We used nonparametric Mann-Whitney tests for group comparisons (i.e., male/female, having/not having current AUD, having/not having current nicotine dependence, having/not having marijuana dependence) of the Internalizing Scale total score and report the generalized Mann-Whitney (θ) effect size measure, because the scales’ total scores were skewed to the right. Theta expresses the degree of overlap of the distributions of the two groups compared (θ’s theoretical range is 0 to 1). The range extremes (0 and 1) indicate no overlap between the distributions, while 0.5 indicates complete overlap. Under the homoscedastic and normal assumptions for each group, θ compares to Cohen’s d in the following way: θ = 0.65 is equivalent to d = 0.55, θ = 0.80 results in d = 1.19, and θ = 0.95 results in d = 2.33.56 We also used Spearman’s correlations (r) to characterize bivariate associations of continuous variables. All statistical tests were performed using all data available in each case, utilising SAS version 9.4,57 R,58 and FACTOR Version 10.7.01 ×64bits.59
