Showing papers on "Effect size published in 1985"

The multiple correlation coefficient and fisher's a statistic1

Abstract: Summary Fisher's A statistic, often called the adjusted R2 statistic, is shown to be a close approximation to the maximum likelihood estimate of the multiple correlation coefficient, p2, based on the marginal distribution of R2. Expansions for the estimate are obtained. The same methods lead to maximum marginal likelihood estimators for the noncentrality parameters for noncentral X2 and F.

QUANTITATIVE METHODS IN PSYCHOLOGY Correlation and the Coefficient of Determination

Abstract: It is common practice in psychological statistics to use the square of the correlation as a coefficient of determination or a percentage measure of variance accounted for. This use of the correlation coefficient requires the adoption of a particular model and attendant assumptions. In a variety of circumstances where the square of the correlation coefficient is used, the required assumptions are not tenable. An alternative, less well-known interpretation of the correlation coefficient is described. In this model, the absolute value of the correlation provides a coefficient of determination . Similarities and differences between these two models are described, and conditions for the appropriate use of each model are discussed. The correlation coefficient and not the correlation squared is recommended for use as an effect size indicator, because evaluating effect size in terms of variance accounted for may lead to interpretations that grossly underestimate the magnitude of a relation. Pearson coefficients of correlation and other derivative statistics (e.g., phi, point-biserial correlations) are used with considerable frequency in the analysis of psychological data. One reason for computing these statistics is to determine the size or magnitude of the relation between two variables. When used for this purpose, it is common to use the square of the correlation coefficient as an index of the size of the relation. This index, referred to by Guilford (1936) as the coefficient of determination , is interpreted as the percentage of variance in one variable that is predicted or explained by the other. Amount of explained variance is one way of expressing the degree to which some relation or phenomenon is present—what Cohen (1969) refers to as effect size. Effect size estimation is an important concern, providing a basis for evaluating the effectiveness of an experimental treatment or perhaps even the success of a basic research program.