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,

$e_{k}={\frac {\sum _{i=1}^{n}w_{i}}{s}}$

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

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