The free parameter k is the value that generates the best fit with the hyperbolic discounting function for each individual. In the present study, k described much of the variance in discounting (mean ± SEM R2 values = 0.73 ± 0.024). The k values were skewed right (skew = 5.28), so they were normalized with a natural-log transform to allow parametric testing (skew = 0.28). An Experiment × Sex × Alcohol Preference univariate ANOVA on natural-log transformed k values revealed a main effect of Alcohol Preference F(1,60) = 12.14, p = 0.001, but no main effects of Sex (p = 0.55), Experiment (p = 0.09), or interactions with these factors (ps > 0.39). A follow-up t-test between the high and low drinking phenotypes revealed a difference by Alcohol Preference t(66) = 3.41, p = 0.001. Mean ln k values were −0.520 and −1.091, which correspond to k values of 0.594 and 0.336 for high and low-alcohol preferring, respectively. Larger values of k represent steeper discounting, i.e., greater impulsivity.
