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A Note on Lancaster's Procedure for the Combination of Independent Events
Author(s) -
Koziol James A.
Publication year - 1996
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.4710380603
Subject(s) - mathematics , degrees of freedom (physics and chemistry) , nonparametric statistics , statistics , random variable , cornish , linguistics , physics , philosophy , quantum mechanics
Lancaster (1961) generalized Fisher's (1932) nonparametric procedure for combining independent p‐values by transforming P i from the i ‐th experiment to a chi‐squared random variable with d i degrees of freedom, with d i not necessarily equal to 2. We explore the relationship between Lancaster's procedure and a weighted Lipták procedure (Koziol and Tuckwell, 1994) under which P i is transformed to the standard normal scale. We investigate approximations to the null distribution of Lancaster's test procedure, chi‐squared with d degrees of freedom. We find that the Cornish‐Fisher (1960) expansions and the Lugannani‐Rice (1980) saddlepoint approximations are quite accurate, for non‐integral values of d , and for values of d as low as 20.