Three or more way ANOVA - overview
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Three or more way ANOVA | Kruskal-Wallis test |
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Independent/grouping variables | Independent/grouping variable | |
Three or more categorical with independent groups | One categorical with $I$ independent groups ($I \geqslant 2$) | |
Dependent variable | Dependent variable | |
One quantitative of interval or ratio level | One of ordinal level | |
THIS TABLE IS YET TO BE COMPLETED | 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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n.a. | 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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n.a. | Assumptions | |
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n.a. | Test statistic | |
- | $H = \dfrac{12}{N (N + 1)} \sum \dfrac{R^2_i}{n_i} - 3(N + 1)$ | |
n.a. | 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. | |
n.a. | Significant? | |
- | For large samples, the table with critical $X^2$ values can be used. If we denote $X^2 = H$:
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n.a. | Example context | |
- | Do people from different religions tend to score differently on social economic status? | |
n.a. | SPSS | |
- | Analyze > Nonparametric Tests > Legacy Dialogs > K Independent Samples...
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n.a. | Jamovi | |
- | ANOVA > One Way ANOVA - Kruskal-Wallis
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Practice questions | Practice questions | |