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Quantitative genetics theory predicts that X-chromosome dosage compensation (DC) will have a detectable effect on the amount of genetic and therefore phenotypic trait variances at associated loci in males and females. Here, we systematically examine the role of DC in humans in 20 complex traits in a sample of more than 450,000 individuals from the UK Biobank and 1600 gene expression traits from a sample of 2000 individuals as well as across-tissue gene expression from the GTEx resource. We find approximately twice as much X-linked genetic variation across the UK Biobank traits in males (mean h2SNP=0.63%) compared to females (mean h2SNP=0.30%), confirming the predicted DC effect. Our DC estimates for complex traits and gene expression are consistent with a small proportion of genes escaping X-inactivation in a trait- and tissue-dependent manner. Finally, we highlight examples of biologically relevant X-linked heterogeneity between the sexes that bias DC estimates if unaccounted for.