Statistics and Its Interface

Volume 5 (2012)

Number 4

Type I error for a chi-square test when the response probability changes during a trial

Pages: 471 – 478



Feifang Hu (Department of Statistics, University of Virginia, Charlottesville, Va., U.S.A.)

Jiandong Lu (Clinical Biostatistics, Janssen Research and Development, Springhouse, Pennsylvania, U.S.A.)

Feng Tai (Department of Biostatistics, University of Minnesota, Minneapolis, Minn., U.S.A.)


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

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