An alternative to Cohen's standardized mean difference effect size: a robust parameter and confidence interval in the two independent groups case.

The authors argue that a robust version of Cohen's effect size constructed by replacing population means with 20% trimmed means and the population standard deviation with the square root of a 20% Winsorized variance is a better measure of population separation than is Cohen's effect size. The authors investigated coverage probability for confidence intervals for the new effect size measure. The confidence intervals were constructed by using the noncentral t distribution and the percentile bootstrap. Over the range of distributions and effect sizes investigated in the study, coverage probability was better for the percentile bootstrap confidence interval.

[1]  K. McGraw,et al.  A common language effect size statistic. , 1992 .

[2]  J Carpenter,et al.  Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians. , 2000, Statistics in medicine.

[3]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[4]  R. Wilcox.  Applying Contemporary Statistical Techniques , 2003 .

[5]  Ken Kelley,et al.  Sample size for multiple regression: obtaining regression coefficients that are accurate, not simply significant. , 2003, Psychological methods.

[6]  N. Cliff.  Answering Ordinal Questions with Ordinal Data Using Ordinal Statistics. , 1996, Multivariate behavioral research.

[7]  H. Keselman,et al.  Modern robust data analysis methods: measures of central tendency. , 2003, Psychological methods.

[8]  N. L. Johnson,et al.  APPLICATIONS OF THE NON-CENTRAL t-DISTRIBUTION , 1940 .

[9]  James Algina,et al.  Sample Size Requirements for Accurate Estimation of Squared Semi-Partial Correlation Coefficients , 2002, Multivariate behavioral research.

[10]  Ronald C. Serlin,et al.  Rationality in psychological research: The good-enough principle. , 1985 .

[11]  Jeffrey D. Kromrey,et al.  Robust Confidence Intervals for Effect Sizes: A Comparative Study of Cohen's d and Cliff's Delta Under Non-normality and Heterogeneous Variances , 2004 .

[12]  G. Cumming,et al.  A Primer on the Understanding, Use, and Calculation of Confidence Intervals that are Based on Central and Noncentral Distributions , 2001 .

[13]  James Algina,et al.  Determining Sample Size for Accurate Estimation of the Squared Multiple Correlation Coefficient , 2000, Multivariate behavioral research.

[14]  W. J. Dixon,et al.  The approximate behaviour and performance of the two-sample trimmed t , 1973 .

[15]  R. Wilcox.  Introduction to Robust Estimation and Hypothesis Testing , 1997 .

[16]  E. Ziegel.  Introduction to Robust Estimation and Hypothesis Testing (2nd ed.) , 2005 .

[17]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[18]  S. Sheather,et al.  Robust Estimation and Testing , 1990 .

[19]  N. Cliff.  Dominance statistics: Ordinal analyses to answer ordinal questions. , 1993 .

[20]  L. Harlow,et al.  What if there were no significance tests , 1997 .

[21]  B. Wolman,et al.  Handbook of clinical psychology , 1965 .

[22]  Jacob Cohen,et al.  The statistical power of abnormal-social psychological research: a review. , 1962, Journal of abnormal and social psychology.

[23]  Leland Wilkinson,et al.  Statistical Methods in Psychology Journals Guidelines and Explanations , 2005 .