On the Computation of the Distribution for the Analysis of Means

Abstract

We discuss the accuracy of the computation and present a fortran program to compute the cumulative distribution function (CDF) for the analysis of means (ANOM).     

Simultaneous Logit-Based Confidence Intervals for Odds Ratios in 2 × k Classification Tables with a Fixed Reference Level

In this article, we consider the problem of constructing simultaneous confidence intervals for odds ratios in 2 × k classification tables with a fixed reference level. We discuss six methods designed to control the familywise error rate and investigate these methods in terms of simultaneous coverage probability and mean interval length. We illustrate the importance and the implementation of these methods using two {\sc hiv} public health studies.     

Using the Fast Fourier Transform to Compute Multiple Comparisons With the Best and Subset Selection Critical Values

Multiple comparison methods are widely implemented in statistical packages and heavily used. To obtain the critical value of a multiple comparison method for a given confidence level, a double integral equation must be solved. Current computer implementations evaluate one double integral for each candidate critical value using Gaussian quadrature. Consequently, iterative refinement of the critical value can slow the response time enough to hamper interactive data analysis. However, for balanced designs, to obtain the critical value for multiple comparisons with the best, subset selection, and one-sided multiple comparison with a control, if one regards the inner integral as a function of the outer integration variable, then this function can be obtained by discrete convolution using the Fast Fourier Transform (FFT). Exploiting the fact that this function need not be re-evaluated during iterative refinement of the critical value, it is shown that the FFT method obtains critical values at least four times as accurate and two to five times as fast as the Gaussian quadrature method.     

Expanded confidence intervals

Confidence intervals for location parameters are expanded (in either direction) to some “crucial” points and the resulting increase in the confidence coefficient investigated.Particaular crucial points are chosen to illuminate some hypothesis testing problems.Special results are dervied for the normal distribution with estimated variance and, in particular, for the problem of classifiying treatments as better or worse than a control.For this problem the usual two-sided Dunnett procedure is seen to be inefficient.Suggestions are made for the use of already published tables for this problem.Mention is made of the use of expanded confidence intervals for all pairwise comparisons of treatments using an “honest ordering difference” rather than Tukey's “honest siginificant difference”.     

Detecting a change in variances

The likelihood ratio test for testing for a change in a sequence of variances of normal populations is derived. The alternative hypothesis considered is of a one-sided nature. For the test, the conservativeness of the Sidak bound is shown and the asymptotic version of the Sidak bound is also constructed. These bound are compared with the Bonferroni bound and the Worsley bound, using the Monte Carlo method. Finally Hsu's data of stock market returns is reanalysed, using the test.     

Supporting families with a mentally ill parent: European perspectives on interagency cooperation

This paper reports on the findings of a cross-country comparison of cooperation between services for community mental health and child protection in 11 states. The authors consider the implications of the findings for English practice. When children have a parent with mental health problems, they have needs over and above those of other children. Often these needs are met by the family, but this is not always possible. There are increasing numbers of these children, and they feature disproportionately in the case loads of child welfare professionals, health visitors and social workers. The cross-country comparisons demonstrate the ways in which differences in structures, resources, expectations and attitudes affect professional responses and the experiences of families. The findings provide information on several levels. A comparison of commonalities and differences highlights the problems that are shared across countries, and alternative ways of responding to them at ground level are discussed. The factors that facilitate a good outcome are analysed in relation to English practice and service structures. The research findings are relevant for British social welfare strategies, and the paper highlights the implications of the findings for policy and practice. Copyright © 2001 John Wiley & Sons, Ltd.     

Variance of the number of false discoveries

Summary.  In high throughput genomic work, a very large number d of hypotheses are tested based on n ≪ d data samples. The large number of tests necessitates an adjustment for false discoveries in which a true null hypothesis was rejected. The expected number of false discoveries is easy to obtain. Dependences between the hypothesis tests greatly affect the variance of the number of false discoveries. Assuming that the tests are independent gives an inadequate variance formula. The paper presents a variance formula that takes account of the correlations between test statistics. That formula involves O ( d ²) correlations, and so a naïve implementation has cost O ( nd ²). A method based on sampling pairs of tests allows the variance to be approximated at a cost that is independent of d .     

Multiple comparisons of several populations with more than one control with respectto scale parameter

In this paper, one-sided and two-sided test procedures for comparing several treatments with more than one control with respect to scale parameter are proposed. The proposed test procedures are inverted to obtain the associated simultaneous confidence intervals. The multiple comparisons of test treatments with the best control are also developed. The computation of the critical points, required to implement the proposed procedures, is discussed by taking the normal probability model. Applications of the proposed test procedures to two-parameter exponential probability model are also demonstrated.     

A Bayesian False Discovery Rate for Multiple Testing

Case-control studies of genetic polymorphisms and gene-environment interactions are reporting large numbers of statistically significant associations, many of which are likely to be spurious. This problem reflects the low prior probability that any one null hypothesis is false, and the large number of test results reported for a given study. In a Bayesian approach to the low prior probabilities, Wacholder et al. (2004) suggest supplementing the p-value for a hypothesis with its posterior probability given the study data. In a frequentist approach to the test multiplicity problem, Benjamini & Hochberg (1995) propose a hypothesis-rejection rule that provides greater statistical power by controlling the false discovery rate rather than the family-wise error rate controlled by the Bonferroni correction. This paper defines a Bayes false discovery rate and proposes a Bayes-based rejection rule for controlling it. The method, which combines the Bayesian approach of Wacholder et al. with the frequentist approach of Benjamini & Hochberg, is used to evaluate the associations reported in a case-control study of breast cancer risk and genetic polymorphisms of genes involved in the repair of double-strand DNA breaks.