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In paired randomized experiments units are grouped in pairs, often based on covariate information, with randomized assignment within the pairs. Average treatment effects are then estimated by averaging the within-pair differences in outcomes. Typically the unconditional variance of the average treatment effect estimator is estimated using the sample variance of the within-pair differences. Conditional on the covariates the variance may be substantially smaller. Here we propose a simple way ofdoi:10.2307/27917244 fatcat:xj5gsos6nvbydiuw6c6qihurqi