Lexis Ratio

Definition

The Lexis ratio is a statistic used to measure overdispersion for clustered data. $Q=\frac{{\sum }_{i=1}^k({\hat{p}}_i-\hat{p}{)}^2/(k-1)}{\hat{p}(1-\hat{p})/n}$ where ${\hat{p}}_i$ is sample proportion of the group $i$, $\hat{p}$ is total proportion, $k$ is the number of groups, and $n$ is the number of total trials.