Most studies of high-dimensional phenotypes focus on assessing differences in mean levels (location) of the phenotype by exposure, e.g. epigenome-wide association studies of DNA methylation at CpG sites. However, identifying effects on the variability (scale) of these outcomes, and combining tests of mean and variability (location-and-scale), could provide additional insights into biological mechanisms. Here, we review variability tests, specifically an extended (for continuous exposures) version of the Brown-Forsythe test, and develop a novel joint location-and-scale score test for both categorical and continuous exposures (JLSsc). The Brown-Forsythe test and JLSsc performed well in comparison to alternative approaches in simulations. These approaches identified >7500 CpG sites that were associated with either mean or variability with gender or gestational age in cord blood methylation in ARIES (Accessible Resource for Integrated Studies). The Brown-Forsythe test and JLSsc are robust tests that can be used to detect associations not solely driven by a mean effect. ### Competing Interest Statement James Staley became a full-time employee of UCB while this manuscript was being written.
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