= Joint conditional independence test for stratified contingency tables
{title2=$X^2_{\mathrm{joint}}=\sum_{k=1}^K X_k^2$}
For $K$ <independent> strata, each containing an $r\times c$ <contingency table>, test <independence> of the two table variables within every stratum. Under adequate expected counts and the usual <multinomial distribution> sampling assumptions, each stratum's <Pearson chi-squared statistic> has asymptotic <chi-squared distribution> with $(r-1)(c-1)$ <statistical degrees of freedom>. Their sum has asymptotic <chi-squared distribution> with $K(r-1)(c-1)$ <statistical degrees of freedom>, by the additivity of <independent> <chi-squared distributions>. This is a test of conditional <independence>, not of equality of a common effect across strata; the latter needs an <interaction contrast> or another specified homogeneity test.
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