37 – Statistical Process Control and Quality Assurance
Do Preliminary Tests Validate the Main Tests?
Xuwen Zhu
University of Alabama
Subhabrata Chakraborti
University of Alabama
Yinaze Dovoedo
University of North Alabama
In practice, it is common to precede the main test of interest with one or more preliminary tests (pretests). Depending on the results of the preliminary test, one decides what main test to perform. Thus the type I error rate of the main test is actually a "conditional type I error" and there arise questions about whether or not the main test maintains the specified nominal level. In this paper, we revisit the literature on the methodology that is used to estimate the conditional type I error rate. Results are then extended to estimating and deriving the conditional type I error rate in some other situations. The work uses extensive simulations and some exact derivations.