In This Article Expand or collapse the "in this article" section Inferential Statistics in Psychology

  • Introduction
  • Support for Null Hypothesis Significance Testing
  • Attacks on Null Hypothesis Significance Testing in the 20th Century
  • Attacks on Null Hypothesis Significance Testing in the 21st Century
  • General Overviews of Effect Sizes and Confidence Intervals
  • Support for Confidence Intervals
  • Attacks on Confidence Intervals
  • General Overviews of Bayesian Procedures
  • How to Handle Prior Probabilities in Bayesian Contexts
  • Comparing Bayesian Reasoning against Frequentist Reasoning
  • Power Analysis as a Solution to Underpowered Research
  • Suggestions for Particular Methods Pertaining to Power Analyses
  • A Priori Procedure

Psychology Inferential Statistics in Psychology
David Trafimow
  • LAST REVIEWED: 29 July 2020
  • LAST MODIFIED: 29 July 2020
  • DOI: 10.1093/obo/9780199828340-0264


There are two main inferential statistical camps in psychology: frequentists and Bayesians. Within the frequentist camp, most researchers support the null hypothesis significance testing procedure but support is growing for using confidence intervals. The Bayesian camp holds a diversity of views that cannot be covered adequately here. Many researchers advocate power analysis to determine sample sizes. Finally, the a priori procedure is a promising new way to think about inferential statistics.

Support for Null Hypothesis Significance Testing

The lion’s share of inferential statistical literature in psychology has pertained to null hypothesis significance testing. Because null hypothesis significance testing has been subjected to attacks for approximately a century, it is not surprising that many defensive pieces have also appeared. Abelson 1997; Chow 1998; Fisher 1941; Hagen 1997; and Mulaik, et al. 1997 are some of the more well-known defenses. More balanced perspectives too have been offered that nevertheless remain at least slightly supportive of null hypothesis significance testing, such as Nickerson 2000 and Wilkinson and the Task Force on Statistical Inference 1999.

  • Abelson, Robert P. 1997. A retrospective on the significance test ban of 1999 (if there were no significance tests, they would be invented). In What if there were no significance tests? Edited by Lisa L. Harlow, Stanley A. Mulaik, and James H. Steiger, 117–141. Mahwah, NJ: Erlbaum.

    This famous book chapter supports null hypothesis significance testing.

  • Bakan, David. 1966. The test of significance in psychological research. Psychological Bulletin 66.6: 423–437.

    This early article supports null hypothesis significance testing and warns about misinterpretations.

  • Chow, Siu L. 1998. Précis of statistical significance: Rationale, validity, and utility. Behavioral and Brain Sciences 21.2: 169–239.

    DOI: 10.1017/S0140525X98001162

    This précis uses a more philosophical approach than most pieces to support null hypothesis significance testing.

  • Fisher, Ronald A. 1941. Statistical methods for research workers. New York: G. E. Strechart.

    The eighth of thirteen editions published in at least seven languages. Originally published in 1925 in Edinburgh by Oliver and Boyd; it was the go-to book for inferential statistics for several decades.

  • Hagen, Richard L. 1997. In praise of the null hypothesis statistical test. American Psychologist 52.1: 15–24.

    The article attempts to refute the arguments of Cohen 1994 (cited under Attacks on Null Hypothesis Significance Testing in the 20th Century), arguments against null hypothesis significance testing.

  • Mulaik, Stanley A., Nambury S. Raju, and Richard A. Harshman. 1997. There is a time and a place for significance testing. In What if there were no significance tests? Edited by Lisa L. Harlow, Stanley A. Mulaik, and James H. Steiger, 65–115. Mahwah, NJ: Erlbaum.

    Supports significance testing, based on the underlying assumption is that it is useful to find out, under the sample size used, whether it is possible to detect a deviation from the tested hypothesis.

  • Nickerson, Raymond S. 2000. Null hypothesis significance testing: A review of an old and continuing controversy. Psychological Methods 5.2: 241–301.

    This article provides a more balanced perspective than most about the merits, demerits, and interpretations of significance tests.

  • Wilkinson, Leland, and the Task Force on Statistical Inference. 1999. Statistical methods in psychology journals: Guidelines and explanations. American Psychologist 54.8: 594–604.

    Provides a balanced account or an indecisive account, depending on the reader’s perspective.

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