of one another|
|Two different types of test statistics can be used; both will result in the same test outcome. The first is the Wilcoxon rank sum statistic $W$:
Note: we could just as well base W and U on group 2. This would only 'flip' the right and left sided alternative hypotheses.
|Sampling distribution of $W$ and of $U$ if H0 were true|
Sampling distribution of $W$:
Sampling distribution of $U$:
For small samples, the exact distribution of $W$ or $U$ should be used.Note: the formula for the standard deviations $\sigma_W$ and $\sigma_U$ is more complicated if ties are present in the data.
|For large samples, the table for standard normal probabilities can be used:|
|If no ties in the data: two sided Mann-Whitney-Wilcoxon test is equivalent to Kruskal-Wallis test with an independent variable with 2 levels ($I = 2$)|
|Do men tend to score higher on social economic status than women?|