Fig. 4

After conversion to a one-sided metric, the confidence intervals for the Task Score (and M-Score) become asymmetric. a) A simulated distribution of n = 10,000 Z-scores drawn from the standard Normal distribution (μ = 0, σ = 1). The cumulative density function (CDF) is plotted as a thick black line. Lower and upper bounds of the confidence interval (±1 for simplicity) are plotted in thin black lines. b) Conversion of the Z-Task Score to the true Task Score causes the CDF of a) to compress to the right, such that all values below zero become positive (thick black line). A Task Score of 1 has ~ 68.3% of the area of the curve underneath it, comparable to the area underneath ±1 of the standard Normal CDF. Upper and lower bounds of the confidence interval are plotted as thin black lines. The confidence interval is now asymmetric. c) The distance between the upper bound (UB) of the confidence interval to the Task Score grows more slowly than the distance between the lower bound (LB) of the confidence interval and the Task Score (thin black lines). The distance from the Z-Task Score to both the UB and the LB asymptotes to ±1, which corresponds to that of the original Z-Task Score in panel a