The two-stage δ-corrected Kolmogorov-Smirnov test

The delta-corrected Kolmogorov-Smirnov test has been shown to be uniformly more powerful than the classical Kolmogorov-Smirnov test for small to moderate sample sizes. However, the delta-corrected test consists of two tests, leading to a slight inflation of the experimentwise type I error rate. The critical values of the delta-corrected test are adjusted to take into account the two-stage nature of the test, ensuring an experimentwise error rate at the nominal level. A power study confirms that the resulting so-called two-stage delta-corrected test is uniformly more powerful than the classical Kolmogorov-Smirnov test, with power improvements of up to 46 percentage points.