Chi-squared test for the relationship between two categorical variables - overview
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Chi-squared test for the relationship between two categorical variables | Multilevel multinomial logistic regression |
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Independent /column variable | Independent variables | |
One categorical with $I$ independent groups ($I \geqslant 2$) | 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 /row variable | Dependent variable | |
One categorical with $J$ independent groups ($J \geqslant 2$) | One categorical with $J$ independent groups ($J \geqslant 2$) | |
Null hypothesis | THIS TABLE IS YET TO BE COMPLETED | |
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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Alternative hypothesis | n.a. | |
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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Assumptions | n.a. | |
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Test statistic | n.a. | |
$X^2 = \sum{\frac{(\mbox{observed cell count} - \mbox{expected cell count})^2}{\mbox{expected cell count}}}$
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. | - | |
Sampling distribution of $X^2$ if H0 were true | n.a. | |
Approximately the chi-squared distribution with $(I - 1) \times (J - 1)$ degrees of freedom | - | |
Significant? | n.a. | |
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Example context | n.a. | |
Is there an association between economic class and gender? Is the distribution of economic class different between men and women? | - | |
SPSS | n.a. | |
Analyze > Descriptive Statistics > Crosstabs...
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Jamovi | n.a. | |
Frequencies > Independent Samples - $\chi^2$ test of association
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Practice questions | Practice questions | |