Null hypothesis significance testing (NHST) has been the subject of debate for decades and alternative approaches to data analysis have been proposed. This article addresses this debate from the perspective of scientific inquiry and inference. Inference is an inverse problem and application of statistical methods cannot reveal whether effects…

It is suggested that the binomial theorem be used to compute the probability that a given number of Type I errors would occur when a group of null hypotheses are true and that this result be used as the level of significance for the test of an overall hypothesis. (Author/BW)

Too often researchers rely upon the classical normal theory parametric tests to analyze non-normal data, even though the tests may not be robust to violations of that assumption. Fligner's class of two-sample tests for scale is an important development because the test is distribution-free and has desirable properties. This paper outlines the…

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…

The normative implications of applying significance tests in evaluation research are examined. The authors conclude that evaluators often make normative decisions, based on the traditional .05 significance level in studies with small samples. Additional reporting of the magnitude of impact, the significance level, and the power of the test is…

Describes some of the situations in which a psychologist is likely to violate the assumption of independent errors. A Monte-Carlo study of the effects of this violation is then described. (Author/RC)

Two stage multiple-comparison procedures give an exact solution to problems of power and Type I errors, but require equal sample sizes in the first stage. This paper suggests a method of evaluating the experimentwise Type I error probability when the first stage has unequal sample sizes. (Author/BW)

A correction of the standard F-ratio for unreliability of the dependent measure has recently been proposed by Winne; the rationale is analogous to that of correcting a correlation for attenuation. However, there are two problems associated with Winne's correction of which potential users should be aware. First, the corrected statistic, F*, has…

An equation was derived to determine the relationship between the pooled within-subgroup r (correlation coefficient) and the r obtained from the total group data. It was, thus, possible to assess the amount of distortion introduced by pooling heterogeneous subgroups. As a basis for deciding whether to pool two subgroups in order to calculate a…

A novel solution to the statistical problems in an evaluation of rare events is described. The significance of variations in the number of child homicides is analyzed in a binary time series of "active" months for monitoring future incidence and related systemic events. (Author/CM)

This paper is concerned with testing hypotheses about main effects, simple effects, and interaction effects by means of analysis of variance. It presents alternative strategies for analyzing data sets for which a factorial model with two completely crossed, fixed factors is appropriate. (CTM)

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…

The basic notion of variability is generalized from a univariate context to a multivariate context using two matrix functions, a determinant, and a trace, yielding a number of alternative multivariate indices of shared variation. Some problems in the interpretation of tests of multivariate hypotheses are reviewed. (Author/BW)

The purpose of the present study was to investigate empirically the effects of violations of the assumption of homogeneity of within-group regression slopes on levels of significance in the F test of fixed-effects ANCOVA (analysis of covariance). The study used a Monte Carlo computer simulation procedure to generate data under the following…