In his early exposition of path analysis, Duncan (1966) noted that the method "provides a calculus for indirect effects." Despite the interest in indirect causal effects, most users treat them as if they are population parameters and do not test whether they are statistically significant. Sobel (1982) has recently derived the asymptotic…

Although the primary responsibility rests with the authors of articles reporting nonsignificant results to demonstrate the worth of the results by discussing the power of the tests, consumers should be prepared to conduct their own power analyses. This article demonstrates the use of power analysis for the interpretation of nonsignificant…

Power is an indicator of the ability of a statistical analysis to detect a phenomenon that does in fact exist. The issue of power is crucial for social science research because sample size, effects, and relationships studied tend to be small and the power of a study relates directly to the size of the effect of interest and the sample size.…

Each of the four classic multivariate analysis of variance (MANOVA) tests of statistical significance may lead a researcher to different decisions as to whether a null hypothesis should be rejected: (1) Wilks' lambda; (2) Lawley-Hotelling trace criterion; (3) Roy's greatest characteristic root criterion; and (4) Pillai's trace criterion. These…

In the educational research literature alpha, the a priori level of significance, and p, the a posteriori probability of obtaining a test statistic of at least a certain value when the null hypothesis is true, are often confused. Explanations for this confusion are offered. Paradoxically, alpha retains a prominent place in textbook discussions of…

Attempts to distill a growing technical literature on repeated-measures analysis of variance into a few simple principles for selecting an analytic technique. Argues that researchers ought not opt for a general analysis strategy when current computer technology makes it possible to select the optimal analysis technique for a given data set. (RH)

Using a Monte Carlo approach, comparison was made between traditional procedures and a multiple linear regression approach to test for differences between values of r sub 1 and r sub 2 when sample data were dependent and independent. For independent sample data, results from a z-test were compared to results from using multiple linear regression.…

This article first outlines the logic of null hypothesis testing and the problems of using it to evaluate special education research. It then presents three alternative metrics, a binomial effect size display, a relative risk ratio, and an odds ratio, that can better identify important treatment effects using illustrative data from recently…

This article compares three models that have been the foundation for approaches to the analysis of statistical significance in early childhood research--the Fisherian and the Neyman-Pearson models (both considered "classical" approaches), and the Bayesian model. The article concludes that all three models have a place in the analysis of research…

This article explains and illustrates the estimation of the power of statistical tests used to analyze data in early childhood special education research, and discusses advantages and disadvantages of various ways to increase power, such as using a directional alternate hypothesis or using a parametric, rather than nonparametric, statistical test.…

A growing controversy surrounds the strict interpretation of statistical significance tests in social research. Statistical significance tests fail in particular to provide estimates for the stability of research results. Methods that do provide such estimates are known as invariance or cross-validation procedures. Invariance analysis is largely…

Theories employed to explain regularities in social behavior often contain explicit or implicit reference to the presence of nonlinear and/or nonadditive (i.e., multiplicative) relationships among germane variables. While such nonadditive features are theoretically important, the inclusion of quadratic or multiplicative terms in structural…

An approach to statistical testing, which combines Neyman-Pearson hypothesis testing and Fisher significance testing, is recommended. The use of P-values in this approach is discussed in some detail. The author also discusses some problems which are often found in introductory statistics textbooks. The problems involve the definitions of…

This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…

This paper reports the results of a Monte Carlo investigation of Type I errors in the single group repeated measures design where multiple measures are collected from each observational unit at each measurement occasion. The Type I error of three multivariate tests were examined. These were the doubly multivariate F test, the multivariate mixed…