GeneralizedpValues and Confidence Intervals for Variance Components: Applications to Army Test and Evaluation

Abstract

Various mixed models that are relevant for analyzing Army test data are described, along with several hypothesis testing and interval estimation problems. The problems come up in the context of investigating gun tube accuracy of an M1 Series tank; in particular, for the study of tube-to-tube dispersion. Factors that affect tube-to-tube variability might include the tanks, ammunition lot, ammunition temperature, firing occasions, and so on. Some of these are fixed factors, and others are random factors. The inference problems that arise in the study of tube-to-tube dispersion are somewhat different from those usually encountered in typical ANOVA situations. A unified approach to solving these problems is presented using the concepts of generalized p values and generalized confidence intervals. The performance of the resulting tests and confidence intervals is numerically investigated and is found to be quite satisfactory. Analysis of some Army test data is presented to illustrate the results.

Generalized p-Values and Generalized Confidence Intervals for Variance Components in General Random Effect Model with Balanced Data

“…Moreover, we investigate the statistical properties of the resulting tests from analytical perspective. As a result, we extend the corresponding work of Zhou and Mathew [2] , Webb and Wilkerson [3] , and Mathew and Webb [4] . In Section 4, we present simulation studies on the type I error probability and power of the proposed test in different situations.…”

“…On the other hand, Mathew and Webb [4] computed confidence intervals for the difference σ α − σ γ and the difference σ 2 α + σ 2 τ − σ 2 γ + σ 2 δ using generalized confidence intervals introduced by Weerahandi [6] . The derivation of these exact tests and confidence intervals has a common feature, that is, they are based on the sums of squares in the analysis of variance decomposition.…”

On the exact interval estimation for the difference in paired areas under the ROC curves

“…McNally et al [16] provide a set of mutually independent GPQs for the variances and covariance of a binormal distribution. Also see Mathew and Webb [24]. We can extend their results to the problem of covariance matrices of two independent binormal distributions.…”

Coverage of generalized confidence intervals

“…Generalized procedures have been successfully applied to several problems of practical importance. The areas of applications include comparison of means, testing and estimation of functions of parameters of normal and related distributions (Weerahandi,(2)(3)(4)(5), Krishnamoorthy and Mathew [6], Johnson and Weerahandi [7], Gamage, Mathew and Weerahandi [8]); testing fixed effects and variance components in repeated measures and mixed effects ANOVA models (Zhou and Mathew [9], Gamage and Weerahandi [10], Chiang [11], Krishnamoorthy and Mathew [6], Weerahandi [5], Mathew and Webb [12], Arendacka [13]); interlaboratory testing (Iyer, Wang and Mathew [14]); bioequivalence (McNally, Iyer and Mathew [15]); growth curve modeling (Weerahandi and Berger [16], Lin and Lee [17]); reliability and system engineering (Roy and Mathew [18], Tian and Cappelleri [19], Mathew, Kurian and Sebastian [20]); process control (Burdick, Borror and Montgomery [21], Mathew, Kurian and Sebastian [22]); environmental health (Krishnamoorthy, Mathew and Ramachandran [23]) and many others. The simulation studies in Johnson and Weerahandi [7], Weerahandi [4,5] Zhou and Mathew [9], Gamage and Weerahandi [10], among others have demonstrated the success of the generalized procedure in many problems where the classical approach fails to yield adequate confidence intervals.…”