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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 r2 (i.e., coefficient of determination) effect size and its practical meaning.

Abelson's example was obtained from the analysis of the r2 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

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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