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

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

where:

$o_{k} = \sum^n_{i=1} w_i I_{x=k}$,

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

$e_{k} = \frac{ \sum^n_{i=1} w_i}{s}$

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

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