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Combining Standardized Mean Differences Using the Method of Maximum Likelihood

Published online by Cambridge University Press:  01 January 2025

Ke-Hai Yuan  and
Brad J. Bushman
Ke-Hai Yuan*
Affiliation:
University of Notre Dame
Brad J. Bushman
Affiliation:
Iowa State University
*
Requests for reprints should be sent to Ke-Hai Yuan, Laboratory for Social Research, 919 Flanner Hall, University of Notre Dame IN 46556. E-Mail: kyuan@nd.edu
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Abstract

A maximum likelihood procedure for combining standardized mean differences based on a noncentratt-distribution is proposed. With a proper data augmentation technique, an EM-algorithm is developed. Information and likelihood ratio statistics are discussed in detail for reliable inference. Simulation results favor the proposed procedure over both the existing normal theory maximum likelihood procedure and the commonly used generalized least squares procedure.

Keywords

noncentral t-distributiondata augmentationEM-algorithmobserved informationMonte-Carlometa-analysiseffect sizemaximum likelihoodweighted least squares

Information

Type
Articles
Information
Psychometrika , Volume 67 , Issue 4 , December 2002 , pp. 589 - 607
Copyright
Copyright © 2002 The Psychometric Society

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References

Cohen, J.J. (1977). Statistical power analysis for the behavioral sciences 2nd ed., Hillsdale, NJ: Erlbaum.Google Scholar
Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with Discussion). Journal of the Royal Statistical Society, Series B, 39, 1–38.CrossRefGoogle Scholar
Efron, B., & Hinkley, D.V. (1978). The observed versus the expected information. Biometrika, 65, 457–487.CrossRefGoogle Scholar
Glass, G.V. (1976). Primary, secondary, and meta-analysis of research. Educational Researcher, 5, 3–8.CrossRefGoogle Scholar
Hedges, L.V. (1980). Combining the results of experiments using different scales of measurement. Stanford, CA: Stanford University.Google Scholar
Hedges, L.V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6, 107–128.CrossRefGoogle Scholar
Hedges, L.V. (1982). Estimating effect size from a series of independent experiments. Psychological Bulletin, 92, 490–499.CrossRefGoogle Scholar
Hedges, L.V., Giaconia, R.M., & Gage, N.L. (1981). The empirical evidence on the effectiveness of open education. Stanford, CA: Stanford University School of Education.Google Scholar
Hedges, L.V., Olkin, I. (1985). Statistical methods for meta-analysis. San Diego, CA: Academic Press.Google Scholar
Jamshidian, M., & Jennrich, R.I. (1993). Conjugate gradient acceleration of the EM algorithm. Journal of the American Statistical Association, 88, 221–228.CrossRefGoogle Scholar
Little, R.J.A. (1988). Robust estimation of the mean and covariance matrix from data with missing values. Applied Statistics, 37, 23–38.CrossRefGoogle Scholar
Little, R.J.A., & Rubin, D.B. (1987). Statistical analysis with missing data. New York, NY: Wiley.Google Scholar
Liu, C.H., & Rubin, D.B. (1995). ML estimation of the multivariatet distribution with unknown degrees of freedom. Statistica Sinica, 5, 19–39.Google Scholar
Louis, T.A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B, 44, 226–233.CrossRefGoogle Scholar
McLachlan, G.J., & Krishnan, T. (1997). The EM algorithm and extensions. New York, NY: Wiley.Google Scholar
Meilijson, I. (1989). A fast improvement to the EM algorithm on its own terms. Journal of the Royal Statistical Society, Series B, 51, 127–138.CrossRefGoogle Scholar
Neyman, J., & Scott, E.L. (1948). Consistent estimates based on partially consistent observations. Econometrika, 16, 1–32.CrossRefGoogle Scholar
Rosenthal, R., & Rubin, D.B. (1982). Comparing effect sizes of independent studies. Psychological Bulletin, 92, 500–504.CrossRefGoogle Scholar
Rubin, D.B. (1983). Iteratively reweighted least squares. In Johnson, N.L., & Kotz, S. (Eds.), Encyclopedia of statistical sciences, Volume 4 (pp. 272–275). New York, NY: Wiley.Google Scholar
Stuart, A., & Ord, J.K. (1991). Kendall's advanced theory of statistics 5th ed., New York, NY: Oxford University Press.Google Scholar
Tanner, M.A. (1996). Tools for statistical inference: Methods for the exploration of posterior distributions and likelihood functions 3rd ed., New York, NY: Springer-Verlag.CrossRefGoogle Scholar
Wang, M.C., & Bushman, B.J. (1999). Integrating results through meta-analytic review using SAS software. Cary, NC: SAS Institute.Google Scholar
Yuan, K.-H., Jennrich, R.I. (1998). Asymptotics of estimating equations under natural conditions. Journal of Multivariate Analysis, 65, 245–260.CrossRefGoogle Scholar
Zhang, Z., & Schoeps, N. (1997). On robust estimation of effect size under semiparametric models. Psychometrika, 62, 201–214.CrossRefGoogle Scholar