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Sample size in factor analysis.

MacCallum, Robert C., Widaman, Keith F., Zhang, Shaobo, Hong, Sehee·1999·Psychological Methods

DOI 10.1037/1082-989x.4.1.84

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Abstract

The factor analysis literature includes a range of recommendations regarding the minimum sample size necessary to obtain factor solutions that are adequately stable and that correspond closely to population factors. A fundamental misconception about this issue is that the minimum sample size, or the minimum ratio of sample size to the number of variables, is invariant across studies. In fact, necessary sample size is dependent on several aspects of any given study, including the level of communality of the variables and the level of overdetermination of the factors. The authors present a theoretical and mathematical framework that provides a basis for understanding and predicting these effects. The hypothesized effects are verified by a sampling study using artificial data. Results demonstrate the lack of validity of common rules of thumb and provide a basis for establishing guidelines for sample size in factor analysis. In the factor analysis literature, much attention has be;;n given to the issue of sample size. It is widely understood that the use of larger samples in applica-tions of factor analysis tends to provide results such that sample factor loadings are more precise estimates of population loadings and are also more stable, or les s variable, across repeated sampling. Despite gen-eral agreement on this matter, there is considerable di'/ergence of opinion and evidence about the ques-tion of how large a sample is necessary to adequately acnieve these objectives. Recommendations and find-ings about this issue are diverse and often contradic-tory. The objectives of this article are to provide a

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Authors: MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S.
Affiliations: The Ohio State University (US)
University of California, Riverside (US)
ORCID: Widaman, Keith F.
Zhang, Shaobo
Hong, Sehee
Venue: Psychological Methods
Publisher: American Psychological Association (APA)
Published: 1999-03
Volume: 4
Issue: 1
Pages: 84-99
ISSN: 1082-989X (ISSN-L)
1939-1463
DOI: 10.1037/1082-989x.4.1.84
OpenAlex: W2122376319
Cited by: 5,497
References: 50
Citations by year: 2026: 456 · 2025: 418 · 2024: 359 · 2023: 311 · 2022: 359 · 2021: 396 · 2020: 413 · 2019: 318 · 2018: 286 · 2017: 276 · 2016: 259 · 2015: 226 · 2014: 230 · 2013: 233 · 2012: 177
FWCI: 27.00
Type: journal article
Language: en
Open access: closed
Locations: Psychological Methods (publishedVersion)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords: sample size, factor analysis, minimum sample size, communality, rules of thumb

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