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Cronbach's alpha
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==History== In his initial 1951 publication, [[Lee Cronbach]] described the coefficient as ''Coefficient'' ''alpha''<ref name=c1951/> and included an additional derivation.<ref name="Cronbach">{{cite journal|first=L.J.|last=Cronbach|title=Coefficient alpha and the internal structure of tests|journal=Psychometrika|volume=16|issue=3|pages=297–334|date=1951|doi=10.1007/BF02310555|s2cid=13820448|hdl=10983/2196|hdl-access=free}}</ref> ''Coefficient alpha'' had been used implicitly in previous studies,<ref name="Hoyt">{{cite journal|first=C.|last=Hoyt|title=Test reliability estimated by analysis of variance|journal=Psychometrika|volume=6|issue=3|pages=153–160|date=1941|doi=10.1007/BF02289270|s2cid=122361318}}</ref><ref name="Guttman">{{cite journal|first=L.|last=Guttman|title=A basis for analyzing test-retest reliability|journal=Psychometrika|volume=10|issue=4|pages=255–282|date=1945|doi=10.1007/BF02288892|pmid=21007983|s2cid=17220260}}</ref><ref name="JF">{{cite journal|last1=Jackson|first1=R. W. B.|last2=Ferguson|first2=G. A.|title=Studies on the reliability of tests|journal=University of Toronto Department of Educational Research Bulletin|volume=12|issue=|pages=132|date=1941}}</ref><ref name="Gulliksen">{{cite book|first=H.|last=Gulliksen|title=Theory of mental tests|publisher=Wiley|date=1950|doi=10.1037/13240-000}}</ref> but his interpretation was thought to be more intuitively attractive relative to previous studies and it became quite popular.<ref>{{Cite journal|last=Cronbach|first=Lee|date=1978|title=Citation Classics|url=http://www.garfield.library.upenn.edu/classics1978/A1978EQ39200002.pdf|journal=[[Current Contents]]|volume=13|issue=8|access-date=2022-10-21|archive-date=2022-10-22|archive-url=https://web.archive.org/web/20221022201253/http://www.garfield.library.upenn.edu/classics1978/A1978EQ39200002.pdf|url-status=live}}</ref> * In 1967, [[Melvin R. Novick|Melvin Novick]] and Charles Lewis proved that it was equal to reliability if the true scores{{efn|The true score is the difference between the score observed during the test or measurement and the error in that observation. See [[classical test theory]] for further information.|name=Footnote|group=lower-roman}} of the compared tests or measures vary by a constant, which is independent of the people measured. In this case, the tests or measurements were said to be "essentially tau-equivalent."<ref name="NL">{{cite journal|last1=Novick|first1=M. R.|last2=Lewis|first2=C.|title=Coefficient alpha and the reliability of composite measurements|journal=Psychometrika|volume=32|issue=1|pages=1–13|date=1967|doi=10.1007/BF02289400|pmid=5232569|s2cid=186226312}}</ref> * In 1978, Cronbach asserted that the reason the initial 1951 [[publication]] was widely cited was "mostly because [he] put a brand name on a common-place coefficient."<ref name="c1978" />{{rp|263}}<ref name="Cho" /> He explained that he had originally planned to name other types of reliability coefficients, such as those used in [[inter-rater reliability]] and [[Repeatability|test-retest reliability]], after consecutive Greek letters (i.e., <math>\beta</math>, <math>\gamma</math>, etc.), but later changed his mind. * Later, in 2004, Cronbach and [[Richard Shavelson]] encouraged readers to use [[generalizability theory]] rather than <math>\rho_{T}</math>. Cronbach opposed the use of the name "Cronbach's alpha" and explicitly denied the existence of studies that had published the general formula of [[Kuder–Richardson formulas|KR-20]] before Cronbach's 1951 publication of the same name.<ref name="c2004" />
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