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===Parallel analysis===
{{Main|Parallel analysis}}
To carry out the PA test, users compute the eigenvalues for the correlation matrix and plot the values from largest to smallest and then plot a set of random eigenvalues. The number of eigenvalues before the intersection points indicates how many factors to include in your model.<ref name=Humphreys>{{cite journal | last1 = Humphreys | first1 = L. G. | last2 = Montanelli | first2 = R. G. Jr | year = 1975 | title = An investigation of the parallel analysis criterion for determining the number of common factors | url = | journal = Multivariate Behavioral Research | volume = 10 | issue = 2| pages = 193–205 | doi = 10.1207/s15327906mbr1002_5 }}</ref><ref>{{cite journal|last=Horn|first=John L.|title=A rationale and test for the number of factors in factor analysis|journal=Psychometrika|date=1 June 1965|volume=30|issue=2|pages=179–185|doi=10.1007/BF02289447|pmid=14306381}}</ref><ref>{{cite journal|last=Humphreys|first=L. G.|author2=Ilgen, D. R.|title=Note On a Criterion for the Number of Common Factors|journal=Educational and Psychological Measurement|date=1 October 1969|volume=29|issue=3|pages=571–578|doi=10.1177/001316446902900303}}</ref> This procedure can be somewhat arbitrary (i.e. a factor just meeting the cutoff will be included and one just below will not).<ref name =Fabrigar/> Moreover, the method is very sensitive to sample size, with PA suggesting more factors in datasets with larger sample sizes.<ref>{{cite journal | last1 = Warne | first1 = R. G. | last2 = Larsen | first2 = R. | year = 2014 | title = Evaluating a proposed modification of the Guttman rule for determining the number of factors in an exploratory factor analysis | url = | journal = Psychological Test and Assessment Modeling | volume = 56 | issue = | pages = 104–123 }}</ref> Despite its shortcomings, this procedure performs very well in simulation studies and is one of Courtney's recommended procedures.
===Ruscio and Roche's comparison data===
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