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Statistical significance

In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis. More precisely, a study's defined significance level, denoted by α {\displaystyle \alpha } , is the probability of the study rejecting the null hypothesis, given that the null hypothesis was assumed to be true; and the p-value of a result, p {\displaystyle p} , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is statistically significant, by the standards of the study, when p α {\displaystyle p\leq \alpha } . The significance level for a study is chosen before data collection, and is typically set to 5% or much lower—depending on the field of study.

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. But if the p-value of an observed effect is less than (or equal to) the significance level, an investigator may conclude that the effect reflects the characteristics of the whole population, thereby rejecting the null hypothesis.

This technique for testing the statistical 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 significance, theoretical significance, or practical significance. For example, the term clinical significance refers to the practical importance of a treatment effect.

Contents

Main article: History of statistics

Statistical significance dates to the 1700s, in the work of John Arbuthnot and Pierre-Simon Laplace, who computed the p-value for the human sex ratio at birth, assuming a null hypothesis of equal probability of male and female births; see p-value § History for details.

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. Fisher suggested a probability of one in twenty (0.05) as a convenient cutoff level to reject the null hypothesis. In a 1933 paper, Jerzy Neyman and Egon Pearson called this cutoff the significance level, which they named α {\displaystyle \alpha } . They recommended that α {\displaystyle \alpha } be set ahead of time, prior to any data collection.

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.

Related concepts

The significance level α {\displaystyle \alpha } is the threshold for p {\displaystyle p} below which the null hypothesis is rejected even though by assumption it were true, and something else is going on. This means that α {\displaystyle \alpha } is also the probability of mistakenly rejecting the null hypothesis, if the null hypothesis is true. This is also called false positive and type I error.

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

In a two-tailed test, the rejection region for a significance level ofα = 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. 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 α {\displaystyle \alpha } .

To determine whether a result is statistically significant, a researcher calculates a p-value, which is the probability of observing an effect of the same magnitude or more extreme given that the null hypothesis is true. The null hypothesis is rejected if the p-value is less than (or equal to) a predetermined level, α {\displaystyle \alpha } . α {\displaystyle \alpha } is also 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 {\displaystyle \alpha } is set to 5%, the conditional probability of a type I error, given that the null hypothesis is true, is 5%, and a statistically significant result is one where the observed p-value is less than (or equal to) 5%. When drawing data from a sample, this means that the rejection region comprises 5% of the sampling distribution. 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. 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. 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.

Significance thresholds in specific fields

Further information: 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). 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.

In other fields of scientific research such as genome-wide association studies, significance levels as low as5×10−8 are not uncommon—as the number of tests performed is extremely large.

Researchers focusing solely on whether their results are statistically significant might report findings that are not substantive and not replicable. 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.

Effect size

Main article: Effect size

Effect size is a measure of a study's practical significance. 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 coefficient between two variables or its square, and other measures.

Reproducibility

Main article: Reproducibility

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

Overuse in some journals

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

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." Some statisticians prefer to use alternative measures of evidence, such as likelihood ratios or Bayes factors. Using Bayesian statistics can avoid confidence levels, but also requires making additional assumptions, and may not necessarily improve practice regarding statistical testing.

The widespread abuse of statistical significance represents an important topic of research in metascience.

Redefining significance

In 2016, the American Statistical Association (ASA) published a statement on p-values, saying that "the widespread use of 'statistical significance' (generally interpreted as 'p ≤ 0.05') as a license for making a claim of a scientific finding (or implied truth) leads to considerable distortion of the scientific process". In 2017, a group of 72 authors proposed to enhance reproducibility by changing the p-value threshold for statistical significance from 0.05 to 0.005. Other researchers responded that imposing a more stringent significance threshold would aggravate problems such as data dredging; alternative propositions are thus to select and justify flexible p-value thresholds before collecting data, or to interpret p-values as continuous indices, thereby discarding thresholds and statistical significance. Additionally, the change to 0.005 would increase the likelihood of false negatives, whereby the effect being studied is real, but the test fails to show it.

