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=== Controversy around overuse in some journals ===
=== Controversy around overuse in some journals ===
Starting in the 2010s, some journals began questioning whether significance testing, and particularly using a threshold of α=5%, was being relied on too heavily as the primary measure of validity of a hypothesis.<ref>{{Cite web|url=http://www.education.leeds.ac.uk/events/2015/cssme-seminar-series-the-argument-over-p-values-and-the-null-hypothesis-significance-testing-nhst-paradigm|title=CSSME Seminar Series: The argument over p-values and the Null Hypothesis Significance Testing (NHST) paradigm » School of Education » University of Leeds|website=www.education.leeds.ac.uk|access-date=2016-12-01}}</ref> Some journals encouraged authors to do more detailed analysis than just a statistical significance test. In social psychology, the Journal of Basic and Applied Social Psychology banned the use of significance testing altogether from papers it published,<ref>{{cite web | title=Psychology Journal Bans Significance Testing | author=Novella, Steven | date=February 25, 2015 | publisher=Science-Based Medicine | url=https://www.sciencebasedmedicine.org/psychology-journal-bans-significance-testing}}</ref> requiring authors to use other measures to evaluate hypotheses and impact.<ref>{{Cite journal|last=Woolston|first=Chris|date=2015-03-05|title=Psychology journal bans P values|url=http://www.nature.com/news/psychology-journal-bans-p-values-1.17001|journal=Nature|volume=519|issue=7541|pages=9–9|doi=10.1038/519009f}}</ref><ref>{{Cite news|url=https://www.sciencenews.org/blog/context/p-value-ban-small-step-journal-giant-leap-science|title=P value ban: small step for a journal, giant leap for science|last=Siegfried|first=Tom|date=2015-03-17|newspaper=Science News|access-date=2016-12-01}}</ref>
Starting in the 2010s, some journals began questioning whether significance testing, and particularly using a threshold of α=5%, was being relied on too heavily as the primary measure of validity of a hypothesis.<ref>{{Cite web|url=http://www.education.leeds.ac.uk/events/2015/cssme-seminar-series-the-argument-over-p-values-and-the-null-hypothesis-significance-testing-nhst-paradigm|title=CSSME Seminar Series: The argument over p-values and the Null Hypothesis Significance Testing (NHST) paradigm » School of Education » University of Leeds|website=www.education.leeds.ac.uk|access-date=2016-12-01}}</ref> Some journals encouraged authors to do more detailed analysis than just a statistical significance test. In social psychology, the Journal of Basic and Applied Social Psychology banned the use of significance testing altogether from papers it published,<ref>{{cite web | title=Psychology Journal Bans Significance Testing | author=Novella, Steven | date=February 25, 2015 | publisher=Science-Based Medicine | url=https://www.sciencebasedmedicine.org/psychology-journal-bans-significance-testing}}</ref> requiring authors to use other measures to evaluate hypotheses and impact.<ref>{{Cite journal|last=Woolston|first=Chris|date=2015-03-05|title=Psychology journal bans P values|url=http://www.nature.com/news/psychology-journal-bans-p-values-1.17001|journal=Nature|volume=519|issue=7541|pages=9–9|doi=10.1038/519009f}}</ref><ref>{{Cite news|url=https://www.sciencenews.org/blog/context/p-value-ban-small-step-journal-giant-leap-science|title=P value ban: small step for a journal, giant leap for science|last=Siegfried|first=Tom|date=2015-03-17|newspaper=Science News|access-date=2016-12-01}}</ref>

