The present paper is concerned with measuring the size of an effect for fixed effects factorial analysis of variance (ANOVA) experimental designs. A brief review of the literature is provided, emphasizing the need to use such a measure in actual research. Measuring strength of effect is discussed in correlational terms, taking advantage of the linear model formulation for fixed effects ANOVA. It is concluded that a squared partial correlation between factor and response (partialing out effects of other factors) is usually to be preferred to the corresponding un-partialled measure (ω2) advocated by Hays (1963) and others. Examples are provided to illustrate the practical implications of this distinction.
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References
1.
Appelbaum, M. I. and Cramer, E. M.Some problems in the nonorthogonal analysis of variance . Psychological Bulletin, 1974, 81, 325-343.
2.
Binder. A.Further considerations on testing the null hypothesis and the strategy and tactics of investigating theoretical models. Psychological Review, 1963, 70, 107-115.
3.
Bakan, D.The test of significance in psychological research. Psychological Bulletin, 1966, 66, 423-437.
4.
Cohen, J.Some statistical issues in psychological research. In B. B. Wolman (Ed.), Handbook of clinical psychology. New York: McGraw-Hill, 1968.
5.
Cohen, J.Statistical power analysis for the behavioral sciences. New York: Academic Press, 1969.
6.
Dodd, D. H. and Schultz, R. F.Computational procedures for estimating magnitude of effect for some analysis of variance designs. Psychological Bulletin, 1973, 79, 391-395.
7.
Dooling, D. J. and Danks, J. H.Going beyond tests of significance: Is psychology ready? Bulletin of the Psychonomic Society, 1975, 5, 15-17.
8.
Dwyer, J. H.Analysis of variance and the magnitude of effects: A general approach. Psychological Bulletin , 1974, 81, 731-737.
9.
Fisher, R. A.Statistical methods for research workers. New York: Hafner, 1958.
10.
Glass, V. G. and Hakstian, A. R.Measures of association in comparative experiments: Their development and interpretation. American Educational Research Journal, 1969, 6, 403-414.
11.
Grant, D. A.Testing the null hypothesis and the strategy and tactics of investigating theoretical models. Psychological Review, 1962, 69, 54-61.
12.
Greenwald, A. G.Consequences of prejudice against the null hypothesis. Psychological Bulletin, 1975, 82, 1-20.
13.
Harris, J. A.On the calculation of intra-class and inter-class correlations. Biometrika, 1913, 9, 446-472.
14.
Hays, W. L.Statistics. New York: Holt, Rinehart and Winston, 1963.
15.
Humphreys, L. F. and Fleishman, A.Pseudo-orthogonal and other analysis of variance designs involving individual differences variables. Journal of Educational Psychology, 1974, 66, 464-472.
16.
Kelley, T. L.An unbiased correlation ratio measure. Proceedings of the National Academy of Sciences , 1935, 21, 554-559.
17.
Keppel, G.Design and analysis: A researcher's handbook. Englewood Cliffs, New Jersey: Prentice-Hall, 1973.
18.
Keren G.Some considerations of two alleged kinds of selective attention. Journal of Experimental Psychology: General, 1976, 105, 349-374.
19.
Keren, G. and Lewis, C.Nonorthogonal designs: Sample versus population. Psychological Bulletin, 1976, 83, 917-926.
20.
Overall, J. E. and Spiegel, D. K.concerning least squares analysis of experimental data. Psychological Bulletin, 1969, 72, 311-322.
21.
Pearson, K.On the theory of skew correlations and non-linear regression. Mathematical contributions to the theory of evolution , Biometric Laboratory Publications; University of London, Cambridge University Press, 1905.
22.
Peters, C. and Van Voorhis, W.Statistical procedures and their mathematical bases. New York: McGraw-Hill, 1940.
23.
Rao, C. R.Linear statistical inferences and its applications. New York: Wiley, 1965.
24.
Rozeboom, W. W.The fallacy of the null-hypothesis significance test. Psychological Bulletin, 1960, 57, 416-428.
25.
Vaughan, G. M. and Corballis, M. C.Beyond tests of significance: Estimating strength of effects in selected ANOVA designs, Psychological Bulletin , 1969, 62, 204-218.
26.
Venables, W.Calculation of confidence intervals for noncentrality parameters. Journal of the Royal Statistical Society, Series, B, 1975, 37, 406-412.