In 2019, over 800 statisticians and scientists signed a message calling for the abandonment of the term "statistical significance" in science, and the American Statistical Association published a further official statement declaring (page 2):

We conclude, based on our review of the articles in this special issue and the broader literature, that it is time to stop using the term "statistically significant" entirely. Nor should variants such as "significantly different," " p 0.05 {\displaystyle p\leq 0.05} ," and "nonsignificant" survive, whether expressed in words, by asterisks in a table, or in some other way.

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Wikiversity has learning resources about Statistical significance

Statistical significance
Statistical significance Article Talk Language Watch Edit 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 a study s defined significance level denoted by a displaystyle alpha is the probability of the study rejecting the null hypothesis given that the null hypothesis was assumed to be true 4 and the p value of a result p displaystyle p is the probability of obtaining a result at least as extreme given that the null hypothesis is true 5 The result is statistically significant by the standards of the study when p a displaystyle p leq alpha 6 7 8 9 10 11 12 The significance level for a study is chosen before data collection and is typically set to 5 13 or much lower depending on the field of study 14 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 15 16 But if the p value of an observed effect is less than or equal to the significance level an investigator may conclude that the effect reflects the characteristics of the whole population 1 thereby rejecting the null hypothesis 17 This technique for testing the statistical 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 significance theoretical significance or practical significance 1 2 18 19 For example the term clinical significance refers to the practical importance of a treatment effect 20 Contents 1 History 1 1 Related concepts 2 Role in statistical hypothesis testing 2 1 Significance thresholds in specific fields 3 Limitations 3 1 Effect size 3 2 Reproducibility 4 Challenges 4 1 Overuse in some journals 4 2 Redefining significance 5 See also 6 References 7 Further reading 8 External linksHistory EditMain article History of statistics Statistical significance dates to the 1700s in the work of John Arbuthnot and Pierre Simon Laplace who computed the p value for the human sex ratio at birth assuming a null hypothesis of equal probability of male and female births see p value History for details 21 22 23 24 25 26 27 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 28 29 30 Fisher suggested a probability of one in twenty 0 05 as a convenient cutoff level to reject the null hypothesis 31 In a 1933 paper Jerzy Neyman and Egon Pearson called this cutoff the significance level which they named a displaystyle alpha They recommended that a displaystyle alpha be set ahead of time prior to any data collection 31 32 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 31 Related concepts Edit The significance level a displaystyle alpha is the threshold for p displaystyle p below which the null hypothesis is rejected even though by assumption it were true and something else is going on This means that a displaystyle alpha is also the probability of mistakenly rejecting the null hypothesis if the null hypothesis is true 4 This is also called false positive and type I error Sometimes researchers talk about the confidence level g 1 a instead This is the probability of not rejecting the null hypothesis given that it is true 33 34 Confidence levels and confidence intervals were introduced by Neyman in 1937 35 Role in statistical hypothesis testing EditMain 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 a 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 36 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 a displaystyle alpha To determine whether a result is statistically significant a researcher calculates a p value which is the probability of observing an effect of the same magnitude or more extreme given that the null hypothesis is true 5 12 The null hypothesis is rejected if the p value is less than or equal to a predetermined level a displaystyle alpha a displaystyle alpha is also 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 a