Figure 3 shows PP-plots for the simulations in which T and M are correlated via A (upper part), via C (middle part) or via E (lower part). In these plots, the p-values observed in the simulations are plotted against the nominal p-values. The observed p-value for each χdiff2-value observed in the 2000 simulations, is calculated as the proportion of the remaining 1999 χdiff2-values that is equal to or larger than this specific χdiff2-value. The nominal p-value for each χdiff2-value observed in the 2000 simulations, is obtained by reference to the χ2(1)-distribution. Deviations from the 45° line show whether the use of the regular χ2(1) test would result in conservative (above the line) or liberal (below the line) decision. The figures also show the percentage of hits calculated across the 2000 simulations. Given α = .05, the percentage of hits is expected to be close to 5%. Note that the standard error of the ML estimator of the p-value in the simulations is calculated as sqrt(p * (1 − p)/N), where p denotes the percentage of significant tests observed in the
