The accuracy of normal approximations to the binomial test was evaluated with and without a continuity correction, regarding control of Type I errors and power. Both tests exhibited substantial power loss in comparison to the exact binomial test, although they are easier to apply and are sometimes desirable. (SLD)

The power functions of Student t tests performed on initial scores, ordinary ranks, 3 kinds of modular ranks, and dichotomies were investigated for 1 normal and 3 nonnormal distributions using 2 samples of 26 simulated scores each. Advantages of extending the rank transformation concept are discussed. (SLD)

It is argued that outlier-prone distributions reduce the power of nonparametric tests, but power can be restored through procedures usually associated with parametric tests. Computer simulation is used to show how an outlier detection and downweighting procedure augments the power of the t-test and the Wilcoxon-Mann-Whitney test. (SLD)

The results of a study of find alternative techniques for testing distributional normality are presented. A group of statistical techniques--some established and some new--were compared using empirical techniques. One new technique which appears to have higher power than the Lilliefors test was subjected to a better definition. Distributions under…

Some results on how the Alexander-Govern heteroscedastic analysis of variance (ANOVA) procedure (R. Alexander and D. Govern, 1994) performs under nonnormality are presented. This method can provide poor control of Type I errors in some cases, and in some situations power decreases as differences among the means get large. (SLD)

Assessed the relative merits of the Student "t" test and the Wilcoxon rank sum test under four population distributions and six sample-size pairings through Monte Carlo methods. The Wilcoxon rank sum test demonstrated an advantage in statistical power for nonnormal distributions (but not normal distributions), with fewer Type III errors…

Two-stage sampling procedures for comparing two population means when variances are heterogeneous have been developed by D. G. Chapman (1950) and B. K. Ghosh (1975). Both procedures assume sampling from populations that are normally distributed. The present study reports on the effect that sampling from non-normal distributions has on Type I error…

This study was concerned with the effects of reliability of observations, sample size, magnitudes of treatment effects, and the shape of the sampled population on the relative power of the paired samples rank transform statistic and Wilcoxon's signed ranks statistic. (Author/LMO)

A generalization of the usual random-effects model based on trimmed means is proposed. The resulting test of no differences among J randomly sampled groups has advantages in terms of Type I errors and can yield gains in power when distributions have heavy tails and outliers. (SLD)

Central limit theorem (CLT) is considered an important topic in statistics, because it serves as the basis for subsequent learning in other crucial concepts such as hypothesis testing and power analysis. There is an increasing popularity in using dynamic computer software for illustrating CLT. Graphical displays do not necessarily clear up…

The assumption of normality underlies much of the standard statistical methodology. Knowing how to determine whether a sample of measurements is from a normally distributed population is crucial both in the development of statistical theory and in practice. W. Ware and J. Ferron have developed a new test statistic, modeled after the K-squared test…

The present investigation developed power curves for two parametric and two nonparametric procedures for testing the equality of population variances. Both normal and non-normal distributions were considered for the two group design with equal and unequal sample frequencies. The results indicated that when population distributions differed only in…

Results of a Monte Carlo study with 4 populations (3,072 conditions) indicate that when distributions depart markedly from normality, nonparametric analysis and parametric analysis of transformed data show superior power to parametric analysis of raw data. Under conditions studied, parametric analysis of transformed data is more powerful than…

The test of homogeneity developed by L. V. Hedges (1982) for the fixed effects model is frequently used in quantitative meta-analyses to test whether effect sizes are equal. Despite its widespread use, evidence of the behavior of this test for the less-than-ideal case of small study sample sizes paired with large numbers of studies is…

A method of comparing one-step M-estimates of location for heavy tailed distributions is proposed and investigated. Simulations indicate that the new procedure provides good control over Type I errors and has more power than do some other methods for dealing with heavy tailed distributions. (SLD)