Chi-squared tests

Goodness of fit and contingency tables

Compare observed frequencies $O$ with those expected under $H_0$, $E$, using $X^2=\sum\frac{(O-E)^2}E$. Large values mean poor fit. Compare with $\chi^2_\nu$ where $\nu=$ number of classes $-1-$ parameters estimated, or $(r-1)(c-1)$ for a contingency table. Expected frequencies should be at least $5$.