Testing for imbalance of covariates in controlled experiments
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TL;DR
Results of a controlled experiment are often adjusted for covariates found by a preliminary test to differ significantly between the treatment and control groups because the resulting test's true significance level is lower than the nominal level.
Abstract
Results of a controlled experiment are often adjusted for covariates found by a preliminary test to differ significantly between the treatment and control groups. The resulting test's true significance level is lower than the nominal level. Greater power can be achieved by always adjusting for a covariate that is highly correlated with the response regardless of its distribution between groups.