Measures of effect size and correlation appropriate to nonparametric testing were calculated for each candidate cluster. The Common language effect size (CLES) indicates the probability of PAC being greater in someone randomly selected from the AUD group compared to someone randomly selected from the unaffected group. The rank biserial correlation coefficient, r, represents the magnitude and direction of the relationship between AUD diagnosis and ordinal dependent variable of ranked PAC strength. This coefficient has a range [−1,1], where a perfect positive relationship (r = 1) would be obtained if ranks from AUD group are all higher than those from the unaffected group. Conversely, a perfect negative relationship (r = −1) would result if all ranks from AUD group were lower than any from the unaffected group. In both cases, the rank distributions of the two groups are non-overlapping. A coefficient r = 0 indicates perfect overlap of the two rank distributions, i.e., where there are no differences between the distribution of ranks for AUD and unaffected groups.
