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When Null Hypothesis Significance Testing Is Unsuitable for Research: A Reassessment

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Szucs, Denes, Ioannidis, John P. A.·2017·Frontiers in Human Neuroscience
DOI 10.3389/fnhum.2017.00390PMC PMC5540883

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Abstract

Null hypothesis significance testing (NHST) has several shortcomings that are likely contributing factors behind the widely debated replication crisis of (cognitive) neuroscience, psychology, and biomedical science in general. We review these shortcomings and suggest that, after sustained negative experience, NHST should no longer be the default, dominant statistical practice of all biomedical and psychological research. If theoretical predictions are weak we should not rely on all or nothing hypothesis tests. Different inferential methods may be most suitable for different types of research questions. Whenever researchers use NHST they should justify its use, and publish pre-study power calculations and effect sizes, including negative findings. Hypothesis-testing studies should be pre-registered and optimally raw data published. The current statistics lite educational approach for students that has sustained the widespread, spurious use of NHST should be phased out.

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Figure 1 NHST concepts make sense in the context of a long run of studies. 3 × 10,000 studies with normally distributed data were simulated for 3 situations (A: True H0 situation: Mean = 0; SD = 1; n = 16. B: Mean = 0.5; SD = 1; n = 16; Power = 0.46. C: Mean = 0.5; SD = 1; n = 32; Power = 0.78.). One sample two-tailed t-tests determined whether the sample means were zero. The red dots in the top panels show t scores for 3 × 1,000 studies (not all studies are shown for better visibility). The vertical dashed lines mark the critical rejection thresholds for H0, t(α/2) for the two-tailed test. The studies producing a t statistic more extreme than these thresholds are declared statistically significant. The middle panels show the distribution of t scores for all 3 × 10,000 studies (bins = 0.1). The bottom panels show the distribution of p-values for all 3 × 10,000 studies (bins = 0.01) and state the proportion of significant studies. The inset in the bottom right panel shows the mean absolute effect sizes in standard deviation units for situations A-C from all significant (Sig.) and non-significant (n.s.) studies with 95% bias corrected and accelerated bootstrap confidence intervals (10,000 permutations). The real effect size was 0 in situation (A) and 0.5 in situations (B,C). Note that the less is the power the more statistically significant studies overstate the effect size. Also note that p-values are randomly distributed and the larger is power the more right skewed is the distribution of p-values. In the true H0 situation the distribution of p-values is uniform between 0 and 1. See further explanation of this figure in Appendix 2 in Supplementary Material.
Figure 1 NHST concepts make sense in the context of a long run of studies. 3 × 10,000 studies with normally distributed data were simulated for 3 situations (A: True H0 situation: Mean = 0; SD = 1; n = 16. B: Mean = 0.5; SD = 1; n = 16; Power = 0.46. C: Mean = 0.5; SD = 1; n = 32; Power = 0.78.). One sample two-tailed t-tests determined whether the sample means were zero. The red dots in the top panels show t scores for 3 × 1,000 studies (not all studies are shown for better visibility). The vertical dashed lines mark the critical rejection thresholds for H0, t(α/2) for the two-tailed test. The studies producing a t statistic more extreme than these thresholds are declared statistically significant. The middle panels show the distribution of t scores for all 3 × 10,000 studies (bins = 0.1). The bottom panels show the distribution of p-values for all 3 × 10,000 studies (bins = 0.01) and state the proportion of significant studies. The inset in the bottom right panel shows the mean absolute effect sizes in standard deviation units for situations A-C from all significant (Sig.) and non-significant (n.s.) studies with 95% bias corrected and accelerated bootstrap confidence intervals (10,000 permutations). The real effect size was 0 in situation (A) and 0.5 in situations (B,C). Note that the less is the power the more statistically significant studies overstate the effect size. Also note that p-values are randomly distributed and the larger is power the more right skewed is the distribution of p-values. In the true H0 situation the distribution of p-values is uniform between 0 and 1. See further explanation of this figure in Appendix 2 in Supplementary Material.CC BY · PubMed Central
Figure 2 The distribution of p-values if the alternative hypothesis (H1) is true. Each line depicts the distribution of p-values resulting from one-sample two-tailed t-tests testing whether the sample mean was zero. Effect sizes (ES) indicate the true sample means for normally distributed data with standard deviation 1. For each effect size one million simulations were run with 16 cases in each simulation. The distribution of the p-value is becoming increasingly right skewed with increasing effect size and power. Note that α, the Type I error rate, is fix irrespective of what p-value is found in an experiment.
Figure 2 The distribution of p-values if the alternative hypothesis (H1) is true. Each line depicts the distribution of p-values resulting from one-sample two-tailed t-tests testing whether the sample mean was zero. Effect sizes (ES) indicate the true sample means for normally distributed data with standard deviation 1. For each effect size one million simulations were run with 16 cases in each simulation. The distribution of the p-value is becoming increasingly right skewed with increasing effect size and power. Note that α, the Type I error rate, is fix irrespective of what p-value is found in an experiment.CC BY · PubMed Central
Figure 3 The relationship of the p-value, test statistic and effect sizes. (A) The relationship of t values, degrees of freedoms and p-values for Pearson correlation studies (df = n–2). (B) The relationship of Pearson correlation (r) values, degrees of freedoms, and p-values [r = t/sqrt(df + t2)]. (C) The relationship of r- and t-value pairs for each degree of freedom at various p-values. The bold black lines mark the usual significance level of α = 0.05. Note that typically only results which exceed the α = 0.05 threshold are reported in papers. Hence, papers mostly report exaggerated effect sizes.
Figure 3 The relationship of the p-value, test statistic and effect sizes. (A) The relationship of t values, degrees of freedoms and p-values for Pearson correlation studies (df = n–2). (B) The relationship of Pearson correlation (r) values, degrees of freedoms, and p-values [r = t/sqrt(df + t2)]. (C) The relationship of r- and t-value pairs for each degree of freedom at various p-values. The bold black lines mark the usual significance level of α = 0.05. Note that typically only results which exceed the α = 0.05 threshold are reported in papers. Hence, papers mostly report exaggerated effect sizes.CC BY · PubMed Central
Figure 4 Illustration of long run False Positive Probability (FRP) and True Positive Probability (TRP) of studies. Let's assume that we run 2 × 100 studies, H0 is true in 100 studies and H1 is true in 100 studies with α = 0.05 and Power = 1−β = 0.6. (A) Shows the outcome of true H0 studies, 5 of the 100 studies coming up statistically significant. (B) Shows the outcome of true H1 studies, 60 of the 100 studies coming up statistically significant [note that realistically the 60 studies would be scattered around just as in panel (A) but for better visibility they are represented in a block]. (C) Illustrates that true H0 and true H1 studies would be indistinguishable. That is, researchers do not know which study tested a true H0 or true H1 situation (i.e., they could not distinguish studies represented by black and gray squares). All they know is whether the outcome of a particular study out of the 200 studies run was statistically significant or not. FRP is the ratio of false positive (H0 is true) statistically significant studies to all statistically significant studies: 5/65 = 0.0769. TRP is the ratio of truly positive (H1 is true) statistically significant studies to all statistically significant studies: 60/65 = 0.9231 = 1 − FRP = 1 − 0.0769.
Figure 4 Illustration of long run False Positive Probability (FRP) and True Positive Probability (TRP) of studies. Let's assume that we run 2 × 100 studies, H0 is true in 100 studies and H1 is true in 100 studies with α = 0.05 and Power = 1−β = 0.6. (A) Shows the outcome of true H0 studies, 5 of the 100 studies coming up statistically significant. (B) Shows the outcome of true H1 studies, 60 of the 100 studies coming up statistically significant [note that realistically the 60 studies would be scattered around just as in panel (A) but for better visibility they are represented in a block]. (C) Illustrates that true H0 and true H1 studies would be indistinguishable. That is, researchers do not know which study tested a true H0 or true H1 situation (i.e., they could not distinguish studies represented by black and gray squares). All they know is whether the outcome of a particular study out of the 200 studies run was statistically significant or not. FRP is the ratio of false positive (H0 is true) statistically significant studies to all statistically significant studies: 5/65 = 0.0769. TRP is the ratio of truly positive (H1 is true) statistically significant studies to all statistically significant studies: 60/65 = 0.9231 = 1 − FRP = 1 − 0.0769.CC BY · PubMed Central

