Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF

Abstract | References | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] A. W. F. Edwards, The measure of association in a $ 2 \times 2$ table, Roy. Statist. Soc. J. A 126, 109-114 (1963)
  • [2] 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

Additional Information

DOI: https://doi.org/10.1090/qam/99609
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society