Annotated Bibliography of Some Papers on Combining Significances or p-values

A question that comes up repeatedly is how to combine the results of two experiments if all that is known is that one experiment had a n-sigma effect and another experiment had a m-sigma effect. This question is not well-posed: depending on what additional assumptions are made, the preferred answer is different. The note lists some of the more prominent papers on the topic, with some brief comments and excerpts.

[1]  W. Allen Wallis,et al.  Compounding Probabilities from Independent Significance Tests , 1942 .

[2]  F. James.  Statistical Methods in Experimental Physics , 1973 .

[3]  A. Hayes,et al.  Combining independent p values: extensions of the Stouffer and binomial methods. , 2000, Psychological methods.

[4]  S. P. Wright,et al.  Adjusted P-values for simultaneous inference , 1992 .

[5]  W. G. Cochran.  Some Methods for Strengthening the Common χ 2 Tests , 1954 .

[6]  Robert Cousins.  A method which eliminates the discreteness in Poisson confidence limits and lessens the effect of moving cuts specifically to eliminate candidate events , 1994 .

[7]  P. Janot,et al.  Optimally combined confidence limits , 1998 .

[8]  B S Weir,et al.  Truncated product method for combining P‐values , 2002, Genetic epidemiology.

[9]  J. Marden,et al.  Combining Independent Noncentral Chi Squared or $F$ Tests , 1982 .

[10]  M. Whitlock.  Combining probability from independent tests: the weighted Z‐method is superior to Fisher's approach , 2005, Journal of evolutionary biology.

[11]  R. Rosenthal.  Combining results of independent studies. , 1978 .

[12]  Allan Birnbaum,et al.  Combining Independent Tests of Significance , 1954 .

[13]  T. Mathew,et al.  Some Statistical Procedures for Combining Independent Tests , 1993 .

[14]  H. O. Lancaster.  THE COMBINATION OF PROBABILITIES: AN APPLICATION OF ORTHONORMAL FUNCTIONS , 1961 .

[15]  Thomas Lumley,et al.  Kendall's advanced theory of statistics. Volume 2A: classical inference and the linear model. Alan Stuart, Keith Ord and Steven Arnold, Arnold, London, 1998, No. of pages: xiv+885. Price: £85.00. ISBN 0‐340‐66230‐1 , 2000 .

[16]  Henry C. Tuckwell,et al.  A Bayesian method for combining statistical tests , 1999 .

[17]  A. Gardner.  Methods of Statistics , 1941 .

[18]  J. B. Marquette,et al.  Limits on Galactic dark matter with 5 years of EROS SMC data , 2002, astro-ph/0212176.

[19]  B WILKINSON,et al.  A statistical consideration in psychological research. , 1951, Psychological bulletin.

[20]  Margareta Westberg,et al.  Combining independent statistical tests , 1985 .

[21]  Thomas M. Loughin,et al.  A systematic comparison of methods for combining p , 2004, Comput. Stat. Data Anal..

[22]  J. Marden.  Combining Independent One-Sided Noncentral $t$ or Normal Mean Tests , 1985 .

[23]  W. R. van Zwet,et al.  On the Combination of Independent Test Statistics , 1967 .

[24]  R. Fisher.  Statistical Methods for Research Workers , 1971 .

[25]  Arthur Cohen,et al.  Asymptotically Optimal Methods of Combining Tests , 1979 .

[26]  Ramon C. Littell,et al.  Combining One-Sided Binomial Tests , 1986 .

[27]  Frederick Mosteller,et al.  Selected quantitative techniques and attitude measurement , 1954 .

[28]  D R Griffin,et al.  Letters to the editor. , 1974, Science.

[29]  J. Hemelrijk,et al.  Some remarks on the combination of independent tests , 1953 .

[30]  George Casella,et al.  Assessing Evidence in Multiple Hypotheses , 1996 .

[31]  J. Oosterhoff.  Combination of one-sided statistical tests , 1969 .

[32]  Xiao-Hua Zhou,et al.  Statistical Methods for Meta‐Analysis , 2008 .

[33]  Michael D. Perlman,et al.  Combining Independent Chi-Squared Tests , 1978 .

[34]  I. J. Good,et al.  On the Weighted Combination of Significance Tests , 1955 .

[35]  Lancaster Ho.  The combination of probabilities. , 1967 .

[36]  Chien—Pai Han.  Combining Tests for Correlation Coefficients , 1989 .

[37]  E. S. Pearson.  THE PROBABILITY INTEGRAL TRANSFORMATION FOR TESTING GOODNESS OF FIT AND COMBINING INDEPENDENT TESTS OF SIGNIFICANCE , 1938 .

[38]  Frank Bretz,et al.  Adaptive designs based on the truncated product method , 2005, BMC medical research methodology.

[39]  Nikolai Krasnikov,et al.  On the Combining Significances , 2006 .

[40]  Frank Yates,et al.  A note on the application of the combination of probabilities test to a set of 2×2 tables , 1955 .

[41]  Ramon C. Littell,et al.  Asymptotic Optimality of Fisher's Method of Combining Independent Tests , 1971 .

[42]  K. Pearson.  ON A METHOD OF DETERMINING WHETHER A SAMPLE OF SIZE n SUPPOSED TO HAVE BEEN DRAWN FROM A PARENT POPULATION HAVING A KNOWN PROBABILITY INTEGRAL HAS PROBABLY BEEN DRAWN AT RANDOM , 1933 .

[43]  E. S. Pearson,et al.  On questions raised by the combination of tests based on discontinuous distributions. , 1950, Biometrika.

[44]  A. L. Edwards.  The American soldier: Volume I, Adjustment during army life; Volume II, Combat and its aftermath. , 1949 .

[45]  James A. Koziol.  A Note on Lancaster's Procedure for the Combination of Independent Events , 1996 .

[46]  M. Kendall,et al.  Kendall's advanced theory of statistics , 1995 .