통계적 유의성 문서 원본 보기

{{위키데이터 속성 추적}}

'''통계적 유의성''' (統計的 有意性, statistical significance)은 [[모집단]]에 대한 [[가설]]이 [[확률]]적으로 우연이라고 생각하기 어렵고, 의미가 있다고 생각되는 정도이다.<ref name="Myers et al-p652">{{서적 인용|title=Research design and statistical analysis|last1=Myers|first1=Jerome L.|last2=Well|first2=Arnold D.|year=2010|edition=3rd|publisher=Routledge|location=New York, NY|pages=65–90|chapter=Developing fundamentals of hypothesis testing using the binomial distribution|isbn=978-0-8058-6431-1|last3=Lorch|first3=Robert F. Jr.}}</ref><ref name="Dalgaard">{{서적 인용|title=Introductory Statistics with R|url=https://archive.org/details/introductorystat0000dalg|last=Dalgaard|first=Peter|year=2008|series=Statistics and Computing|publisher=Springer|location=New York|pages=[https://archive.org/details/introductorystat0000dalg/page/n172 155]–56|chapter=Power and the computation of sample size|doi=10.1007/978-0-387-79054-1_9|isbn=978-0-387-79053-4}}</ref> 즉, 어떤 실험 결과 자료를 두고 "통계적으로 유의하다."라고 하는 것은 단순한 우연이라고 생각되지 않을 정도로 의미가 있다는 뜻이다. 반대로 "통계적으로 유의하지 않다."라고 하는 것은 실험 결과가 단순한 우연일 수도 있다는 뜻이다. 통계적 유의성은 [[귀무 가설]]을 기각할 확률인 [[유의 확률]](p-value)을 통해 평가하며, 이 값이 [[유의 수준]] 이하일 때 특별히 유의하다고 말한다.<ref name=":0">{{웹 인용|url=http://www.dartmouth.edu/~matc/X10/Show.htm|title=Statistical Hypothesis Testing|website=www.dartmouth.edu|archive-url=https://web.archive.org/web/20200802050104/http://www.dartmouth.edu/~matc/X10/Show.htm|archive-date=2020-08-02|url-status=dead|access-date=2019-11-11}}</ref><ref name="Johnson">{{저널 인용|title=Revised standards for statistical evidence|journal=Proceedings of the National Academy of Sciences|last=Johnson|first=Valen E.|date=October 9, 2013|volume=110|issue=48|pages=19313–19317|bibcode=2013PNAS..11019313J|doi=10.1073/pnas.1313476110|pmc=3845140|pmid=24218581|doi-access=free}}</ref><ref name="Redmond and Colton">{{서적 인용|title=Biostatistics in Clinical Trials|url=https://archive.org/details/isbn_9780471822110|last1=Redmond|first1=Carol|last2=Colton|first2=Theodore|year=2001|edition=3rd|series=Wiley Reference Series in Biostatistics|publisher=John Wiley & Sons Ltd|location=West Sussex, United Kingdom|pages=[https://archive.org/details/isbn_9780471822110/page/n58 35]–36|chapter=Clinical significance versus statistical significance|isbn=978-0-471-82211-0}}</ref><ref name="Cumming-p27">{{서적 인용|title=Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis|last1=Cumming|first1=Geoff|year=2012|publisher=Routledge|location=New York, USA|pages=27–28}}</ref><ref name="Krzywinski and Altman">{{저널 인용|title=Points of significance: Significance, P values and t-tests|journal=Nature Methods|last1=Krzywinski|first1=Martin|last2=Altman|first2=Naomi|date=30 October 2013|volume=10|issue=11|pages=1041–1042|doi=10.1038/nmeth.2698|pmid=24344377|doi-access=free}}</ref><ref name="Sham and Purcell">{{저널 인용|title=Statistical power and significance testing in large-scale genetic studies|journal=Nature Reviews Genetics|last1=Sham|first1=Pak C.|last2=Purcell|first2=Shaun M|date=17 April 2014|volume=15|issue=5|pages=335–346|doi=10.1038/nrg3706|pmid=24739678|s2cid=10961123}}</ref><ref name="Altman">{{서적 인용|url=https://archive.org/details/isbn_9780412276309|title=Practical Statistics for Medical Research|last1=Altman|first1=Douglas G.|year=1999|publisher=Chapman & Hall/CRC|location=New York, USA|pages=[https://archive.org/details/isbn_9780412276309/page/167 167]|isbn=978-0-412-27630-9|url-access=registration}}</ref><ref name="Devore">{{서적 인용|title=Probability and Statistics for Engineering and the Sciences|last1=Devore|first1=Jay L.|year=2011|edition=8th|publisher=Cengage Learning|location=Boston, MA|pages=300–344|isbn=978-0-538-73352-6}}</ref> 과학적 연구에서 유의 수준은 5%나 그 이하로 설정함이 일반적이다.<ref name="Salkind">{{백과사전 인용|year=2007|title=Significance level|encyclopedia=Encyclopedia of Measurement and Statistics|publisher=SAGE Publications|location=Thousand Oaks, CA|editor-last1=Salkind|editor-first1=Neil J.|volume=3|pages=889–891|isbn=978-1-4129-1611-0|last1=Craparo|first1=Robert M.}}</ref> 적절한 유의수준은 학계의 관례를 따른다.<ref name="Sproull">{{서적 인용|title=Handbook of Research Methods: A Guide for Practitioners and Students in the Social Science|last1=Sproull|first1=Natalie L.|year=2002|edition=2nd|publisher=Scarecrow Press, Inc.|location=Lanham, MD|pages=[https://archive.org/details/handbookofresear00spro/page/49 49–64]|chapter=Hypothesis testing|isbn=978-0-8108-4486-5|chapter-url=https://archive.org/details/handbookofresear00spro/page/49}}</ref>

