When is statistical significance not significant?


The article provides a non-technical introduction to the p value statistics. Its main purpose is to help researchers make sense of the appropriate role of the p value statistics in empirical political science research. On methodological grounds, we use replication, simulations and observational data to show when statistical significance is not significant. We argue that: (1) scholars must always graphically analyze their data before interpreting the p value; (2) it is pointless to estimate the p value for non-random samples; (3) the p value is highly affected by the sample size, and (4) it is pointless to estimate the p value when dealing with data on population.

p value statistics; statistical significance; significance tests

  • ANSCOMBE, F. J. (1973), Graphs in Statistical Analysis, The American Statistician, vol. 27, nº 1, pp. 17-21.
  • BARRO, Robert J., and LEE, Jong-Wha. (2000), International Data on Educational Attainment: Updates and Implications, Center for International Development (CID) -Working Paper nº 42, Harvard University, <http://www.hks.harvard.edu/centers/cid/publications/faculty-working-papers/cid-working-paper-no.-42>
  • BEGG, Collin B. and BERLIN, Jesse A. (1988), Publication Bias: A Problem in Interpreting Medical Data, Journal of the Royal Statistical Society – Series A, vol. 151, nº 3, pp. 419-463.
  • CARVER, Ronald P. (1978), The case against statistical significance testing, Harvard Educational Review, vol. 48, nº 3, pp. 378-399.
  • CARVER, Ronald P. (1993), The Case Against Statistical Significance Testing, Revisited, The Journal of Experimental Education, vol. 61, nº4, pp. 287-292.
  • COHEN, Jacob. (1988), Statistical Power Analysis for the Behavioral Sciences – 2nd Edition. Mahwah, NJ: Lawrence Erlbaum Associates.
  • COURSOUL, Allan and WAGNER, Edwin E. (1986), Effect of Positive Findings on Submission and Acceptance Rates: A Note on Meta-Analysis Bias, Professional Psychology, vol. 17, nº 2, pp. 136-137.
  • CRAMER, Duncan and HOWITT, Dennis L. (2004), The SAGE Dictionary of Statistics: A Practical Resource for Students in the Social Sciences SAGE Publications Ltd., London.
  • DANIEL, Larry G. (1998), Statistical significance testing: A historical overview of misuse and misinterpretation with implications for the editorial policies of educational journals, Research in the Schools, vol. 5, nº 2, pp. 23-32.
  • DAVIDSON, Julia. (2006), Non-probability (non-random) sampling. The Sage Dictonary of Social Research Methods, <http://srmo.sagepub.com/view/the-sage-dictionary-of-social-research-methods/n130.xml>
  • DE LONG, J. Bradford and LANG, Kevin. (1992), Are All Economic Hypotheses False? Journal of Political Economy, vol. 100, nº 6, pp. 1257-1272.
  • EVERITT, Brian S. (2006), The Cambridge Dictionary of Statistics – 3rd edition. New York: Cambridge University Press.
  • EVERITT, Brian S. and SKRONDAL, Anders (2010), The Cambridge Dictionary of Statistics. New York: Cambridge University Press.
  • FISHER, Ronald A. (1923), Statistical Tests of Agreement Between Observation and Hipothesys, Economica, nº 8, pp. 139-147.
  • _____ (1925), Theory of Statistical Estimation, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 22, 700-725.
  • GELMAN, Andrew, CARLIN, John B., STERN, Hal S. and RUBIN, Donald B. (2003), Bayesian Data Analysis – 2nd edition. New York: Chapman and Hall/CRC Texts in Statistical Science.
  • GELMAN, Andrew and STERN, Hal. (2006), The Difference Between "Significant" and "Not Significant" is not Itself Statistically Significant, The American Statistician, vol. 60, nº 4, pp. 328-331.
  • GELMAN, Andrew (2007), Bayesian statistics Basel Statistical Society, Switzerland.
  • GELMAN, Andrew and WEAKLIEM, David. (2009), Of Beauty, Sex and Power, American Scientist, vol. 97, pp. 310-317.
  • GELMAN, Andrew. (2012a), The inevitable problems with statistical significance and 95% intervals, Statistical Modeling, Causal Inference, and Social Science, < http://andrewgelman.com/2012/02/02/the-inevitable-problems-with-statistical-significance-and-95-intervals/>
