Abelson's paradox

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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[1] 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.

[2] Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, New York: Erlbaum, p. 535.

[3] Sawilowsky, S., Sawilowsky, J., & Grissom, R. J. (2010). Effect size. In M. Lovric, (Ed.), International Encyclopedia of Statistical Science. NY: Springer.

[4] 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.

[5] 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.

[6] 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

[7] Marzano, R. J. (2003). What works in schools, Alexandria, Virginia: Association for Supervision and Curriculum Development, p. 190.

[8] Sawilowsky, S. (2005). "Abelson’s paradox and the Michelson-Morley experiment." Journal of Modern Applied Statistical Methods, 4, 352.

[9] 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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See also

References