Statistics and Its Interface
Volume 5 (2012)
Type I error for a chi-square test when the response probability changes during a trial
Pages: 471 – 478
Chi-square test is a commonly used method for testing null hypothesis of no difference between treatment groups in a binary response in a randomized clinical trial. The Type I error is considered well controlled with a homogeneous population. In this article, we investigate the type I error of the chi-square test when the underlying response probability changes in the middle of a trial. In particular, we derive the asymptotic properties of the chi-square test under such an assumption and show that the type I error of the chi-square test is well controlled. Therefore, the chi-square test is still valid under change in response probability. Additionally, we present the computation of the actual type I error and some numerical results in an example to illustrate impact on Type I error by a change in response probability.
response probability, Cochran-Mantel-Haenzsel test, asymptotic property