Are Your Covariates Under Control? How Normalization Can Re-introduce Covariate Effects

Many statistical tests rely on the assumption that the residuals of a model are normally distributed. Rank-based inverse normal transformation (INT) of the dependent variable is one of the most popular approaches to satisfy the normality assumption. Studies regularly adjust for covariates and then normalize the residuals. This study investigated the effect of regressing covariates against the dependent variable and then applying rank-based INT to the residuals. The correlation between the dependent variable and covariates at each stage of processing was assessed. An alternative approach was tested of applying rank-based INT to the dependent variable before regressing covariates was tested. Analyses based on both simulated and real data examples demonstrated that applying rank-based INT to the dependent variable residuals after regressing out covariates re-introduces a linear correlation between the dependent variable and covariates in almost all situations. This will increase type-1 errors and reduce power. Our proposed alternative approach, where rank-based INT was applied prior to controlling for covariate effects, gave residuals that were normally distributed and linearly uncorrelated with covariates. This approach is therefore recommended.