The purposes of this paper are to: (1) describe some of the serious shortcomings in the current use of tests of statistical significance, (2) discuss how misuses are perpetuated in some widely used references, and (3) present an alternative significance testing model that overcomes some, but not all, of the shortcomings of the currently used…

A statistical test for cheating is developed. The case of a single examinee who has taken parallel forms of the same selection test on three occasions, obtaining scores x, y, z, is used to illustrate the development. It is assumed that each score is normally distributed with the same known variance, that is, the variance of the errors of…

The inferences allowable with a significant F in regression analysis are discussed. Included in this discussion are the effects of specificity of the research hypothesis, incorporation of covariates, directional hypotheses, and the manipulation of variables on the interpretation of significance for such purposes as causal and directional…

Illustrates a simple nonparametric alternative that can be used to test a hypothesis that two proximity matrices on the same set of variables or objects reflect a similar pattern of high and low entries. (RC)

Investigates the Tukey statistic for the empirical probability of a Type II error under numerous parametric specifications defined by Cohen (1969) as being representative of behavioral research data. For unequal numbers of observations per treatment group and for unequal population variancies, the Tukey test was simulated when sampling from a…

Describes a computer program for calculating the power of the F-test. Approach is based upon two independent approximations-- a normalization of the non-central F distribution and an integration of the normal distribution. Comparison of the calculated values of power with exact values revealed a high degree of accuracy. (Author/RC)

The asymptotic power of the Cramer-von Mises test when parameters are estimated from the data is studied under certain local (contiguous) alternatives. Notion of (asymptotic) direction and distance from the null hypothesis of alternatives is introduced, and it is shown that there exist directions with maximum, minimum, and arbitrary intermediate…

A general procedure is provided for comparing correlation coefficients between optimal linear composites. It allows computationally efficient significance tests on independent or dependent multiple correlations, partial correlations, and canonical correlations, with or without the assumption of multivariate normality. Evidence from Monte Carlo…

The concept of statistical significance is explained, with specific numerical illustrations. (MNS)

Considered methods of evaluating the pattern of subtest scores on the Wechsler Adult Intelligence Scale-Revised. The rationale and method for calculating the size of the significant difference between a subtest and the mean of the subtests scores for an individual are described. (JAC)

Extending the definitions of part and bipartial correlation to sets of variates, the notion of part and bipartial canonical correlation analysis are developed and illustrated. (Author)

The present paper discusses criticisms of statistical significance testing from both historical and contemporary perspectives. Statistical significance testing is greatly influenced by sample size and often results in meaningless information being over-reported. Variance-accounted-for-effect sizes are presented as an alternative to statistical…

Over the years, methodologists have been recommending that researchers use magnitude of effect estimates in result interpretation to highlight the distinction between statistical and practical significance (cf. R. Kirk, 1996). A magnitude of effect statistic (i.e., effect size) tells to what degree the dependent variable can be controlled,…

This paper summarizes the literature regarding statistical significant testing with an emphasis on recent literature in various discipline and literature exploring why researchers have demonstrably failed to be influenced by the American Psychological Association publication manual's encouragement to report effect sizes. Also considered are…

D. Robinson and J. Levin (1997) proposed what they called a two-step procedure for analyzing statistical data in which researchers first evaluate the probability of an observed effect statistically (i.e., statistical significance), and, if and only if, it can be concluded that the underlying finding is too improbable to be due to chance, then they…