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The Asymptotic Proportion of Subdivisions of a 2×2 Table that Result in Simpson's Paradox

Published online by Cambridge University Press:  01 December 1998

PETROS HADJICOSTAS
PETROS HADJICOSTAS
Affiliation:
Department of Public and Business Administration, University of Cyprus, P.O. Box 537, Nicosia CY 1678, Cyprus (e-mail: bapeter@atlas.pba.ucy.ac.cy)
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Abstract

A 2×2 table of nonnegative integers is subdivided additively into n 2×2 subtables of nonnegative integers in an arbitrary way. The first case of Simpson's Paradox (SP) occurs when the determinant of the original table is less than zero, but the determinant of each of the n 2×2 subtables is greater than or equal to zero. The second case of SP occurs when the previous inequalities hold with ‘less than’ and ‘greater than or equal’ replaced by ‘greater than’ and ‘less than or equal’, respectively. For the case n=2, this paper calculates the asymptotic proportion of the subdivisions of the original 2×2 table such that SP occurs. It is shown that this asymptotic proportion is bounded above by 1/12.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 4 , December 1998 , pp. 387 - 396
Copyright
1998 Cambridge University Press

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