The effects of the violations normality and homogeneity variances assumptions on power one-way ANOVA F-test is studied in this paper. Simulation experiments were conducted to compare parametric with non-parametric Kruskal‒Wallis (KW) test normal/non-normal, equal/unequal scenarios sample group means. Each these 184 simulation was replicated N = 1000 times obtained for both F KW tests. Shapiro‒W...

The quality of estimation of variance components depends on the design used as well as on the unknown values of the variance components. In this article, three designs are compared, namely, the balanced, staggered, and inverted nested designs for the three-fold nested random model. The comparison is based on the so-called quantile dispersion graphs, introduced in Khuri (1997), using analysis of...

In the numerous forms of analysis of variance (ANOVA) discussed in previous chapters, variance components were estimated by equating observed mean squares to expressions describing their expected values, these being functions of the variance components. ANOVA has the nice feature that the estimators for the variance components are unbiased regardless of whether the data are normally distributed...

A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice of block size allows control over the tradeoff between test power and computation time. In this respect, the B-test family combines favorable properties of p...

The one-way random-effect ANOVA model is presented, and two simulated datasets are analyzed. and discussed from three points of view: (1) The standard ANOVA table, F test, and method-of-moments estimates of variance components, which can lead to negative estimates. (2) Maximum likelihood estimates of variance components. (3) Bayesian probability intervals for variance components based on flat p...

Andrew Gelman’s contribution shifts the focus of “Analysis of Variance” (ANOVA) from the limited sense in which it has been commonly used in classical statistics, as a method of testing, to the broader framework of estimation and inference. The term more commonly used in this sense, “variance components modeling,” also captures the same spirit. The essential idea is that of constructing distrib...

OBJECTIVES Three strength tests (compressive, three point flexure and biaxial) were performed on three glass ionomer (GI) restoratives to assess the most appropriate methodology in terms of validity and reliability. The influence of mixing induced variability on the data sets generated were eliminated by using encapsulated GIs. METHODS Specimen groups of 40 (eight batches of n=5) cylinders (6...