AbstractThe usual form of the Mantel–Haenszel test statistic assumes independent observations. This is inappropriate for data from a stratified multistage survey. Two alternative adjustments to the test statistic are developed to deal with this: (a) a modification of the effective sample size for each row of each table, using the design effects, extending a method proposed by Donald and Donner for familial aggregation studies; (b) a Taylor series approximation to the variance of the square root of the numerator of the Mantel‐Haenszel statistic. Both methods are evaluated by application to both simulated and real data. The two methods perform equally well, and offer a considerable improvement over the unadjusted test statistic when observations from the same cluster are highly correlated. A simplified adjustment is also considered, as is the need for correction to the variance of the odds ratio estimator.