Comparing Variances and Other Measures of Dispersion

Comparing Variances and Other Measures of Dispersion

Testing hypotheses about variance parameters arises in contexts where uniformity is important and also in relation to checking assumptions as a preliminary to analysis of variance (ANOVA), dose-response modeling, discriminant analysis and so forth. In contrast to procedures for tests on means, tests for variances derived assuming normality of the parent populations are highly nonrobust to nonno...

Inequalities Relating Maximal Moments to Other Measures of Dispersion

Let X; X 1 ; : : : ; X k be i.i.d. random variables, and for k 2 IN let D k (X) = E(X 1 _ _ X k+1) ? EX be the k-th centralized maximal moment. A sharp lower bound is given for D 1 (X) in terms of the L evy concentration Q l (X) = sup x2IR P (X 2 x; x + l]). This inequality, which is analogous to P. L evy's concentration-variance inequality, illustrates the fact that maximal moments are a gauge...

Dispersion measures and dispersive orderings

In this paper, the comparison of random variables according to the functionals of a general class of dispersion measures is characterized in terms of the dilation order. The Gini’s mean di¤erence is a particular member of this general class. In addition, a new and weaker order, called the second-order absolute Lorenz ordering, is introduced, and we judge random variables according to certain fu...

Comparing the Statistical Tests for Homogeneity of Variances

Comparing the Statistical Tests for Homogeneity of Variances by Zhiqiang Mu Testing the homogeneity of variances is an important problem in many applications since statistical methods of frequent use, such as ANOVA, assume equal variances for two or more groups of data. However, testing the equality of variances is a difficult problem due to the fact that many of the tests are not robust agains...

Measures of Central Tendency and Dispersion.