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P-value

A p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct.[1] A very small p-value means that such an extreme outcome would be very unlikely under the null hypothesis.[2]

Before a study is conducted, one first chooses a model (the null hypothesis) and an alpha level, most commonly 0.05.[3] The alpha level is not derived from the data but is set by the researcher before examining the data.[4] If the p-value is less than alpha, this is taken to mean that the observed data are sufficiently inconsistent with the null hypothesis for it to be rejected.[3]

However, this does not prove that the null hypothesis is false.[3] The p-value does not, in itself, establish probabilities of hypotheses, and it is a tool for deciding whether to reject the null hypothesis.[3] It does not measure the size of an effect or the importance of a result.[5]

The 0.05 level was originally proposed by Ronald Fisher in 1925.[4] A 2019 task force of the American Statistical Association concluded that p-values and significance tests, when properly applied and interpreted, increase the rigor of the conclusions drawn from data.[6]

Why it matters to investors

One practice that has been particularly criticised is accepting the alternative hypothesis for any p-value nominally below 0.05 without other supporting evidence.[7] Contextual factors must also be considered, such as the design of a study, the quality of the measurements, the external evidence for the phenomenon under study, and the validity of the assumptions behind the data analysis.[7]

According to the American Statistical Association, there is widespread agreement that p-values are often misused and misinterpreted.[7]

Related: Confidence interval, Randomized controlled trial

Sources

  1. Aschwanden C (2015-11-24). "Not Even Scientists Can Easily Explain P-values" . FiveThirtyEight . Archived from the original on 25 September 2019 . Retrieved 11 October 2019 . web.archive.org; Wasserstein RL, Lazar NA (7 March 2016). "The ASA's Statement on p-Values: Context, Process, and Purpose" . The American Statistician . 70 (2): 129– 133. doi : 10.1080/00031305.2016.1154108 . doi.org (via Wikipedia: P-value)
  2. Hubbard R, Lindsay RM (2008). "Why P Values Are Not a Useful Measure of Evidence in Statistical Significance Testing". Theory & Psychology . 18 (1): 69– 88. doi : 10.1177/0959354307086923 . S2CID 143487211 . doi.org; Munafò MR , Nosek BA, Bishop DV, Button KS, Chambers CD, du Sert NP, et al. (January 2017). "A manifesto for reproducible science" . Nature Human Behaviour . 1 (1) 0021. doi : 10.1038/s41562-016-0021 . PMC 7610724 . PMID 33954258 . S2CID 6326747 . ncbi.nlm.nih.gov (via Wikipedia: P-value)
  3. Nuzzo R (February 2014). "Scientific method: statistical errors" . Nature . 506 (7487): 150– 152. Bibcode : 2014Natur.506..150N . doi : 10.1038/506150a . hdl : 11573/685222 . PMID 24522584 . doi.org (via Wikipedia: P-value)
  4. Fisher, R. A. (1992), "Statistical Methods for Research Workers", in Kotz, Samuel; Johnson, Norman L. (eds.), Breakthroughs in Statistics: Methodology and Distribution , Springer Series in Statistics, New York, NY: Springer, pp. 66– 70, doi : 10.1007/978-1-4612-4380-9_6 , ISBN 978-1-4612-4380-9 doi.org (via Wikipedia: P-value)
  5. Wasserstein, Ronald L.; Lazar, Nicole A. (2016-04-02). "The ASA Statement on p -Values: Context, Process, and Purpose" . The American Statistician . 70 (2): 129– 133. doi : 10.1080/00031305.2016.1154108 . ISSN 0003-1305 . S2CID 124084622 . doi.org (via Wikipedia: P-value)
  6. Benjamini, Yoav; De Veaux, Richard D.; Efron, Bradley; Evans, Scott; Glickman, Mark; Graubard, Barry I.; He, Xuming; Meng, Xiao-Li; Reid, Nancy M.; Stigler, Stephen M.; Vardeman, Stephen B.; Wikle, Christopher K.; Wright, Tommy; Young, Linda J.; Kafadar, Karen (2021-10-02). "ASA President's Task Force Statement on Statistical Significance and Replicability" . Chance . 34 (4). Informa UK Limited: 1 doi.org (via Wikipedia: P-value)
  7. Wasserstein RL, Lazar NA (7 March 2016). "The ASA's Statement on p-Values: Context, Process, and Purpose" . The American Statistician . 70 (2): 129– 133. doi : 10.1080/00031305.2016.1154108 . doi.org (via Wikipedia: P-value)

Checked 16 October 2026. How we check sources