Sage Journals: Discover world-class research

Abstract

This article reviews the concepts and methods of Bayesian statistical analysis, which can offer innovative and powerful solutions to some challenging analytical problems that characterize developmental research. In this article, we demonstrate the utility of Bayesian analysis, explain its unique adeptness in some circumstances, address some concerns and misconceptions about the approach, and illustrate some applications of Bayesian analysis to issues that frequently arise in developmental research. The illustrations of the approach provided here reflect several important issues within the domain of moral reasoning development (such as assessing patterns of stage change over time); however, the methods are readily applicable across content areas in developmental research.

Keywords

Bayesian statistics frequentist statistics moral reasoning

Get full access to this article

View all access options for this article.

References

Berger, J.O. (1985). Statistical decision theory and Bayesian analysis . New York: Springer.

Bernardo, J.M. , & Smith, A.F.M. (1994). Bayesian theory. New York: Wiley.

Colby, A. , & Kohlberg, L. (1987). The measurement of moral judgment (Vols 1—2). New York: Cambridge University Press.

Congdon, P. (2003). Applied Bayesian modelling. New York: Wiley.

Gelfand, A.E. , & Smith, A.F.M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398—409.

Gelman, A. , Carlin, J.B. , Stern, H.S. , & Rubin, D.B. (2004). Bayesian data analysis (2nd ed.). Boca Raton, FL: Chapman and Hall/CRC.

Gill, J. (2002). Bayesian methods: A social and behavioral sciences approach. Boca Raton, FL: Chapman and Hall/CRC.

Harlow, L.L. , Mulaik, S.A. , & Steiger, J.H. (Eds.) (1997). What if there were no significance tests? Mahwah, NJ: Erlbaum.

Ibrahim, J.G. , Chen, M.-H. , Lipsitz, S.R. , & Herring, A.H. (2005). Missing-data methods for generalized linear models: A comparative review. Journal of the American Statistical Association, 100, 332—346.

10.

Ioannidis, J.P.A. (2005). Why most published research findings are false . PLoS Medicine, 2(8), Article e124. Available [accessed 20 November 2005] http://dx.doi.org/10.1371/journal.pmed.0020124

11.

Kohlberg, L. (1984). Essays on moral development:Vol. 2. The psychology of moral development San Francisco: Harper & Row.

12.

Lanza, S.T. , Collins, L.M. , Schafer, J.L. , & Flaherty, B.P. (2005). Using data augmentation to obtain standard errors and conduct hypothesis tests in latent class and latent transition analysis. Psychological Methods, 10, 84—100.

13.

Lanza, S.T. , Flaherty, B.P. , & Collins, L.M. (2003). Latent class and latent transition analysis. In J.A. Schinka & W.F. Velicer (Eds.), Handbook of psychology: Vol. 2. Research methods in psychology (pp. 663—685). Hoboken, NJ: Wiley.

14.

Lapsley, D.K. (2006). Moral stage theory. In M. Killen & J.G. Smetana (Eds.), Handbook of moral development (pp. 37—66). Mahwah, NJ: Erlbaum.

15.

Lindley, D.V. (1975). The future of statistics — A Bayesian 21st century. Advances in Applied Probability, 7(Suppl.), 106—115.

16.

Marin, J.-M. , Mengersen, K. , & Robert, C.P. (2005). Bayesian modelling and inference on mixtures of distributions. In D.K. Dey & C.R. Rao (Eds.), Handbook of statistics: Vol. 25. Bayesian thinking, modeling and computation (pp. 459—507). Amsterdam: Elsevier.

17.

Spiegelhalter, D. , Thomas, A. , Best, N. , & Lunn, D. (2003). WinBUGS user manual (Version 1.4). Cambridge: Cambridge University, MRC Biostatistics Unit. Available [accessed 25 November 2005] http://www.mrcbsu.cam.ac.uk/bugs

18.

Trafimow, D. (2003). Hypothesis testing and theory evaluation at the boundaries: Surprising insights from Bayes's theorem. Psychological Review, 110, 526—535.

19.

Walker, L.J. (1988). The development of moral reasoning. Annals of Child Development, 5, 33—78.

20.

Walker, L.J. (1996). Kohlberg's cognitive-developmental contributions to moral psychology. World Psychology, 2, 273—296.

21.

Walker, L.J. , Gustafson, P. , & Hennig, K.H. (2001). The consolidation/transition model in moral reasoning development. Developmental Psychology, 37, 187—197.

The application of Bayesian analysis to issues in developmental research

Abstract

Keywords

Get full access to this article

References