Kruskal-Wallis test - overview
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Kruskal-Wallis test |
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Independent/grouping variable | |
One categorical with $I$ independent groups ($I \geqslant 2$) | |
Dependent variable | |
One of ordinal level | |
Null hypothesis | |
If the dependent variable is measured on a continuous scale and the shape of the distribution of the dependent variable is the same in all $I$ populations:
Formulation 1:
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Alternative hypothesis | |
If the dependent variable is measured on a continuous scale and the shape of the distribution of the dependent variable is the same in all $I$ populations:
Formulation 1:
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Assumptions | |
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Test statistic | |
$H = \dfrac{12}{N (N + 1)} \sum \dfrac{R^2_i}{n_i} - 3(N + 1)$ | |
Sampling distribution of $H$ if H0 were true | |
For large samples, approximately the chi-squared distribution with $I - 1$ degrees of freedom. For small samples, the exact distribution of $H$ should be used. | |
Significant? | |
For large samples, the table with critical $X^2$ values can be used. If we denote $X^2 = H$:
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Example context | |
Do people from different religions tend to score differently on social economic status? | |
SPSS | |
Analyze > Nonparametric Tests > Legacy Dialogs > K Independent Samples...
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Jamovi | |
ANOVA > One Way ANOVA - Kruskal-Wallis
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Practice questions | |