Chisquared test for the relationship between two categorical variables  overview
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Chisquared test for the relationship between two categorical variables 


Independent /column variable  
One categorical with $I$ independent groups ($I \geqslant 2$)  
Dependent /row variable  
One categorical with $J$ independent groups ($J \geqslant 2$)  
Null hypothesis  
H_{0}: 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:
 
Alternative hypothesis  
H_{1}: 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:
 
Assumptions  
 
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.  
Sampling distribution of $X^2$ if H_{0} were true  
Approximately the chisquared distribution with $(I  1) \times (J  1)$ degrees of freedom  
Significant?  
 
Example context  
Is there an association between economic class and gender? Is the distribution of economic class different between men and women?  
SPSS  
Analyze > Descriptive Statistics > Crosstabs...
 
Jamovi  
Frequencies > Independent Samples  $\chi^2$ test of association
 
Practice questions  