Power of the independent samples t test under a prevalent psychometric measure distribution.

Studies in psychology often have low power because of inadequate sample size. Thus, recent articles in the Journal of Consulting and Clinical Psychology have suggested making sample size determinations through readily available tables that are based on population normality. Questions have been raised on the use of these power tables because prevalent psychometric distributions, such as the discrete mass at zero with gap that occurs with 1st use or onset variables, are radically nonnormal. In addition to demonstrating the robustness of the independent samples t test with respect to Type I error, the major finding of this study shows that researchers may use these power tables without modification for this radically nonnormal distribution. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Comments on using alternatives to normal theory statistics in social and behavioural science.

Comments on the article by M. A. Hunter and R. B. May (see record 1994-24054-001) on the myths and misconceptions of parametric and nonparametric statistics, particularly with reference to power, robustness, scale of measurement, the null hypothesis, and generality of application. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Analysis of Likert scale data in disability and medical rehabilitation research.

Many clinical evaluations are subjective, resulting in ordinal level measurements. A widely used example in medical rehabilitation is the Functional Independence Measure (FIM), which provides a measure of disability. The FIM is an 18-item, 7-point Likert scale ranging from complete dependence to complete independence. Parametric statistics are commonly used for the analysis of ordinal data. However, Likert scales often lead to violation of many underlying assumptions. This study examined the comparative power of the t test with the Wilcoxon rank-sum test using real pretest/posttest data sets measured on an ordinal scale. FIM scores were obtained on 714 geriatric patients at admit and discharge from a rehabilitation hospital. A Fortran 77 program was written to sample with replacement from each admit and discharge data distribution. Results indicated the Wilcoxon rank-sum test outperformed the t test for almost every sample size and alpha level examined. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A more realistic look at the robustness and Type II error properties of the t test to departures from population normality.

The Type I and II error properties of the t test were evaluated by means of a Monte Carlo study that sampled 8 real distribution shapes identified by T. Micceri (1986, 1989) as being representative of types encountered in psychology and education research. Results showed the independent-samples t tests to be reasonably robust to Type I error when (1) sample sizes are equal, (2) sample sizes are fairly large, and (3) tests are 2-tailed rather than 1-tailed. Nonrobust results were obtained primarily under distributions with extreme skew. The t test was robust to Type II error under these nonnormal distributions, but researchers should not overlook robust nonparametric competitors that are often more powerful than the t test when its underlying assumptions are violated. (PsycINFO Database Record (c) 2010 APA, all rights reserved)