The posterior probability of a null hypothesis given a statistically significant result
- When researchers carry out a null hypothesis significance test, it is tempting to assume that a statistically significant result lowers Prob(H0), the probability of the null hypothesis being true. Technically, such a statement is meaningless for various reasons: e.g., the null hypothesis does not have a probability associated with it. However, it is possible to relax certain assumptions to compute the posterior probability Prob(H0) under repeated sampling. We show in a step-by-step guide that the intuitively appealing belief, that Prob(H0) is low when significant results have been obtained under repeated sampling, is in general incorrect and depends greatly on: (a) the prior probability of the null being true; (b) type-I error rate, (c) type-II error rate, and (d) replication of a result. Through step-by-step simulations using open-source code in the R System of Statistical Computing, we show that uncertainty about the null hypothesis being true often remains high despite a significant result. To help the reader develop intuitionsWhen researchers carry out a null hypothesis significance test, it is tempting to assume that a statistically significant result lowers Prob(H0), the probability of the null hypothesis being true. Technically, such a statement is meaningless for various reasons: e.g., the null hypothesis does not have a probability associated with it. However, it is possible to relax certain assumptions to compute the posterior probability Prob(H0) under repeated sampling. We show in a step-by-step guide that the intuitively appealing belief, that Prob(H0) is low when significant results have been obtained under repeated sampling, is in general incorrect and depends greatly on: (a) the prior probability of the null being true; (b) type-I error rate, (c) type-II error rate, and (d) replication of a result. Through step-by-step simulations using open-source code in the R System of Statistical Computing, we show that uncertainty about the null hypothesis being true often remains high despite a significant result. To help the reader develop intuitions about this common misconception, we provide a Shiny app (https://danielschad.shinyapps.io/probnull/). We expect that this tutorial will help researchers better understand and judge results from null hypothesis significance tests.…
Author details: | Daniel SchadORCiDGND, Shravan VasishthORCiDGND |
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DOI: | https://doi.org/10.20982/tqmp.18.2.p011 |
ISSN: | 1913-4126 |
ISSN: | 2292-1354 |
Title of parent work (English): | The quantitative methods for psychology |
Publisher: | University of Montreal, Department of Psychology |
Place of publishing: | Montreal |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/04/16 |
Publication year: | 2022 |
Release date: | 2023/11/27 |
Tag: | Bayesian inference; Null hypothesis significance testing; power; statistical |
Volume: | 18 |
Issue: | 2 |
Number of pages: | 12 |
First page: | 130 |
Last Page: | 141 |
Organizational units: | Humanwissenschaftliche Fakultät / Strukturbereich Kognitionswissenschaften / Department Linguistik |
Humanwissenschaftliche Fakultät / Strukturbereich Kognitionswissenschaften / Department Psychologie | |
DDC classification: | 1 Philosophie und Psychologie / 15 Psychologie / 150 Psychologie |
4 Sprache / 41 Linguistik / 410 Linguistik | |
Peer review: | Referiert |
Publishing method: | Open Access / Gold Open-Access |
DOAJ gelistet | |
License (German): | CC-BY - Namensnennung 4.0 International |