ERIC Number: ED448175
Record Type: Non-Journal
Publication Date: 2000-Nov
Reference Count: N/A
The Corrected Eta-Squared Coefficient: A Value Added Approach.
Barnette, J. Jackson; McLean, James E.
Eta-Squared (ES) is often used as a measure of strength of association of an effect, a measure often associated with effect size. It is also considered the proportion of total variance accounted for by an independent variable. It is simple to compute and interpret. However, it has one critical weakness cited by several authors (C. Huberty, 1994; P. Snyder and S. Lawson, 1993; and T. Snijders, 1996), and that is a sampling bias that leads to an inflated judgment of true effect. The purpose of this study was to determine the degree of inflation by determining how large ES is likely to be by chance, find methods of predicting the mean inflation, and then proposing the use of a corrected ES coefficient that is the observed ES minus the mean expected ES, a value added approach. A Monte Carlo study was set up using a number of samples from 2 to 10 and sample sizes from 5 to 100 in steps of 5. In each number of samples and sample size configuration, 10,000 one-way analysis of variance replications, using samples drawn from the unit normal distribution, were conducted for a total of 1,800,000 replications. Patterns of observed ES values were examined for influences of number and size samples. It was clear that ES was influenced by both of these factors. Trend analysis was conducted to determine equations that could be used to predict the mean chance-based ES for given number and size of samples. In a given research situation, the expected ES coefficient may be determined for comparison with the observed ES. Such an approach removes the bias cited as the major weakness of the use of ES as a measure of strength of association and makes it a more useful measure of non-chance influence. (Contains 6 figures, 3 tables, and 43 references.) (Author/SLD)
Publication Type: Numerical/Quantitative Data; Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A