Other editors, commenting on this ban have noted: "Banning the reporting of p-values, as Basic and Applied Social Psychology recently did, is not going to solve the problem because it is merely treating a symptom of the problem. There is nothing wrong with hypothesis testing and p-values per se as long as authors, reviewers, and action editors use them correctly." <ref>{{Cite journal|last=Antonakis|first=John|date=February 2017|title=On doing better science: From thrill of discovery to policy implications|url=http://www.sciencedirect.com/science/article/pii/S104898431730070X|journal=The Leadership Quarterly|volume=28|issue=1|pages=5–21|doi=10.1016/j.leaqua.2017.01.006}}</ref> Moreover, using Bayesian statistics, as some suggest comes with additional assumptions <ref>{{Cite journal|last=Wasserstein|first=Ronald L.|last2=Lazar|first2=Nicole A.|date=2016-04-02|title=The ASA's Statement on p-Values: Context, Process, and Purpose|url=http://dx.doi.org/10.1080/00031305.2016.1154108|journal=The American Statistician|volume=70|issue=2|pages=129–133|doi=10.1080/00031305.2016.1154108|issn=0003-1305}}</ref>, and may not necessarily improve practice regarding statistical testing.<ref>{{Cite journal|last=García-Pérez|first=Miguel A.|date=2016-10-05|title=Thou Shalt Not Bear False Witness Against Null Hypothesis Significance Testing|url=http://journals.sagepub.com/doi/abs/10.1177/0013164416668232|journal=Educational and Psychological Measurement|language=en|pages=0013164416668232|doi=10.1177/0013164416668232|issn=0013-1644}}</ref>


==See also==
==See also==

Revision as of 20:18, 24 June 2017

In statistical hypothesis testing,[1][2] a result has statistical significance when it is very unlikely to have occurred given the null hypothesis.[3] More precisely, the significance level defined for a study, α, is the probability of the study rejecting the null hypothesis, given that it were true;[4] and the p-value of a result, p, is the probability of obtaining a result at least as extreme, given that the null hypothesis were true. The result is statistically significant, by the standards of the study, when p < α. [5][6][7][8][9][10][11]

The significance level for a study is chosen before data collection, and typically set to 5%[12] or much lower, depending on the field of study.[13] In any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone.[14][15] But if the p-value of an observed effect is less than the significance level, an investigator may conclude that the effect reflects the characteristics of the whole population,[1] thereby rejecting the null hypothesis.[16] This technique for testing the significance of results was developed in the early 20th century.

The term significance does not imply importance here, and the term statistical significance is not the same as research, theoretical, or practical significance.[1][2][17] For example, the term clinical significance refers to the practical importance of a treatment effect.

History

Main article: History of statistics

In 1925, Ronald Fisher advanced the idea of statistical hypothesis testing, which he called "tests of significance", in his publication Statistical Methods for Research Workers.[18][19][20] Fisher suggested a probability of one in twenty (0.05) as a convenient cutoff level to reject the null hypothesis.[21] In a 1933 paper, Jerzy Neyman and Egon Pearson called this cutoff the significance level, which they named α. They recommended that α be set ahead of time, prior to any data collection.[21][22]

Despite his initial suggestion of 0.05 as a significance level, Fisher did not intend this cutoff value to be fixed. In his 1956 publication Statistical methods and scientific inference, he recommended that significance levels be set according to specific circumstances.[21]

Related concepts

The significance level α is the threshold for p below which the experimenter assumes the null hypothesis is false, and something else is going on. This means α is also the probability of mistakenly rejecting the null hypothesis, if the null hypothesis is true.[23]

Sometimes researchers talk about the confidence level γ = (1 − α) instead. This is the probability of not rejecting the null hypothesis given that it is true. [24][25] Confidence levels and confidence intervals were introduced by Neyman in 1937.[26]

Role in statistical hypothesis testing

Main articles: Statistical hypothesis testing, Null hypothesis, Alternative hypothesis, p-value, and Type I and type II errors
In a two-tailed test, the rejection region for a significance level of α=0.05 is partitioned to both ends of the sampling distribution and makes up 5% of the area under the curve (white areas).

Statistical significance plays a pivotal role in statistical hypothesis testing. It is used to determine whether the null hypothesis should be rejected or retained. The null hypothesis is the default assumption that nothing happened or changed.[27] For the null hypothesis to be rejected, an observed result has to be statistically significant, i.e. the observed p-value is less than the pre-specified significance level.

To determine whether a result is statistically significant, a researcher calculates a p-value, which is the probability of observing an effect given that the null hypothesis is true.[11] The null hypothesis is rejected if the p-value is less than a predetermined level, α. α is called the significance level, and is the probability of rejecting the null hypothesis given that it is true (a type I error). It is usually set at or below 5%.