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Research works printed but not linked: 5

  1. Chaisson, 2017, Astronomy Today
  2. Cohen, 1988, Statistical Power Analysis for the Behavioural Sciences
  3. Fisher, 1925, Statistical Methods for Research Workers, First Edition.
  4. Jeffreys, The Theory of Probability.
  5. Smolin, 2006, The Trouble with Physics

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Metadata

Authors
Szucs, D., & Ioannidis, J. P. A.
Affiliations
Stanford Medicine (US)
ORCID
Ioannidis, John P. A.
Venue
Frontiers in Human Neuroscience
Publisher
Frontiers Media SA
Published
2017-08-03
Volume
11
Pages
390-390
ISSN
1662-5161 (ISSN-L)
DOI
10.3389/fnhum.2017.00390
PMC
PMC5540883
OpenAlex
W2951307730
Cited by
298
References
197
Citations by year
2026: 18 · 2025: 28 · 2024: 21 · 2023: 34 · 2022: 44 · 2021: 31 · 2020: 48 · 2019: 39 · 2018: 29 · 2017: 6
FWCI
6.14
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Frontiers in Human Neuroscience (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Apollo (University of Cambridge) (submittedVersion, cc-by)
  • Apollo (cc-by)
Funders
James S. McDonnell Foundation (220020370)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
  • Physical Sciences › Mathematics › Statistics and Probability › Statistics Education and Methodologies
Keywords
null hypothesis significance testing, replication crisis, statistical inference, preregistration, power analysis, effect size, negative results, statistics education, research methodology critique, hypothesis testing

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