Chi-Square Test for Compatibility of K Counts

Tests the null hypothesis that all $s$ categories of a categorical variable, $x$, are the same size. The test statistic is

$X^2=\sum _{k=1}^s\frac{(o_{kj}-e_{kj}{)}^2}{e_{kj}}$

where:

$o_k=\sum _{i=1}^n{w}_i{I}_{x=k}$,

$w_i$ is the Calibrated Weight of the $i$th of $n$ observations,

$e_k=\frac{\sum _{i=1}^n{w}_i}{s}$

$p\approx \mathrm{Pr}({\chi }_{(s-1)}^2\ge X^2)$

See also

• ANOVA-Type Tests - Comparing Three or More Groups
• Planned ANOVA-Type Tests
• Second Order Rao-Scott Test of Independence of a Contingency Table