For example, when α is set to 5%, the conditional probability of a type I error, given that the null hypothesis is true, is 5%,[28] and a statistically significant result is one where the observed p-value is less than 5%.[29] When drawing data from a sample, this means that the rejection region comprises 5% of the sampling distribution.[30] These 5% can be allocated to one side of the sampling distribution, as in a one-tailed test, or partitioned to both sides of the distribution as in a two-tailed test, with each tail (or rejection region) containing 2.5% of the distribution.

The use of a one-tailed test is dependent on whether the research question or alternative hypothesis specifies a direction such as whether a group of objects is heavier or the performance of students on an assessment is better.[3] A two-tailed test may still be used but it will be less powerful than a one-tailed test because the rejection region for a one-tailed test is concentrated on one end of the null distribution and is twice the size (5% vs. 2.5%) of each rejection region for a two-tailed test. As a result, the null hypothesis can be rejected with a less extreme result if a one-tailed test was used.[31] The one-tailed test is only more powerful than a two-tailed test if the specified direction of the alternative hypothesis is correct. If it is wrong, however, then the one-tailed test has no power.

Stringent significance thresholds in specific fields

Main articles: Standard deviation and Normal distribution

In specific fields such as particle physics and manufacturing, statistical significance is often expressed in multiples of the standard deviation or sigma (σ) of a normal distribution, with significance thresholds set at a much stricter level (e.g. 5σ).[32][33] For instance, the certainty of the Higgs boson particle's existence was based on the 5σ criterion, which corresponds to a p-value of about 1 in 3.5 million.[33][34]

In other fields of scientific research such as genome-wide association studies significance levels as low as 5×10−8 are not uncommon.[35][36]

Limitations

Researchers focusing solely on whether their results are statistically significant might report findings that are not substantive[37] and not replicable.[38] There is also a difference between statistical significance and practical significance. A study that is found to be statistically significant, may not necessarily be practically significant. [39]

Effect size

Main article: Effect size

Effect size is a measure of a study's practical significance. [40] A statistically significant result may have a weak effect. To gauge the research significance of their result, researchers are encouraged to always report an effect size along with p-values. An effect size measure quantifies the strength of an effect, such as the distance between two means in units of standard deviation (cf. Cohen's d), the correlation between two variables or its square, and other measures.[41]

Reproducibility

Main article: Reproducibility

A statistically significant result may not be easy to reproduce.[citation needed] In particular, some statistically significant results will in fact be false positives. Each failed attempt to reproduce a result increases the belief that the result was a false positive. [42]

Controversy around overuse in some journals

Starting in the 2010s, some journals began questioning whether significance testing, and particularly using a threshold of α=5%, was being relied on too heavily as the primary measure of validity of a hypothesis.[43] Some journals encouraged authors to do more detailed analysis than just a statistical significance test. In social psychology, the Journal of Basic and Applied Social Psychology banned the use of significance testing altogether from papers it published,[44] requiring authors to use other measures to evaluate hypotheses and impact.[45][46]

Other editors, commenting on this ban have noted: "Banning the reporting of p-values, as Basic and Applied Social Psychology recently did, is not going to solve the problem because it is merely treating a symptom of the problem. There is nothing wrong with hypothesis testing and p-values per se as long as authors, reviewers, and action editors use them correctly." [47] Moreover, using Bayesian statistics, as some suggest comes with additional assumptions [48], and may not necessarily improve practice regarding statistical testing.[49]

