James K. Brewer

On the Power of Statistical Tests in the "American Educational Research Journal"

It is almost universally accepted by educational researchers that the power (probability of rejecting Ho when Ho is false, that is, 1-0-) of a statistical test is important and should be substantial. What is not universally accepted or known is that the power can and should be calculated and reported for every standard statistical test. The power of statistical tests already conducted in educational research is equally unknown. It is the purpose of this paper to report the level of power for recent statistical tests reported in the AERJ and to propose alternative reporting schemes relative to hypothesis testing to include power and effect size as well as the traditional a. Cohen (1962, 1969), Tversky and Kahnman (1971), Overall (1969) and others argue quite strongly that explicit computation of power relative to reasonable hypotheses should be made before any study is completed and subsequently reported. Tversky and Kahnman (1971) suggest three reasons why this computation is important: (1) Such computations can lead the researcher to the conclusion that there is no point in running the study unless the sample size is materially increased; (2) The computation is essential to the interpretation of negative results, that is, failures to reject the null hypothesis; and (3) Computed power gives the researcher an indication of the level of the probability of a valid rejection of the null hypothesis.

Behavioral Statistics Textbooks: Source of Myths and Misconceptions?

Six behavioral statistics textbooks listed by their publishers as “bestsellers” during 1982 were reviewed by the author. The intent was to detect the presence of and discuss the nature of some theoretical inferential inaccuracies, misinterpretations, and errors, that is, statistical “myths and misconceptions.” Approximately 43 quotes were found that to some degree reflected misconceptions of statistical theory and that may mislead the behavioral researcher. These quotes were classified in general categories of half-truths, definitional errors, constant-cum-variable, cart-before-the-horse, and unitary inference.

Univariate selection: The effects of size of correlation, degree of skew, and degree of restriction

Pearsons formula for univariate selection was derived with the assumption of normality of variates before and after selection. This study examined the influence of skew upon estimates from Pearsons formula under certain conditions. It was found that even with essentially symmetric distributions, a large proportion of the data is necessary to obtain reasonably precise estimates of low correlations. With increasing skew, estimates become increasingly erroneous, the direction of the error depending upon which tail of the distribution is the basis of the estimates. Difficulties in applying correction for univariate selection in several studies of the predictability of college-grades for Negroes from scores on standard aptitude tests are discussed.

An Analysis of the Power of Statistical Tests Reported in the Research Quarterly

Abstract This study was designed to investigate the power of the research studies published in the Research Quarterly. A survey of major articles dating from October 1969 to May 1971 was made in regard to statistical tests used, levels of significance, the sample size, and power. It was noted that statistical inferential testing was conducted in 136 of the 151 articles, with the t and A NOVA tests being the most commonly used. Cohens (3) tables and metric free values for effect size were used to estimate the power of the 82 t and 179 F tests which were reported in 106 of the studies. An analysis of the results showed that the researchers would have made a valid rejection of H0 on the average approximately 78% of the time when using a large effect size, 50% of the time when using a medium effect size, and 13% when using a small effect size. Some suggestions were presented to assist in increasing the power of statistical tests used.

A note on a cognitive probability model incorporating the serial position effect.

A generalization of a cognitive probability model is proposed utilizing the serial position effect to account for decay in probability of recall. The general nature of the model permits the incorporation of almost any of the recent free-recall serial position curve results. Two examples, hypothesizing different serial position curves, are given.

Frequency ratios and oscillatory behavior in the two-choice situation

The present study was undertaken to determine if different frequency ratios resulted in different oscillatory predictive behavior in the two-choice situation. Four different frequency ratios were used on four groups of Ss and for each group an autocovariance analysis was conducted on the Ss’ responses. The resulting autocovariance plots indicated differential oscillatory patterns for the four frequency ratio groups.

Predicting early educational program placement with discrete discriminant analysis

The purpose of this study was to predict placement and nonplacement outcomes for mildly handicapped three through five year old children given knowledge of developmental screening test data. Discrete discriminant analysis (Anderson, 1951; Cochran & Hopkins, 1961; Goldstein & Dillon, 1978) was used to classify children into either a placement or nonplacement group using developmental information retrieved from longitudinal Child Find records (1982-89). These records were located at the Florida Diagnostic and Learning Resource System (FDLRS) in Sarasota, Florida and provided usable data for 602 children. The developmental variables included performance on screening test activities from the Comprehensive Identification Process (Zehrbach, 1975), and consisted of: (a) gross motor skills, (b) expressive language skills, and (c) social-emotional skills. These three dichotomously scored developmental variables generated eight mutually exclusive and exhaustive combinations of screening data. Combined with one of t...

A cumulative autoregressive model for choice behavior

The group choice behavior of human subjects is assumed to be, in part, oscillatory in nature. A true a priori predictive model based on the integrated autoregressive moving-average process proposed by G.E.P. Box is presented and compared with human subject data from a two-choice predictive situation with @p = 0.60. The oscillatory patterns and predictions of the model are shown to be quite similar to those found in the subject data.

Book Reviews : Frank Restle. Mathematical Models in Psychology: An Introduction, Middlesex, England: Penguin Press Ltd., 1971. Pp. 158.

from such publications as the Journal o f Criminal Law, Criminology, and Police Science which may not be at everyone’s fingertips. There is also one paper written especially for the book by Loren and Jean Chapman summarizing their research on beliefs of clinicians and &dquo;psychodiagnostic folklore.&dquo; Unlike Personality Assessment which is bright and attractive to the eye, and easily entered through the index for selective reading, Readings in Personality Assessment suffers from a subdued type face which flutters late at night and a design shortcoming in that the articles follow immediately upon the heels of the preceding selection along with an absence of identifying signposts at the top of the page to guide the reader who is hunting for an article. If one opens the book a page too soon or too late, there is no help but to return to the index. On the other hand, any publisher able to deliver a hardback book of nearly 800 pages in length for under

2.45 (paperback:

12.00 in these days is perhaps entitled to cut a few corners.