Equivalent changes/differences for percentages and probabilities
Author:
Yew-Kwang Ng
Journal:
Quart. Appl. Math. 49 (1991), 289-301
DOI:
https://doi.org/10.1090/qam/99609
MathSciNet review:
QAM99609
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Abstract |
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Abstract: For percentages and probabilities or other fractions that have to lie between zero and one, it is not legitimate to take equal proportionate or absolute differences for two variables to register equivalent changes, since this may require one variable to exceed one. Reasonable properties for equivalent changes including Interchangeability, Parity, Identity, Differentiability, Monotonicity, Complementarity, Anonymity, and Transitivity are proposed. A specific function satisfying all these properties is provided and the question of the uniqueness of this function is discussed. The acceptance of the proposed function may lead to widespread practical application.
A. W. F. Edwards, The measure of association in a $2 \times 2$ table, Roy. Statist. Soc. J. A 126, 109–114 (1963)
- Leo A. Goodman and William H. Kruskal, Measures of association for cross classifications, Springer Series in Statistics, vol. 1, Springer-Verlag, New York-Berlin, 1979. With a foreword by Stephen E. Fienberg. MR 553108
A. W. F. Edwards, The measure of association in a $2 \times 2$ table, Roy. Statist. Soc. J. A 126, 109–114 (1963)
L. A. Goodman and W. H. Kruskal, Measures of Association for Cross Classifications, Springer-Verlag, New York, 1979
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Article copyright:
© Copyright 1991
American Mathematical Society