Mantel–Haenszel pooled odds ratio (${\widehat{\mathrm{OR}}}_{\mathrm{MH}}=\frac{{\sum }_i{a}_i{d}_i/n_i}{{\sum }_i{b}_i{c}_i/n_i}$)

For independent two-by-two tables with counts $a_i,b_i,c_i,d_i$ and total $n_i$, the Mantel–Haenszel pooled odds ratio is the displayed ratio of sums. When all $b_i{c}_i>0$, it is also the weighted arithmetic mean of study odds ratios with weights $b_i{c}_i/n_i$. These differ from inverse estimated variance weights for log odds ratios. Both constructions can represent a fixed-effect meta-analysis, but they should not be silently interchanged when interpreting a supplied plot.