Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-07T10:01:30.599Z Has data issue: false hasContentIssue false
  • English
  • Français

A Conservative Inverse Normal Test Procedure for Combining P-Values in Integrative Research

Published online by Cambridge University Press:  01 January 2025

Hilary Saner
Hilary Saner*
Affiliation:
The RAND Corporation
*
Requests for reprints should be sent to H. Saner, The RAND Corporation, P.O. Box 2138, Santa Monica, CA 90407-2138.
Get access Rights & Permissions [Opens in a new window]

Abstract

The use of p-values in combining the results of independent studies often involves studies that are potentially aberrant either in quality or in actual values. A robust data analysis suggests the use of a statistic that takes these aberrations into account by trimming some of the largest and smallest p-values. We present a trimmed statistic based on an inverse cumulative normal transformation of the ordered p-values, together with a simple and convenient method for approximating the distribution and first two moments of this statistic.

Keywords

approximationsmeta-analysisordered p-valuessimulationStouffer's methodtrimmed order statistics
Type
Original Paper
Information
Psychometrika , Volume 59 , Issue 2 , June 1994 , pp. 253 - 267
Copyright
Copyright © 1994 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The author thanks Ingram Olkin, David Rogosa, Jim Hodges and two anonymous reviewers for providing many useful comments and suggestions.

References

Bjérve, S. (1974). Asymptotic results for L-statistics, Berkeley: University of California.Google Scholar
Cramer, H. (1946). Mathematical methods of statistics, Princeton: Princeton University Press.Google Scholar
David, H. A. (1967). Order statistics, New York: John Wiley.Google Scholar
Fisher, R. A. (1925). Statistical methods for research workers, Edinburgh: Oliver and Boyd.Google Scholar
Hedges, L., Olkin, I. (1985). Statistical methods for meta-analysis, New York: Academic Press.Google Scholar
Lin, J. (1989). Approximating the normal tail probability and its inverse for use on a pocket calculator. Applied Statistics, 38, 69–70.CrossRefGoogle Scholar
Page, E. (1979). Approximations to the cumulative normal function and its inverse for use on a pocket calculator. Applied Statistics, 26, 75–76.CrossRefGoogle Scholar
Raudenbush, S. W. (1984). Magnitude of teacher expectancy effects on pupil IQ as a function of the credibility of the expectancy induction: A synthesis of findings from 18 experiments. Journal of Educational Psychology, 76, 85–97.CrossRefGoogle Scholar
Rosenthal, R., Jacobson, L. (1968). Pygmalion in the classroom, New York: Holt, Rinehart and Winston.CrossRefGoogle Scholar
Ross, S. (1984). A first course in probability, London: Macmillan.Google Scholar
Saner, H. L. (1992). Robust methods in meta-analysis. Unpublished doctoral dissertation, Stanford University.Google Scholar
Schmeiser, B. W. (1979). Approximations to the inverse normal function for use on hand calculators. Applied Statistics, 28, 176–176.CrossRefGoogle Scholar
Stigler, S. M. (1969). Linear functions of order statistics. Annal of Mathematical Statistics, 40, 770–788.CrossRefGoogle Scholar
Stouffer, S. A., Suchman, E. A., DeVinney, L. C., Star, S. A., Williams, R. M. Jr. (1949). The American soldier: Adjustment during army life (Vol. 1), Princeton, NJ: Princeton University Press.Google Scholar
Tietjen, G. L., Kahaner, D. K., Beckman, R. J. (1977). Variances and covariances of the normal order statistics for sample sizes 2 to 50. Selected Tables in Mathematical Statistics, 5, 1–73.Google Scholar
Tippett, L. H. C. (1931). The methods of statistics 1st ed.,, London: Williams and Norgate.Google Scholar
Zelen, M., Severo, N. C. (1966). Probability functions. In Abramovitz, M., Stegun, I. A. (Eds.), Handbook of mathematical functions (pp. 200–200). Washington, DC: Department of Commerce of the U.S. Government.Google Scholar