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On Asymptotically Distribution‐Free Confidence Bounds for P (X 1 ≥X 2 ) Based on Samples not Necessarily Independent
Author(s) -
Hilgers R.
Publication year - 1981
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710230702
Subject(s) - mathematics , statistics , random variable , combinatorics , confidence interval , sign (mathematics) , statistic , distribution (mathematics) , discrete mathematics , mathematical analysis
If X 1 , X 2 , denote the random variables of measurement under two treatments then the probability P ( X 1 ≥ X 2 ) is a quantity of great practical interest, especially if we consider both to be measured for the same unity. In this case the random variables cannot be assumed to be independent any longer. The following paper describes a procedure to compute approximate confidence bounds for P ( X 1 ≥ X 2 ) where correlations between X 1 , X 2 are admitted as well as between replications of the X j . There is some relation to the FRIEDMAN‐statistic with or without repeated measurements and as a special case to the sign‐test. Application may be extended to ordinal data.