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Matched-group randomization improves power but is not as effective as covariate-constrained randomization. For model-based analysis, adjusting for fewer covariates than were used in a restricted randomization process under any design can produce non-nominal type I error rates and reductions in power. Where comparisons to two-arm cluster trials are possible, the performance of the methods is qualitatively very similar.Figurines of women with obesity or who are pregnant ("Venus figurines" from Upper Paleolithic Europe rank among the earli