View source for Abelson's paradox

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{{Short description|Statistical paradox}}
'''Abelson's paradox''' is an applied statistics [[Philosophy:Paradox|paradox]] identified by Robert P. Abelson.<ref>Abelson, R. P. (1985). "A variance explanation paradox: When a little is a lot." ''Psychological Bulletin'', 97, 129&ndash;133. The phrase "Abelson's paradox," stated explicitly in citations below, is derived from the title of Abelson's article.</ref><ref>Cohen, J. (1988). ''Statistical power analysis for the behavioral sciences'' (2nd ed.). Hillsdale, New York: Erlbaum, p. 535.</ref><ref>Sawilowsky, S., Sawilowsky, J., & Grissom, R. J. (2010). Effect size. In M. Lovric, (Ed.), ''International Encyclopedia of Statistical Science''. NY: Springer.</ref> The paradox pertains to a possible paradoxical relationship between the magnitude of the ''r''<sup>2</sup> (i.e., [[Coefficient of determination|coefficient of determination]]) [[Effect size|effect size]] and its practical meaning.

Abelson's example was obtained from the analysis of the ''r''<sup>2</sup> 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<ref>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.</ref><ref>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}}.</ref><ref>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}}</ref><ref>Marzano, R. J. (2003). ''What works in schools'', Alexandria, Virginia: Association for Supervision and Curriculum Development, p. 190.</ref><ref>Sawilowsky, S. (2005). "Abelson’s paradox and the Michelson-Morley experiment." ''Journal of Modern Applied Statistical Methods'', '''4''', 352.</ref><ref>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}}</ref> 0.003.

== See also ==
* [[List of paradoxes]]

== References ==
{{reflist}}

{{DEFAULTSORT:Abelson's Paradox}}
[[Category:Statistical paradoxes]]



{{Sourceattribution|Abelson's paradox}}