displaystyle alpha is set to 5 the conditional probability of a type I error given that the null hypothesis is true is 5 37 and a statistically significant result is one where the observed p value is less than or equal to 5 38 When drawing data from a sample this means that the rejection region comprises 5 of the sampling distribution 39 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 40 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 Significance thresholds in specific fields Edit Further information 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 s of a normal distribution with significance thresholds set at a much stricter level e g 5s 41 42 For instance the certainty of the Higgs boson particle s existence was based on the 5s criterion which corresponds to a p value of about 1 in 3 5 million 42 43 In other fields of scientific research such as genome wide association studies significance levels as low as 5 10 8 are not uncommon 44 45 as the number of tests performed is extremely large Limitations EditResearchers focusing solely on whether their results are statistically significant might report findings that are not substantive 46 and not replicable 47 48 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 49 19 Effect size Edit Main article Effect size Effect size is a measure of a study s practical significance 49 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 coefficient between two variables or its square and other measures 50 Reproducibility Edit Main article Reproducibility A statistically significant result may not be easy to reproduce 48 In particular some statistically significant results will in fact be false positives Each failed attempt to reproduce a result increases the likelihood that the result was a false positive 51 Challenges EditSee also Misuse of p values Overuse in some journals Edit Starting in the 2010s some journals began questioning whether significance testing and particularly using a threshold of a 5 was being relied on too heavily as the primary measure of validity of a hypothesis 52 Some journals encouraged authors to do more detailed analysis than just a statistical significance test In social psychology the journal Basic and Applied Social Psychology banned the use of significance testing altogether from papers it published 53 requiring authors to use other measures to evaluate hypotheses and impact 54 55 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 56 Some statisticians prefer to use alternative measures of evidence such as likelihood ratios or Bayes factors 57 Using Bayesian statistics can avoid confidence levels but also requires making additional assumptions 57 and may not necessarily improve practice regarding statistical testing 58 The widespread abuse of statistical significance represents an important topic of research in metascience 59 Redefining significance Edit In 2016 the American Statistical Association ASA published a statement on p values saying that the widespread use of statistical significance generally interpreted as p 0 05 as a license for making a claim of a scientific finding or implied truth leads to considerable distortion of the scientific process 57 In 2017 a group of 72 authors proposed to enhance reproducibility by changing the p value threshold for statistical significance from 0 05 to 0 005 60 Other researchers responded that imposing a more stringent significance threshold would aggravate problems such as data dredging alternative propositions are thus to select and justify flexible p value thresholds before collecting data 61 or to interpret p values as continuous indices thereby discarding thresholds and statistical significance 62 Additionally the change to 0 005 would increase the likelihood of false negatives whereby the effect being studied is real but the test fails to show it 63 In 2019 over 800 statisticians and scientists signed a message calling for the abandonment of the term statistical significance in science 64 and the American Statistical Association published a further official statement 65 declaring page 2 We conclude based on our review of the articles in this special issue and the broader literature that it is time to stop using the term statistically significant entirely Nor should variants such as significantly different p 0 05 displaystyle p leq 0 05 and nonsignificant survive whether expressed in words by asterisks in a table or in some other way