A1516
Title: Confirming kappa-cover: A hypothesis test for the overlap of normal distributions based on generalized p-values
Authors: Vera Hofer - University of Graz (Austria) [presenting]
Gerhard Goessler - University of Graz (Austria)
Hans Manner - University of Graz (Austria)
Walter Goessler - University of Graz (Austria)
Abstract: A common task in various industrial applications is to compare quality characteristics of two products in terms of their distributions, DT and DR. Simply comparing their means and variances is often too restrictive, especially when a certain scope of DT is allowed within the range given by DR. At the same time rather strict control of extreme realizations of DT is often demanded, i.e., DR must cover DT such that it ensures the test product being safe regarding the quality characteristic under investigation. This is reflected by the concept of kappa-cover. The problems associated with developing a suitable test for confirming kappa-cover are discussed. Challenges arise from the multiple testing problem of comparing two pairs of quantiles simultaneously, as well as from the formulation of the hypotheses. From a consumer safety perspective, it is preferable to formulate H0 as the assertion of missing kappa-cover. However, this raises the question of how to handle distributional equality, which formally falls under H0 (i.e., no kappa-cover) even though DR evidently covers DT in this situation. The proposed two-stage test procedure ensures that the chosen significance level is asymptotically maintained in this multiple testing problem. According to simulation results, the test procedure controls the type I error in the expected manner, i.e., as the sample size increases, the size and power of the test improve.
