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This paper discusses statistical techniques for the analysis of dichotomous data arising from a design in which the investigator randomly assigns each of two clusters of possibly varying size to interventions within strata. The problem addressed is that of assessing the statistical significance of the intervention effect over all strata. We propose a weighted paired t-test based on the empirical logistic transform for designs that randomize large aggregate clusters in each of several strata.
Donner et al. (1987) studied this question.