See also Edit Mathematics portal A B testing ABX test Estimation statistics Fisher s method for combining independent tests of significance Look elsewhere effect Multiple comparisons problem Sample size Texas sharpshooter fallacy gives examples of tests where the significance level was set too high References Edit a b c Sirkin R Mark 2005 Two sample t tests Statistics for the Social Sciences 3rd ed Thousand Oaks CA SAGE Publications Inc pp 271 316 ISBN 978 1 412 90546 6 a b Borror Connie M 2009 Statistical decision making The Certified Quality Engineer Handbook 3rd ed Milwaukee WI ASQ Quality Press pp 418 472 ISBN 978 0 873 89745 7 a b Myers Jerome L Well Arnold D Lorch Jr Robert F 2010 Developing fundamentals of hypothesis testing using the binomial distribution Research design and statistical analysis 3rd ed New York NY Routledge pp 65 90 ISBN 978 0 805 86431 1 a b Dalgaard Peter 2008 Power and the computation of sample size Introductory Statistics with R Statistics and Computing New York Springer pp 155 56 doi 10 1007 978 0 387 79054 1 9 ISBN 978 0 387 79053 4 a b Statistical Hypothesis Testing www dartmouth edu Retrieved 2019 11 11 Johnson Valen E October 9 2013 Revised standards for statistical evidence Proceedings of the National Academy of Sciences 110 48 19313 19317 doi 10 1073 pnas 1313476110 PMC 3845140 PMID 24218581 Redmond Carol Colton Theodore 2001 Clinical significance versus statistical significance Biostatistics in Clinical Trials Wiley Reference Series in Biostatistics 3rd ed West Sussex United Kingdom John Wiley amp Sons Ltd pp 35 36 ISBN 978 0 471 82211 0 Cumming Geoff 2012 Understanding The New Statistics Effect Sizes Confidence Intervals and Meta Analysis New York USA Routledge pp 27 28 Krzywinski Martin Altman Naomi 30 October 2013 Points of significance Significance P values and t tests Nature Methods 10 11 1041 1042 doi 10 1038 nmeth 2698 PMID 24344377 Sham Pak C Purcell Shaun M 17 April 2014 Statistical power and significance testing in large scale genetic studies Nature Reviews Genetics 15 5 335 346 doi 10 1038 nrg3706 PMID 24739678 S2CID 10961123 Altman Douglas G 1999 Practical Statistics for Medical Research New York USA Chapman amp Hall CRC pp 167 ISBN 978 0412276309 a b Devore Jay L 2011 Probability and Statistics for Engineering and the Sciences 8th ed Boston MA Cengage Learning pp 300 344 ISBN 978 0 538 73352 6 Craparo Robert M 2007 Significance level In Salkind Neil J ed Encyclopedia of Measurement and Statistics 3 Thousand Oaks CA SAGE Publications pp 889 891 ISBN 978 1 412 91611 0 Sproull Natalie L 2002 Hypothesis testing Handbook of Research Methods A Guide for Practitioners and Students in the Social Science 2nd ed Lanham MD Scarecrow Press Inc pp 49 64 ISBN 978 0 810 84486 5 Babbie Earl R 2013 The logic of sampling The Practice of Social Research 13th ed Belmont CA Cengage Learning pp 185 226 ISBN 978 1 133 04979 1 Faherty Vincent 2008 Probability and statistical significance Compassionate Statistics Applied Quantitative Analysis for Social Services With exercises and instructions in SPSS 1st ed Thousand Oaks CA SAGE Publications Inc pp 127 138 ISBN 978 1 412 93982 9 McKillup Steve 2006 Probability helps you make a decision about your results Statistics Explained An Introductory Guide for Life Scientists 1st ed Cambridge United Kingdom Cambridge University Press pp 44 56 ISBN 978 0 521 54316 3 Myers Jerome L Well Arnold D Lorch Jr Robert F 2010 The t distribution and its applications Research Design and Statistical Analysis 3rd ed New York NY Routledge pp 124 153 ISBN 978 0 805 86431 1 a b Hooper Peter What is P value PDF University of Alberta Department of Mathematical and Statistical Sciences Retrieved November 10 2019 Leung W C 2001 03 01 Balancing statistical and clinical significance in evaluating treatment effects Postgraduate Medical Journal 77 905 201 204 doi 10 1136 pmj 77 905 201 ISSN 0032 5473 PMC 1741942 PMID 11222834 Brian Eric Jaisson Marie 2007 Physico Theology and Mathematics 1710 1794 The Descent of Human Sex Ratio at Birth Springer Science amp Business Media pp 1 25 ISBN 978 1 4020 6036 6 John Arbuthnot 1710 An argument for Divine Providence taken from the constant regularity observed in the births of both sexes PDF Philosophical Transactions of the Royal Society of London 27 325 336 186 190 doi 10 1098 rstl 1710 0011 Conover W J 1999 Chapter 3 4 The Sign Test Practical Nonparametric Statistics Third ed Wiley