The first is a randomization approach while the second assumes that the study is a sample of a population. Here, we study the second approach and consider the simplest cases of two treatments with a continuous response and with a binary response. Koch's second approach will be compared with the classical ANCOVA for a continuous response. From this relationship we demonstrate that Koch's method cannot preserve the probability of the type I error. Simulations with continuous responses as well as with binary outcomes confirm the aforementioned theoretical result on the performance of Koch's method under the null hypothesis of no treatment effect. However, this poses only a problem for relatively small to moderate sample sizes. Further, as specified in the original paper of Koch et al., the first approach does preserve the type I error for any sample size, as the P-values can be reported in an exact manner. Finally, we propose a correction factor for Koch's test statistic that better preserves the type I error.
- Covariate adjustment
- Non-parametric methods