  • GELMAN, Andrew. (2012b), What do statistical p-values mean when the sample = the population?, Statistical Modeling, Causal Inference, and Social Science, <http://andrewgelman.com/2012/09/what-do-statistical-p-values-mean-when-the-sample-the-population/>
  • GERBER, Alan, GREEN, Donald P. and NICKERSON, David. (2001), Testing for Publication Bias in Political Science, Political Analysis, vol. 9, nº 4, pp. 385-392.
  • GILL, Jeff. (1999), The Insignificance of Null Hypothesis Significance Testing, Political Research Quarterly, vol. 52, nº 3, pp. 647-674.
  • ______ (2007), Bayesian Methods: A Social and Behavioral Sciences Approach – 2nd edition. New York: Chapman and Hall/CRC Statistics in the Social and Behavioral Sciences.
  • GREENWALD, Anthony G. (1975), Consequences of Prejudice Against the Null Hypothesis, Psychological Bulletin, vol. 82, nº 1, pp. 1-12.
  • HAIR, Joseph F., BLACK, William C., BABIN, Barry J., ANDERSON, Rohph E. and TATHAM, Ronald L. (2006), Multivariate Data Analysis – 6ª edition. Upper Saddle River, NJ: Pearson Prentice Hall.
  • HENKEL, Ramon E. (1976), Tests of significance. Newbury Park, CA: Sage.
  • HUBERTY, Carl J. (1993), Historical origins of statistical testing practices: The treatment of Fisher versus Neyman-Pearson views in textbooks, The Journal of Experimental Education, vol. 61, nº 4, pp. 317-333.
  • JORDAN, Michael I. (2009), Bayesian or Frequentist, Which are You?, Department of Electrical Engineering and Computer Sciences, University of California - Berkeley, Videolectures.net, <http://videolectures.net/mlss09uk_jordan_bfway/>
  • KING, Gary, KEOHANE, Robert and VERBA, Sidney. (1994), Designing Social Inquiry: Scientific Inference in Qualitative Research. Princeton. N.J.: Princeton University Press.
  • LUSKIN, Robert C. (1991), Abusus Non Tollit Usum: Standardized Coefficients, Correlations, and R2s, American Journal of Political Science, vol. 35, nº 4, pp. 1032-1046.
  • MAHONEY, Michael J. (1977), Publication Prejudices: An Experimental Study of Confirmatory Bias in the Peer Review System, Cognitive Therapy Research, vol. 1, nº 2, pp. 161–175.
  • McLEAN, James E., and ERNEST, James M. (1998), The Role of Statistical Significance Testing in Educational Research, Research in the Schools, vol. 5, nº 2, pp. 15-22.
  • MOORE, David S. and McCABE, George P. (2006), Introduction to the Practice of Statistics – 5th edition. New York: Freeman.
  • ROGERS, Tom (n.d), Type I and Type II Errors – Making Mistakes in the Justice System, Amazing Applications of Probability and Statistics, <http://www.intuitor.com/statistics/T1T2Errors.html>
  • SAWILOWSKY, Shlomo. (2003), Deconstructing Arguments From The Case Against Hypothesis Testing, Journal of Modern Applied Statistical Methods, vol. 2, nº 2, pp. 467-474.
  • SCARGLE, Jeffrey D. (2000), Publication Bias: The "File-Drawer Problem" in Scientific Inference, The Journal of Scientific Exploration, vol. 14, nº 1, pp. 91-106.
  • SIGELMAN, Lee. (1999), Publication Bias Reconsidered, Political Analysis, vol. 8, nº 2, pp. 201-210.
  • SIMES, John R. (1986), Publication Bias: The Case for an International Registry of Clinical Trials, Journal of Clinical Oncology, vol. 4, nº 10, pp. 1529-1541.
  • SHAVER, J. (1992), What significance testing is, and what it isn't Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA.
  • SMITH, T. M. F. (1983), On the validity of inferences from Non-random Samples, Journal of the Royal Statistical Society – Series A (General), vol. 146, nº 4, pp. 394–403.
  • THE COCHRANE COLLABORATION. (n.d), What is publication bias? The Cochrane Collaboration open learning material, <http://www.cochrane-net.org/openlearning/html/mod15-2.htm>
  • VAN EVERA, Stephen. (1997), Guide to Methods for Students of Political Science Ithaca, NY: Cornell University Press.
  • YOUTUBE. (2010), What the p-value?, <http://www.youtube.com/watch?v=ax0tDcFkPic&feature=related>

Publication Dates

  • Publication in this collection
    20 Aug 2013
  • Date of issue


  • Received
    Aug 2012
  • Accepted
    Apr 2013
Associação Brasileira de Ciência Política Avenida Prof. Luciano Gualberto, 315, sala 2047, CEP 05508-900, Tel.: (55 11) 3091-3754 - São Paulo - SP - Brazil
E-mail: bpsr@brazilianpoliticalsciencareview.org