pp 157 176 ISBN 978 0 471 16068 7 Sprent P 1989 Applied Nonparametric Statistical Methods Second ed Chapman amp Hall ISBN 978 0 412 44980 2 Stigler Stephen M 1986 The History of Statistics The Measurement of Uncertainty Before 1900 Harvard University Press pp 225 226 ISBN 978 0 67440341 3 Bellhouse P 2001 John Arbuthnot in Statisticians of the Centuries by C C Heyde and E Seneta Springer pp 39 42 ISBN 978 0 387 95329 8 Hald Anders 1998 Chapter 4 Chance or Design Tests of Significance A History of Mathematical Statistics from 1750 to 1930 Wiley p 65 Cumming Geoff 2011 From null hypothesis significance to testing effect sizes Understanding The New Statistics Effect Sizes Confidence Intervals and Meta Analysis Multivariate Applications Series East Sussex United Kingdom Routledge pp 21 52 ISBN 978 0 415 87968 2 Fisher Ronald A 1925 Statistical Methods for Research Workers Edinburgh UK Oliver and Boyd pp 43 ISBN 978 0 050 02170 5 Poletiek Fenna H 2001 Formal theories of testing Hypothesis testing Behaviour Essays in Cognitive Psychology 1st ed East Sussex United Kingdom Psychology Press pp 29 48 ISBN 978 1 841 69159 6 a b c Quinn Geoffrey R Keough Michael J 2002 Experimental Design and Data Analysis for Biologists 1st ed Cambridge UK Cambridge University Press pp 46 69 ISBN 978 0 521 00976 8 Neyman J Pearson E S 1933 The testing of statistical hypotheses in relation to probabilities a priori Mathematical Proceedings of the Cambridge Philosophical Society 29 4 492 510 doi 10 1017 S030500410001152X 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 Prel Jean Baptist du Hommel Gerhard Rohrig Bernd Blettner Maria 2009 Confidence Interval or P Value Deutsches Arzteblatt Online 106 19 335 9 doi 10 3238 arztebl 2009 0335 PMC 2689604 PMID 19547734 StatNews 73 Overlapping Confidence Intervals and Statistical Significance Neyman J 1937 Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability Philosophical Transactions of the Royal Society A 236 767 333 380 doi 10 1098 rsta 1937 0005 JSTOR 91337 Meier Kenneth J Brudney Jeffrey L Bohte John 2011 Applied Statistics for Public and Nonprofit Administration 3rd ed Boston MA Cengage Learning pp 189 209 ISBN 978 1 111 34280 7 Healy Joseph F 2009 The Essentials of Statistics A Tool for Social Research 2nd ed Belmont CA Cengage Learning pp 177 205 ISBN 978 0 495 60143 2 McKillup Steve 2006 Statistics Explained An Introductory Guide for Life Scientists 1st ed Cambridge UK Cambridge University Press pp 32 38 ISBN 978 0 521 54316 3 Health David 1995 An Introduction To Experimental Design And Statistics For Biology 1st ed Boston MA CRC press pp 123 154 ISBN 978 1 857 28132 3 Hinton Perry R 2010 Significance error and power Statistics explained 3rd ed New York NY Routledge pp 79 90 ISBN 978 1 848 72312 2 Vaughan Simon 2013 Scientific Inference Learning from Data 1st ed Cambridge UK Cambridge University Press pp 146 152 ISBN 978 1 107 02482 3 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 978 0 300 18884 4 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 978 0 822 94430 0 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 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 Carver Ronald P 1978 The Case Against Statistical Significance Testing Harvard Educational Review 48 3 378 399 doi 10 17763 haer 48 3 t490261645281841 S2CID 16355113 Ioannidis John P A 2005 Why most published research findings are false PLOS Medicine 2 8 e124 doi 10 1371 journal pmed 0020124 PMC 1182327 PMID 16060722 a b Amrhein Valentin Korner Nievergelt Franzi Roth Tobias 2017 The earth is flat p gt 0 05 significance thresholds and the crisis of unreplicable research PeerJ 5 e3544 doi 10 7717 peerj 3544 PMC 5502092 PMID 28698825 a b Hojat Mohammadreza Xu Gang 2004 A Visitor s Guide to Effect Sizes Advances in Health Sciences Education 9 3 241 9 doi 10 1023 B AHSE 0000038173 00909 f6 PMID 15316274 S2CID 8045624 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 978 0 805 81063 9 Stahel Werner 2016 Statistical Issue in Reproducibility Principles Problems Practices and Prospects Reproducibility Principles Problems Practices and Prospects 87 114 doi 10 1002 9781118865064 ch5 ISBN 9781118864975 CSSME Seminar Series The argument over p values and the Null Hypothesis Significance Testing NHST paradigm www education leeds ac uk School of Education University of Leeds Retrieved 2016 12 01 Novella Steven February 25 2015 Psychology Journal Bans Significance