# Abelson's paradox

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**Abelson's paradox** is an applied statistics paradox identified by Robert P. Abelson.^{[1]}^{[2]}^{[3]} The paradox pertains to a possible paradoxical relationship between the magnitude of the *r*^{2} (i.e., coefficient of determination) effect size and its practical meaning.

Abelson's example was obtained from the analysis of the *r*^{2} of batting average in baseball and skill level. Although batting average is considered among the most significant characteristics necessary for success, the effect size was only a tiny^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}^{[9]} 0.003.

## References Edit

- ↑ Abelson, R. P. (1985). "A variance explanation paradox: When a little is a lot."
*Psychological Bulletin*, 97, 129–133. The phrase "Abelson's paradox," stated explicitly in citations below, is derived from the title of Abelson's article. - ↑ Cohen, J. (1988).
*Statistical power analysis for the behavioral sciences*(2nd ed.). Hillsdale, New York: Erlbaum, p. 535. - ↑ Sawilowsky, S., Sawilowsky, J., & Grissom, R. J. (2010). Effect size. In M. Lovric, (Ed.),
*International Encyclopedia of Statistical Science*. NY: Springer. - ↑ Ellis, P. D. (2010).
*The essential guide to effect sizes: Statistical power, meta-analysis, and the interpretation of research results*. Cambridge: Cambridge University Press, p. 44. - ↑ Pratkanis, A. R., & Greenwald, A. G. (1989). "A sociocognitive model of attitude structure and function." In
*Advances in Experimental Social Psychology*, Leonard Berkowitz (ed.), Academic Press,**22**, 245-285. ISSN 0065-2601, ISBN 978-0-12-015222-3. - ↑ Borenstein, M. (1998). "The shift from significance testing to effect size estimation." In
*Comprehensive Clinical Psychology*, eds. A. S. Bellack and M. Hersen, Pergamon, Oxford, 313-349. ISBN 978-0-08-042707-2 - ↑ Marzano, R. J. (2003).
*What works in schools*, Alexandria, Virginia: Association for Supervision and Curriculum Development, p. 190. - ↑ Sawilowsky, S. (2005). "Abelson’s paradox and the Michelson-Morley experiment."
*Journal of Modern Applied Statistical Methods*,**4**, 352. - ↑ Roseman, I. J., & Read, S. J. (2007). "Psychologist at play: Abelson's life and contributions to psychological science."
*Perspectives on Psychological Science*,**2**(1), p. 91. DOI:10.1111/j.1745-6916.2007.00031.x

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