다만, 검정통계량은 표본 크기의 함수이므로 표본 크기가 커질수록 검정통계량의 값은 커져서 실질적으로는 유의성이 없어도 통계적으로는 유의한 것으로 판정될 수 있다. 이때의 오류는 1종오류가 된다. 즉, 통계적 유의성은 오류가능성을 동반한다.

== 역사 ==
통계적 유의성의 개념을 처음 언급한 이는 [[존 아버스넛]](John Arbuthnot)과 [[피에르시몽 드 라플라스 후작]]이다. 이들은 인간의 성비를 논할 때 신생아의 성비가 1:1일 것이라는 [[귀무 가설]]을 수립하며 [[유의 확률]]의 개념을 처음 도입했다.<ref>{{서적 인용|title=The Descent of Human Sex Ratio at Birth|last1=Brian|first1=Éric|last2=Jaisson|first2=Marie|year=2007|publisher=Springer Science & Business Media|pages=1–25|chapter=Physico-Theology and Mathematics (1710–1794)|isbn=978-1-4020-6036-6}}</ref><ref>{{저널 인용|title=An argument for Divine Providence, taken from the constant regularity observed in the births of both sexes|journal=[[Philosophical Transactions of the Royal Society of London]]|author=John Arbuthnot|url=http://www.york.ac.uk/depts/maths/histstat/arbuthnot.pdf|year=1710|volume=27|issue=325–336|pages=186–190|doi=10.1098/rstl.1710.0011|doi-access=free}}</ref><ref name="Conover1999">{{인용|last=Conover|first=W.J.|title=Practical Nonparametric Statistics|edition=Third|year=1999|publisher=Wiley|isbn=978-0-471-16068-7|pages=157–176|chapter=Chapter 3.4: The Sign Test}}</ref><ref name="Sprent1989">{{인용|last=Sprent|first=P.|title=Applied Nonparametric Statistical Methods|edition=Second|year=1989|publisher=Chapman & Hall|isbn=978-0-412-44980-2}}</ref><ref>{{서적 인용|title=The History of Statistics: The Measurement of Uncertainty Before 1900|last=Stigler|first=Stephen M.|year=1986|publisher=Harvard University Press|pages=[https://archive.org/details/historyofstatist00stig/page/225 225–226]|isbn=978-0-674-40341-3}}</ref><ref name="Bellhouse2001">{{인용|last=Bellhouse|first=David|title=in Statisticians of the Centuries by C.C. Heyde and E. Seneta|year=2001|publisher=Springer|isbn=978-0-387-95329-8|pages=39–42|chapter=John Arbuthnot}}</ref><ref name="Hald1998">{{인용|last=Hald|first=Anders|title=A History of Mathematical Statistics from 1750 to 1930|year=1998|publisher=Wiley|pages=65|chapter=Chapter 4. Chance or Design: Tests of Significance}}</ref>

