Robert J. Grissom

Heterogeneity of variance in clinical data.

Traditional parametric (t, F) and nonparametric (Mann-Whitney-Wilcoxon U, Kruskal-Wallis H) statistics are sensitive to heterogeneity of variance (heteroscedasticity). Moreover, there are theoretical reasons to expect, and empirical results to document, the existence of heteroscedasticity in clinical data. Transformations to reduce heteroscedasticity are problematic. This article reviews the literature on robust methods that are available and that should be widely used to control rate of Type I error and maintain power. No one robust method is ideal for all situations, but such methods are superior to the traditional tests. Specific recommendations are made for application under various conditions of heteroscedasticity.

Review of assumptions and problems in the appropriate conceptualization of effect size.

Estimation of the effect size parameter, D, the standardized difference between population means, is sensitive to heterogeneity of variance (heteroscedasticity), which seems to abound in psychological data. Pooling s2s assumes homoscedasticity, as do methods for constructing a confidence interval for D, estimating D from t or analysis of variance results, formulas that adjust estimates for inflation by main effects or covariates, and the Q statistic. The common language effect size statistic as an estimate of Pr(X1 > X2), the probability that a randomly sampled member of Population 1 will outscore a randomly sampled member of Population 2, also assumes normality and homoscedasticity. Various proposed solutions are reviewed, including measures that do not make these assumptions, such as the probability of superiority estimate of Pr(X1 > X2). Ways to reconceptualize effect size when treatments may affect moments such as the variance are also discussed.

Do Between-Culture Differences Really Mean that People are Different? A Look at Some Measures of Cultural Effect Size

Statistically significant differences in culture means may or may not reflect practically important differences between people of different cultures. To determine whether differences between culture means represent meaningful differences between individuals, further data analyses involving measures of cultural effect sizes are necessary. In this article the authors recommend four such measures and demonstrate their efficacy on two data sets from previously published studies. They argue for their use in future cross-cultural research as a complement to traditional tests of mean differences.

Effect Sizes for Research : Univariate and Multivariate Applications, Second Edition

1. Introduction 2. Confidence Intervals for Comparing the Averages of Two Groups 3. The Standardized Difference Between Means 4. Correlational Effect Sizes and Related Topics 5. Parametric and Nonparametric Effect Size Measures that Go Beyond Comparing Two Averages 6. Effect Sizes for One-Way ANOVA and Nonparametric Approaches 7. Effect Sizes for Factorial Designs 8. Effect Sizes for Categorical Variables 9. Effect Sizes for Ordinal Categorical Dependent Variables (Rating Scales) 10. Effect Sizes for Multiple Regression/Correlation 11. Effect Sizes for Analysis of Covariance 12. Effect Sizes for Multivariate Analysis of Variance

Parametric Analysis of Ordinal Categorical Clinical Outcome

Parametric and nonparametric approaches are compared for testing hypotheses of the superiority of one therapy over another when the outcome is ordinal categorical. The estimation of clinically informative effect sizes, especially the probability that a client given one therapy will have an outcome that is superior to that of a client given another therapy, is emphasized. Parametric and nonparametric estimates of effect size are presented. Considerations for choosing between the two approaches are discussed.