See also

References

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  24. ^ "Conclusions about statistical significance are possible with the help of the confidence interval. If the confidence interval does not include the value of zero effect, it can be assumed that there is a statistically significant result." "Confidence Interval or P-Value?". doi:10.3238/arztebl.2009.0335. {{cite journal}}: Cite journal requires |journal= (help)
  25. ^ StatNews #73: Overlapping Confidence Intervals and Statistical Significance
  26. ^ Neyman, J. (1937). "Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability". Philosophical Transactions of the Royal Society A. 236: 333–380. doi:10.1098/rsta.1937.0005.
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  33. ^ a b Bracken, Michael B. (2013). Risk, Chance, and Causation: Investigating the Origins and Treatment of Disease (1st ed.). New Haven, CT: Yale University Press. pp. 260–276. ISBN 0-300-18884-6.
  34. ^ Franklin, Allan (2013). "Prologue: The rise of the sigmas". Shifting Standards: Experiments in Particle Physics in the Twentieth Century (1st ed.). Pittsburgh, PA: University of Pittsburgh Press. pp. Ii–Iii. ISBN 0-822-94430-8.
  35. ^ Clarke, GM; Anderson, CA; Pettersson, FH; Cardon, LR; Morris, AP; Zondervan, KT (February 6, 2011). "Basic statistical analysis in genetic case-control studies". Nature Protocols. 6 (2): 121–33. doi:10.1038/nprot.2010.182. PMC 3154648. PMID 21293453. {{cite journal}}: |access-date= requires |url= (help)
  36. ^ Barsh, GS; Copenhaver, GP; Gibson, G; Williams, SM (July 5, 2012). "Guidelines for Genome-Wide Association Studies". PLoS Genetics. 8 (7): e1002812. doi:10.1371/journal.pgen.1002812. PMC 3390399. PMID 22792080.{{cite journal}}: CS1 maint: unflagged free DOI (link)
  37. ^ Carver, Ronald P. (1978). "The Case Against Statistical Significance Testing". Harvard Educational Review. 48: 378–399.
  38. ^ Ioannidis, John P. A. (2005). "Why most published research findings are false". PLoS Medicine. 2: e124. doi:10.1371/journal.pmed.0020124. PMC 1182327. PMID 16060722.{{cite journal}}: CS1 maint: unflagged free DOI (link)
  39. ^ Hojat, Mohammadreza; Xu, Gang (2004). "A Visitor's Guide to Effect Sizes". Advances in Health Sciences Education. {{cite journal}}: |access-date= requires |url= (help)
  40. ^ Hojat, Mohammadreza; Xu, Gang (2004). "A Visitor's Guide to Effect Sizes". Advances in Health Sciences Education. {{cite journal}}: |access-date= requires |url= (help)
  41. ^ Pedhazur, Elazar J.; Schmelkin, Liora P. (1991). Measurement, Design, and Analysis: An Integrated Approach (Student ed.). New York, NY: Psychology Press. pp. 180–210. ISBN 0-805-81063-3.
  42. ^ Stahel, Werner (2016). "Statistical Issue in Reproducibility". Principles, Problems, Practices, and Prospects Reproducibility: Principles, Problems, Practices, and Prospects: 87-114. {{cite journal}}: |access-date= requires |url= (help)
  43. ^ "CSSME Seminar Series: The argument over p-values and the Null Hypothesis Significance Testing (NHST) paradigm  » School of Education  » University of Leeds". www.education.leeds.ac.uk. Retrieved 2016-12-01.
  44. ^ Novella, Steven (February 25, 2015). "Psychology Journal Bans Significance Testing". Science-Based Medicine.
  45. ^ Woolston, Chris (2015-03-05). "Psychology journal bans P values". Nature. 519 (7541): 9–9. doi:10.1038/519009f.
  46. ^ Siegfried, Tom (2015-03-17). "P value ban: small step for a journal, giant leap for science". Science News. Retrieved 2016-12-01.
  47. ^ Antonakis, John (February 2017). "On doing better science: From thrill of discovery to policy implications". The Leadership Quarterly. 28 (1): 5–21. doi:10.1016/j.leaqua.2017.01.006.
  48. ^ Wasserstein, Ronald L.; Lazar, Nicole A. (2016-04-02). "The ASA's Statement on p-Values: Context, Process, and Purpose". The American Statistician. 70 (2): 129–133. doi:10.1080/00031305.2016.1154108. ISSN 0003-1305.
  49. ^ García-Pérez, Miguel A. (2016-10-05). "Thou Shalt Not Bear False Witness Against Null Hypothesis Significance Testing". Educational and Psychological Measurement: 0013164416668232. doi:10.1177/0013164416668232. ISSN 0013-1644.

Further reading

External links

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