A: ideal observer curve computed from the combined analysis of the simulated reaction-time and binary data. The horizontal line is 0.975. B: trial-by-trial comparison of the probability that the cognitive state at trial k (x axis) is greater than the cognitive state at trial j (y axis) <k, computed from the combined reaction-time and binary-data analysis, where k = 2,, 100 and j = 1,…, 99. Comparisons for which this probability is ≥0.95 are shown in red.