Mann-Whitney-Wilcoxon test - overview
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Mann-Whitney-Wilcoxon test | Multivariate multilevel analysis |
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Independent/grouping variable | Independent variables | |
One categorical with 2 independent groups | One or more quantitative of interval or ratio level and/or one or more categorical with independent groups, transformed into code variables, plus at least one random factor | |
Dependent variable | Dependent variables | |
One of ordinal level | Two or more quantitative of interval or ratio level | |
Null hypothesis | THIS TABLE IS YET TO BE COMPLETED | |
If the dependent variable is measured on a continuous scale and the shape of the distribution of the dependent variable is the same in both populations:
Formulation 1:
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Alternative hypothesis | n.a. | |
If the dependent variable is measured on a continuous scale and the shape of the distribution of the dependent variable is the same in both populations:
Formulation 1:
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Assumptions | n.a. | |
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Test statistic | n.a. | |
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. Also, tables with critical values for $U$ are often based on the smaller of $U$ for group 1 and for group 2. | - | |
Sampling distribution of $W$ and of $U$ if H0 were true | n.a. | |
Sampling distribution of $W$:
Sampling distribution of $U$: For small samples, the exact distribution of $W$ or $U$ should be used. Note: if ties are present in the data, the formula for the standard deviations $\sigma_W$ and $\sigma_U$ is more complicated. | - | |
Significant? | n.a. | |
For large samples, the table for standard normal probabilities can be used: Two sided:
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Equivalent to | n.a. | |
If there are no ties in the data, the two sided Mann-Whitney-Wilcoxon test is equivalent to the Kruskal-Wallis test with an independent variable with 2 levels ($I$ = 2). | - | |
Example context | n.a. | |
Do men tend to score higher on social economic status than women? | - | |
SPSS | n.a. | |
Analyze > Nonparametric Tests > Legacy Dialogs > 2 Independent Samples...
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Jamovi | n.a. | |
T-Tests > Independent Samples T-Test
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Practice questions | Practice questions | |