Lord's paradox refers to a situation in statistics that arises in the context of analyzing the effects of a treatment or an intervention when heterogeneous treatment effects are present. Specifically, it highlights a contradiction that can occur when assessing the impact of a treatment on a group using summary statistics compared to individual-level data. The paradox is named after the statistician Frederick Lord, who demonstrated that when calculating the average treatment effect on a given population, one can arrive at misleading conclusions if the analysis does not account for individual differences.
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