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==Factor rotation==
Factor rotation is a commonly employed step in EFA, used to aide interpretation of factor matrixes.<ref name="Browne2001">{{cite journal |last1=Browne |first1=Michael W. |title=An Overview of Analytic Rotation in Exploratory Factor Analysis |journal=Multivariate Behavioral Research |date=January 2001 |volume=36 |issue=1 |pages=111–150 |doi=10.1207/S15327906MBR3601_05|s2cid=9598774 }}</ref><ref name="Sass2010">{{cite journal |last1=Sass |first1=Daniel A. |last2=Schmitt |first2=Thomas A. |title=A Comparative Investigation of Rotation Criteria Within Exploratory Factor Analysis |journal=Multivariate Behavioral Research |date=29 January 2010 |volume=45 |issue=1 |pages=73–103 |doi=10.1080/00273170903504810|pmid=26789085 |s2cid=6458980 }}</ref><ref name="Schmitt2011">{{cite journal |last1=Schmitt |first1=Thomas A. |last2=Sass |first2=Daniel A. |title=Rotation Criteria and Hypothesis Testing for Exploratory Factor Analysis: Implications for Factor Pattern Loadings and Interfactor Correlations |journal=Educational and Psychological Measurement |date=February 2011 |volume=71 |issue=1 |pages=95–113 |doi=10.1177/0013164410387348|s2cid=120709021 }}</ref> For any solution with two or more factors there are an infinite number of orientations of the factors that will explain the data equally well. Because there is no unique solution, a researcher must select a single solution from the infinite possibilities. The goal of factor rotation is to [[Rotation of axes|rotate]] factors in multidimensional space to arrive at a solution with best simple structure
# Each row (denoting the loadings of a single item on all ''m'' factors) contains at least one zero
# Each column (denoting the loadings of all items on a single factor) contains at least ''m'' zeros
# All pairs of columns (i.e., factors) have several rows (i.e., items) with a zero loading in one column but not the other (i.e., all pairs of factors have several items that can differentiate the factors)
# If ''m'' ≥ 4, all pairs of columns should have several rows with zeros in both columns
# All pairs of columns should have few rows with non-zero loadings in both columns (i.e., there should be few items with cross-loadings)
There are two main types of factor rotation: [[Orthogonality|orthogonal]] and [[Angle#Types of angles|oblique]] rotation.
===Orthogonal rotation===
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The usefulness of an unrotated solution was emphasized by a [[meta analysis]] of studies of cultural differences. This revealed that many published studies of cultural differences have given similar factor analysis results, but rotated differently. Factor rotation has obscured the similarity between the results of different studies and the existence of a strong general factor, while the unrotated solutions were much more similar.<ref name="Fog2020">{{cite journal|last=Fog|first=A. |title=A Test of the Reproducibility of the Clustering of Cultural Variables |journal=Cross-Cultural Research |year=2020 |volume=55 |pages=29–57 |doi=10.1177/1069397120956948|s2cid=224909443 }}</ref><ref>{{Cite journal|title=Examining Factors in 2015 TIMSS Australian Grade 4 Student Questionnaire Regarding Attitudes Towards Science Using Exploratory Factor Analysis (EFA)|url=https://twasp.info/journal/gi93583P/examining-factors-in-2015-timss-australian-grade-4-student-questionnaire-regarding-attitudes-towards-science-using-exploratory-factor-analysis-efa|journal=North American Academic Research|volume=3}}</ref>
==Factor interpretation==
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