1925년에는 [[로널드 피셔]]가 유의성 검정(tests of significance)이라는 개념을 도입하였다.<ref name="Cumming">{{서적 인용|title=Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis|last1=Cumming|first1=Geoff|year=2011|series=Multivariate Applications Series|publisher=Routledge|location=East Sussex, United Kingdom|pages=21–52|chapter=From null hypothesis significance to testing effect sizes|isbn=978-0-415-87968-2}}</ref><ref name="Fisher1925">{{서적 인용|url=https://archive.org/details/statisticalmethoe7fish/page/43|title=Statistical Methods for Research Workers|last1=Fisher|first1=Ronald A.|year=1925|publisher=Oliver and Boyd|location=Edinburgh, UK|pages=[https://archive.org/details/statisticalmethoe7fish/page/43 43]|isbn=978-0-05-002170-5}}</ref><ref name="Poletiek">{{서적 인용|title=Hypothesis-testing Behaviour|url=https://archive.org/details/hypothesistestin0000pole|last1=Poletiek|first1=Fenna H.|year=2001|edition=1st|series=Essays in Cognitive Psychology|publisher=Psychology Press|location=East Sussex, United Kingdom|pages=[https://archive.org/details/hypothesistestin0000pole/page/n42 29]–48|chapter=Formal theories of testing|isbn=978-1-84169-159-6}}</ref> 여기서 0.05를 기준으로 이보다 유의 확률이 낮을 때 유의하다고 보며 이후로 통용될 관례를 처음으로 만들었다.<ref name="Quinn">{{서적 인용|url=https://archive.org/details/experimentaldesi0000quin/page/46|title=Experimental Design and Data Analysis for Biologists|last1=Quinn|first1=Geoffrey R.|last2=Keough|first2=Michael J.|year=2002|edition=1st|publisher=Cambridge University Press|location=Cambridge, UK|pages=[https://archive.org/details/experimentaldesi0000quin/page/46 46–69]|isbn=978-0-521-00976-8}}</ref> 1933년에는 [[예지 네이만]]과 [[이건 피어슨]]이 유의 확률을 평가하는 기준점을 [[유의 수준]] <math>\alpha</math>라 명명했다. 이들은 이 값을 데이터 수집 전에 먼저 정하고 수집할 것을 권했다.<ref name="Quinn" /><ref name="Neyman">{{저널 인용|title=The testing of statistical hypotheses in relation to probabilities a priori|journal=Mathematical Proceedings of the Cambridge Philosophical Society|last1=Neyman|first1=J.|last2=Pearson|first2=E.S.|year=1933|volume=29|issue=4|pages=492–510|bibcode=1933PCPS...29..492N|doi=10.1017/S030500410001152X|s2cid=119855116}}</ref>

== 같이 보기 ==
* [[유의 수준]]
* [[유의 확률]]

== 각주 ==
{{각주}}


[[분류:통계학]]
[[분류:가설 검정]]