Examples of probability plots for the test statistic t(x) obtained in Monte-Carlo simulations for sample sizes N = 10², 10³, and 10⁴ (top to bottom). In each diagram the solid curve shows, as a function of the critical value C, the probability that t exceeds C under the null hypothesis (r = 0). The dashed curves show the probabilities under the alternative hypothesis (r > 0) for the r-values indicated in the legend. In the bottom diagram the dotted curve gives, for comparison, the expected distribution of for a one-sample K–S test in which F is the true distribution (without adjusting μ and σ); see footnote 3.