MANCOVA - overview
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MANCOVA | Chi-squared test for the relationship between two categorical variables |
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Independent variables | Independent /column variable | |
One or more categorical with independent groups, and one or more quantitative control variables of interval or ratio level (covariates) | One categorical with $I$ independent groups ($I \geqslant 2$) | |
Dependent variables | Dependent /row variable | |
Two or more quantitative of interval or ratio level | One categorical with $J$ independent groups ($J \geqslant 2$) | |
THIS TABLE IS YET TO BE COMPLETED | Null hypothesis | |
- | H0: there is no association between the row and column variable More precisely, if there are $I$ independent random samples of size $n_i$ from each of $I$ populations, defined by the independent variable:
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n.a. | Alternative hypothesis | |
- | H1: there is an association between the row and column variable More precisely, if there are $I$ independent random samples of size $n_i$ from each of $I$ populations, defined by the independent variable:
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n.a. | Assumptions | |
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n.a. | Test statistic | |
- | $X^2 = \sum{\frac{(\mbox{observed cell count} - \mbox{expected cell count})^2}{\mbox{expected cell count}}}$
Here for each cell, the expected cell count = $\dfrac{\mbox{row total} \times \mbox{column total}}{\mbox{total sample size}}$, the observed cell count is the observed sample count in that same cell, and the sum is over all $I \times J$ cells. | |
n.a. | Sampling distribution of $X^2$ if H0 were true | |
- | Approximately the chi-squared distribution with $(I - 1) \times (J - 1)$ degrees of freedom | |
n.a. | Significant? | |
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n.a. | Example context | |
- | Is there an association between economic class and gender? Is the distribution of economic class different between men and women? | |
n.a. | SPSS | |
- | Analyze > Descriptive Statistics > Crosstabs...
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n.a. | Jamovi | |
- | Frequencies > Independent Samples - $\chi^2$ test of association
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Practice questions | Practice questions | |