Past exam of the options I course of the University of Oxford / 2008 / O / O1 / i / Solution

For a two-way contingency table, Pearson's statistic isHere $O_{i+},O_{+j}$ are the observed margins and $N$ their grand total. Under the independence null, its usual large-sample reference distribution has $(r-1)(c-1)$ degrees of freedom for an $r$-by-$c$ table.