Testing Science Based Medicine Woolston Chris 2015 03 05 Psychology journal bans P values Nature 519 7541 9 doi 10 1038 519009f Siegfried Tom 2015 03 17 P value ban small step for a journal giant leap for science Science News Retrieved 2016 12 01 Antonakis John February 2017 On doing better science From thrill of discovery to policy implications PDF The Leadership Quarterly 28 1 5 21 doi 10 1016 j leaqua 2017 01 006 a b c 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 Garcia Perez Miguel A 2016 10 05 Thou Shalt Not Bear False Witness Against Null Hypothesis Significance Testing Educational and Psychological Measurement 77 4 631 662 doi 10 1177 0013164416668232 ISSN 0013 1644 PMC 5991793 PMID 30034024 Ioannidis John P A Ware Jennifer J Wagenmakers Eric Jan Simonsohn Uri Chambers Christopher D Button Katherine S Bishop Dorothy V M Nosek Brian A Munafo Marcus R January 2017 A manifesto for reproducible science Nature Human Behaviour 1 0021 doi 10 1038 s41562 016 0021 PMC 7610724 PMID 33954258 Benjamin Daniel et al 2018 Redefine statistical significance Nature Human Behaviour 1 1 6 10 doi 10 1038 s41562 017 0189 z PMID 30980045 Chawla Dalmeet 2017 One size fits all threshold for P values under fire Nature doi 10 1038 nature 2017 22625 Amrhein Valentin Greenland Sander 2017 Remove rather than redefine statistical significance Nature Human Behaviour 2 1 0224 doi 10 1038 s41562 017 0224 0 PMID 30980046 S2CID 46814177 Vyse Stuart Moving Science s Statistical Goalposts csicop org CSI Retrieved 10 July 2018 McShane Blake Greenland Sander Amrhein Valentin March 2019 Scientists rise up against statistical significance Nature 567 7748 305 307 doi 10 1038 d41586 019 00857 9 PMID 30894741 Wasserstein Ronald L Schirm Allen L Lazar Nicole A 2019 03 20 Moving to a World Beyond p lt 0 05 The American Statistician 73 sup1 1 19 doi 10 1080 00031305 2019 1583913 Further reading EditLydia Denworth A Significant Problem Standard scientific methods are under fire Will anything change Scientific American vol 321 no 4 October 2019 pp 62 67 The use of p values for nearly a century since 1925 to determine statistical significance of experimental results has contributed to an illusion of certainty and to reproducibility crises in many scientific fields There is growing determination to reform statistical analysis Some researchers suggest changing statistical methods whereas others would do away with a threshold for defining significant results p 63 Ziliak Stephen and Deirdre McCloskey 2008 The Cult of Statistical Significance How the Standard Error Costs Us Jobs Justice and Lives Ann Arbor University of Michigan Press 2009 ISBN 978 0 472 07007 7 Reviews and reception compiled by Ziliak Thompson Bruce 2004 The significance crisis in psychology and education Journal of Socio Economics 33 5 607 613 doi 10 1016 j socec 2004 09 034 Chow Siu L 1996 Statistical Significance Rationale Validity and Utility Volume 1 of series Introducing Statistical Methods Sage Publications Ltd ISBN 978 0 7619 5205 3 argues that statistical significance is useful in certain circumstances Kline Rex 2004 Beyond Significance Testing Reforming Data Analysis Methods in Behavioral Research Washington DC American Psychological Association Nuzzo Regina 2014 Scientific method Statistical errors Nature Vol 506 p 150 152 open access Highlights common misunderstandings about the p value Cohen Joseph 1994 1 The earth is round p lt 05 American Psychologist Vol 49 p 997 1003 Reviews problems with null hypothesis statistical testing Amrhein Valentin Greenland Sander McShane Blake 2019 03 20 Scientists rise up against statistical significance Nature 567 7748 305 307 doi 10 1038 d41586 019 00857 9 PMID 30894741 External links EditWikiversity has learning resources about Statistical significanceThe article Earliest Known Uses of Some of the Words of Mathematics S contains an entry on Significance that provides some historical information The Concept of Statistical Significance Testing February 1994 article by Bruce Thompon hosted by the ERIC Clearinghouse on Assessment and Evaluation Washington D C What does it mean for a result to be statistically significant no date an article from the Statistical Assessment Service at George Mason University Washington D C Retrieved from https en wikipedia org w index php title Statistical significance amp oldid 1055311579, wikipedia, wiki, book,

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