Last updated February 8, 2012
In press:
A Note on Consistency of Nonparametric Rank Tests and Related Rank Transformations. British Journal of Mathematical and Statistical Psychology (in press).
The extent to which rank transformations result in the same statistical decisions as their nonparametric counterparts was investigated. The study performed simulations using the Wilcoxon-Mann-Whitney test, the Wilcoxon signed-ranks test, and the Kruskal-Wallis test, together with the rank transformations and t and F tests corresponding to each of those nonparametric methods. In addition to the Type I error rates and power found from 50,000 iterations, the study also examined the consistency of the outcomes of the two methods on each individual sample. The results disclosed how acceptance or rejection of the null hypothesis and differences in p-values of the test statistics depend in a regular and predictable way on sample size, significance level, and differences between means, for normal and various non-normal distributions.
Correcting Two-Sample z and t Tests for Correlation: An Alternative to One-Sample Tests on Difference Scores. Psicologica (in press).
In order to circumvent the influence of correlation in paired-samples and repeated measures experimental designs, researchers typically perform a one-sample Student t test on difference scores. That procedure entails some loss of power, because it employs N – 1 degrees of freedom instead of the 2N – 2 degrees of freedom of the independent-samples t test. In the case of non-normal distributions, researchers typically substitute the Wilcoxon signed-ranks test for the one-sample t test. The present study explored an alternate strategy, using a modified two-sample t test with a correction for correlation analogous to the "z test for correlated samples" used at one time for paired observations. For non-normal distributions, the same modified t test was performed on rank-transformed data. Simulations disclosed that this proceduure protects the Type I error rate for moderate and large sample sizes, maintains power for normal distributions and several symmetric non-normal distributions, and substantially increases power for various skewed non-normal distributions.
Robust Significance Testing and Violation of Three Assumptions. Encyclopedia of Quality of Life Research (in press).
This paper examines some unexpected effects that occur when two or more assumptions underlying commonly used parametric significance tests are violated at the same time. It also emphasizes that nonparametric methods that are robust under non-normality often are ineffective under heterogeneity of variance. Furthermore, violation of independence, not frequently studied, has pronouced effects on all commonly used significance tests, parametric and nonparametric. The problems that arise are illustrated by simulations, using the Student t test and the Wilcoxon-Mann-Whitney rank-sum test applied to data from normal and 9 non-normal distributions, under conditions where homogeneity of variance and independence of sample observations also are violated.
Under review:
Alteration of Type I Error Rates by Selecting Significance Tests After Inspecting Sample Data
Researchers are alert to the shapes of distributions of sample data, because studies have shown that non-normal distributions, especially skewed distributions, adversely affect the Type I error rates and power of significance tests. However, one should recognize that samples from various skewed populations sometimes can be symmetric, and samples from symmetric populations can be skewed. The present study reveals that the probabilities of these occurrences are greater than one might expect. Furthermore, the Type I error rates and power of the significance tests typically chosen upon inspection of these anomalous samples can be severely inflated. For this reason, there are risks in making the choice of a significance test conditional on sample data when the population distribution is unknown.
Reliability of Measurement and the Power of Significance Tests for Normal and Non-Normal Distributions
The dependence of statistical power on the reliability of measurements has been studied extensively for the normal distribution but to a lesser extent for various non-normal distributions that often are encountered in psychological research. The present simulation study examined nine non-normal distributions and found that the influence of reliabillity on power functions is essentially the same as for the normal distribution. However, the value of power for given effect sizes varies widely, depending on the shape of the distribution. In all cases, normal and non-normal, the form of the relation between reliability and power, whether increasing, decreasing, or constant, is determined entirely by whether reliability changes by reduction of error score variance while true score variance remains constant, by increase in true score variance while error score variance remains constant, or by changes in both true and error score variance in such a way that observed score variance remains constant.
A New Look at Drug Interactions (with Richard Williams).
This paper examines the exponential increase in the possible number of interactions that can occur as the number of drugs taken by a patient increases. It emphasizes the practical impossibility of physicians taking account of all possible interactions when as few as 5 or 6 drugs are prescribed.
A Note on the Dependence of Heritability on Variances of Genetic and Environmental Components.
This study derived equations that make possible precise calculations of how the value of heritability is modified as the variability of the genetic and environmental components of the phenotype are systematically altered. Tables and graphs provide a picture of the direction and possible magnitude of changes in heritability that can occur under varuious assumptions about the component variances.
Abstracts of recent publications (1996 and later).
Abstracts of selected earlier publications (before 1996).