Testing the Equality of Dependent Variances

The likelihood ratio test for testing equality of vgE;2 correlated variables is developed. In general, evaluation of the test statistic involves the iterative optimization of a likelihood function with 1 + v(v – 1)/2 parameters. The explicit form of the test statistic is derived in the bivariate case, and an iterative algorithm for determining the maximum likelihood estimates is suggested. A limited Monte Carlo study determines the behavior of the proposed procedure under the null hypothesis and variety of parameter values.     

A genetic and spatial Bayesian analysis of mastitis resistance

A nationwide health card recording system for dairy cattle was introduced in Norway in 1975 (the Norwegian Cattle Health Services). The data base holds information on mastitis occurrences on an individual cow basis. A reduction in mastitis frequency across the population is desired, and for this purpose risk factors are investigated. In this paper a Bayesian proportional hazards model is used for modelling the time to first veterinary treatment of clinical mastitis, including both genetic and environmental covariates. Sire effects were modelled as shared random components, and veterinary district was included as an environmental effect with prior spatial smoothing. A non-informative smoothing prior was assumed for the baseline hazard, and Markov chain Monte Carlo methods (MCMC) were used for inference. We propose a new measure of quality for sires, in terms of their posterior probability of being among the, say 10% best sires. The probability is an easily interpretable measure that can be directly used to rank sires. Estimating these complex probabilities is straightforward in an MCMC setting. The results indicate considerable differences between sires with regards to their daughters disease resistance. A regional effect was also discovered with the lowest risk of disease in the south-eastern parts of Norway.     

On the Comparison of Umbrella Pattern Treatment Means with a Control Mean

This paper is concerned with comparing several increasing dose levels (treatments) with a zero dose control when the prior information about the umbrella pattern treatment means is available. The problem of testing whether there is at least one treatment which is better than the control is considered. Multiple test procedures are then proposed for deciding treatments (if any) which are better than the control. Some approximate criticial values of the proposed tests are reported. The results of a Monte Carlo power study are presented.     

Exact Simultaneous Comparisons with Control in an r × c Contingency Table

Let categorical data coming from a control group and (r - 1) treated groups be given in an r × c contingency table. A simultaneous test procedure of the (r - 1) hypotheses that the probabilities of all c categories do not differ between the i-th treated group and the control is derived. For small tables and small cell frequencies it is exactly performed by generation of all tables having the given marginal sums. If 2 categories or 2 groups only are given the asymptotic distribution of the test statistic is known; otherwise its distribution may be simulated if the computational expenditure of performing an exact test is too large. By means of a Monte Carlo study it is shown that this method meets its level more reliably and that it has a better power than others.     

Properties of the multiallelic trend test

Disease genes can be mapped on the basis of associations between genetic markers and disease status, with the case-control design having the advantage of not requiring individuals from different generations. When the marker loci have multiple alleles, there has been debate on whether the power of tests for association increases or decreases. We show here that the multiple-allele version of Armitage's trend test has increased power over the two-allele version under the requirement of equifrequent alleles, but not in general. The trend test has the advantage of remaining valid even when the sampled population is not in Hardy-Weinberg equilibrium. A departure from Hardy-Weinberg means that association tests depend on gametic and nongametic linkage disequilibrium between marker and disease loci, and we illustrate the magnitude of these effects with simulated data.     

Robust Umbrella Tests for a Generalized Behrens-Fisher Problem

This paper is concerned with testing for umbrella alternatives in a k-sample location problem when the underlying populations have possibly different shapes. Following CHEN and WOLFE (1990b), rank-based modifications of the HETTMANSPERGER-NORTON (1987) tests are considered for both the settings where the peak of the umbrella is known and where it is unknown. The proposed procedures are exactly distribution-free when the continuous populations are identical with any shape. Moreover, the modified test for peak-known umbrella alternatives remains asymptotically distribution-free when the continuous populations are assumed to be symmetric, even if they differ in shapes. Comparative results of a Monte Carlo study are presented.