Permutation techniques for analyzing multi-response data from randomized block experiments

A class of permutation techniques is presented for the randomized block design. This class is specifically devised for analyses involving multivariate data. A numerical example illustrates an application based on multivariate data. Many well known techniques are special cases of this class. Among these special cases are (i) the permutation version of the classical univariate technique for randomized blocks which 1s associated with analysis of variance, (ii) the Friedman randomized block test, (iii) one-sample matched-pair tests, (iv) the Pearson correlation measure, and (v) the Spearman rank correlation and foot-rule measures. Furthermore, variations and multivariate versions among this class suggest a variety of new techniques which have not received any previous attention.     

The Ubiquity of Statistics

The use of biased estimation in data analysis and model building is discussed. A review of the theory of ridge regression and its relation to generalized inverse regression is presented along with the results of a simulation experiment and three examples of the use of ridge regression in practice. Comments on variable selection procedures, model validation, and ridge and generalized inverse regression computation procedures are included. The examples studied here show that when the predictor variables are highly correlated, ridge regression produces coefficients which predict and extrapolate better than least squares and is a safe procedure for selecting variables.     

A Note on Confidence Intervals for Proportions in Finite Populations

An exact confidence interval for the number or proportion of successes in a finite population is developed using the standard technique of inverting a family of tests. The resulting procedure is compared with two methods available in the sampling literature and is shown to be equivalent to one of the methods and superior to the other method.     

News about Members

In this article a natural extension of the beta-binomial distribution is developed. Forced binary choice situations are modeled such that each individual has a probability p of knowing the correct answer. (This probability is distributed f(p) across the population.) Hence each individual will guess at the correct answer with probability 1 – p. The observable random variable R, the total number of correct answers (both by knowing and guessing) out of k trials has a rather complicated distribution. However, when f(p) is distributed beta with parameters m and n, the distribution P(r; k, m, n) can be expressed in terms of the well-known Gaussian hypergeometric function. This distribution has implications for true-false tests, taste tests, and virtually every other forced binary choice situation.     

Tests for the Validity of the Assumption that the Underlying Distribution of Life is Pareto

This article considers the problem of testing the validity of the assumption that the underlying distribution of life is Pareto. For complete and censored samples, the relationship between the Pareto and the exponential distributions could be of vital importance to test for the validity of this assumption. For grouped uncensored data the classical Pearson χ² test based on the multinomial model can be used. Attention is confined in this article to handle grouped data with withdrawals within intervals. Graphical as well as analytical procedures will be presented. Maximum likelihood estimators for the parameters of the Pareto distribution based on grouped data will be derived.     

The Asymptotic Power Of Jonckheere-Type Tests For Ordered Alternatives

For the c -sample location problem with ordered alternatives, the test proposed by Barlow et al . (1972 p. 184) is an appropriate one under the model of normality. For non-normal data, however, there are rank tests which have higher power than the test of Barlow et al ., e.g. the Jonckheere test or so-called Jonckheere-type tests recently introduced and studied by Büning & Kössler (1996). In this paper the asymptotic power of the Jonckheere-type tests is computed by using results of Hájek (1968) which may be considered as extensions of the theorem of Chernoff & Savage (1958). Power studies via Monte Carlo simulation show that the asymptotic power values provide a good approximation to the finite ones even for moderate sample sizes.     

Generalizations of the δ-Corrected Kolmogorov-Smirnov Goodness-of-Fit Test

This paper generalizes the δ-corrected Kolmogorov–Smirnov (K–S) test into a family of tests, and investigates the behaviour of some of the members of the family, comparing them with the usual K–S test, as well as the δ-corrected K–S tests suggested by Harter et al . (1984) and Khamis (1990, 1992, 1993). These investigations and power studies suggest which tests are most powerful for which alternative hypotheses.     

Overcoming Confirmation Bias in Causal Attribution: A Case Study of Antibiotic Resistance Risks

When they do not use formal quantitative risk assessment methods, many scientists (like other people) make mistakes and exhibit biases in reasoning about causation, if‐then relations, and evidence. Decision‐related conclusions or causal explanations are reached prematurely based on narrative plausibility rather than adequate factual evidence. Then, confirming evidence is sought and emphasized, but disconfirming evidence is ignored or discounted. This tendency has serious implications for health‐related public policy discussions and decisions. We provide examples occurring in antimicrobial health risk assessments, including a case study of a recently reported positive relation between virginiamycin (VM) use in poultry and risk of resistance to VM‐like (streptogramin) antibiotics in humans. This finding has been used to argue that poultry consumption causes increased resistance risks, that serious health impacts may result, and therefore use of VM in poultry should be restricted. However, the original study compared healthy vegetarians to hospitalized poultry consumers. Our examination of the same data using conditional independence tests for potential causality reveals that poultry consumption acted as a surrogate for hospitalization in this study. After accounting for current hospitalization status, no evidence remains supporting a causal relationship between poultry consumption and increased streptogramin resistance. This example emphasizes both the importance and the practical possibility of analyzing and presenting quantitative risk information using data analysis techniques (such as Bayesian model averaging (BMA) and conditional independence tests) that are as free as possible from potential selection, confirmation, and modeling biases.     

Generalized orthogonal contrast tests for homogeneity of ordered means

Several procedures have been proposed for testing equality of ordered means. The best-known of these is the likelihood-ratio test introduced by Bartholomew, which possesses generally superior power characteristics to those of its competitors. Difficulties in implementing this test have led to the development of alternative approaches, such as tests based on single and multiple contrasts. Some recent approaches have utilized approximations to the polyhedral cone defining the restricted parameter space, including those of Akkerboom (circular cone) and Mudholkar & McDermott (orthant). This article proposes a class of tests based on an improved orthant approximation to the polyhedral cone. These tests may be viewed as generalizations of the orthogonal contrast test proposed by Mukerjee, Robertson & Wright. Studies of the power functions of several competing tests indicate that the generalized orthogonal contrast tests are effective alternatives to the likelihood-ratio test, especially when the latter is difficult to implement.     

Exact inference for multivariate ordered alternatives

In this paper we discuss three types of ordered alternatives ordered location, stochastic ordering and quadrant dependence. We prove that quadrant dependence is the more general among the three. Then we consider a conditional tests for the equality of c distributions against quadrant dependence in a multivariate setup. An exact simultaneous testing procedure based on dependent conditional tests is presented. Two applications to real data are also given.