Partial Omega Squared for Anova Designs

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.

[1]  J. Dwyer.  Analysis of variance and the magnitude of effects: A general approach. , 1974 .

[2]  J. A. Harris.  ON THE CALCULATION OF INTRA-CLASS AND INTER-CLASS COEFFICIENTS OF CORRELATION FROM CLASS MOMENTS WHEN THE NUMBER OF POSSIBLE COMBINATIONS IS LARGE , 1913 .

[3]  Jacob Cohen.  Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[4]  W. N. Venables.  Calculation of Confidence Intervals for Noncentrality Parameters , 1975 .

[5]  M. Kendall.  Statistical Methods for Research Workers , 1937, Nature.

[6]  G. Keren,et al.  Nonorthogonal designs: Sample versus population. , 1976 .

[7]  D. Bakan,et al.  The test of significance in psychological research. , 1966, Psychological bulletin.

[8]  D. A. Grant,et al.  Testing the null hypothesis and the strategy and tactics of investigating theoretical models. , 1962, Psychological review.

[9]  Joseph H. Danks,et al.  Going beyond tests of significance: Is psychology ready? , 1975 .

[10]  G. Keren.  Some considerations of two alleged kinds of selective attention. , 1976, Journal of experimental psychology. General.

[11]  G. Glass,et al.  Measures of Association in Comparative Experiments: Their Development and Interpretation , 1969 .

[12]  D. J. Bartholomew,et al.  Linear Statistical Inferences and Its Applications , 1975 .

[13]  L. Humphreys,et al.  Pseudo-Orthogonal and Other Analysis of Variance Designs Involving Individual-Differences Variables. , 1974 .

[14]  D. H. Dodd,et al.  Computational procedures for estimating magnitude of effect for some analysis of variance designs. , 1973 .

[15]  T. L. Kelley,et al.  An Unbiased Correlation Ratio Measure. , 1935, Proceedings of the National Academy of Sciences of the United States of America.

[16]  A. Greenwald.  Consequences of Prejudice Against the Null Hypothesis , 1975 .

[17]  P. F. Miller.  Statistical Procedures and their Mathematical Bases , 1941, Nature.

[18]  A BINDER,et al.  Further considerations on testing the null hypothesis and the strategy and tactics of investigating theoretical models. , 1963, Psychological review.

[19]  J. Overall,et al.  Concerning least squares analysis of experimental data. , 1969 .

[20]  Mark I. Appelbaum,et al.  Some problems in the nonorthogonal analysis of variance. , 1974 .

[21]  W. W. Rozeboom.  The fallacy of the null-hypothesis significance test. , 1960, Psychological bulletin.

[22]  G. Keppel,et al.  Design and Analysis: A Researcher's Handbook , 1976 .

[23]  Michael C. Corballis,et al.  Beyond tests of significance: Estimating strength of effects in selected ANOVA designs. , 1969 .

[24]  Rory A. Fisher,et al.  Statistical Methods for Research Workers. , 1956 .