Restricted accessResearch articleFirst published online 2012-6
Impact of Outliers Arising From Unintended and Unknowingly Included Subpopulations on the Decisions About the Number of Factors in Exploratory Factor Analysis
There is a lack of research on the effects of outliers on the decisions about the number of factors to retain in an exploratory factor analysis, especially for outliers arising from unintended and unknowingly included subpopulations. The purpose of the present research was to investigate how outliers from an unintended and unknowingly included subpopulation affected the decisions about the number of factors to retain using four commonly used methods separately. The results showed that all the decision methods could provide biased results and the number of factors could be inflated, deflated, or remain the same depending on the decision methods used and outlier conditions. The findings also revealed that symmetric outliers did not affect the three principal component analysis–based methods but affected chi-square (ML) sequential tests. Finally, sample size did not play a role in the effect of outliers.
AnscombeF. J. (1960). Rejection of outliers. Technometrics, 2, 123-147.
2.
BalakrishnanN.ChildsA. (2001). Outlier. In HazewinkelM. (Ed.), Encyclopaedia of mathematics (online version). New York, NY: Springer-Verlag. Retrieved from http://eom.springer.de/
3.
BarnettV. (1999). Nonattending respondent effects on internal consistency of self-administered surveys: A Monte Carlo simulation study. Educational and Psychological Measurement, 59, 38-46.
4.
BarnettV.LewisT. (1978). Outliers in statistical data (1st ed.). New York, NY: Wiley.
5.
BarnettV.LewisT. (1994). Outliers in statistical data (3rd ed.). New York, NY: Wiley.
6.
BlairR. C.HigginsJ. J. (1980). The power of t and Wilcoxon statistics: A comparison. Evaluation Review, 4, 645-656.
7.
BlischkeW. S. (1978). Mixtures of distributions. In KruskalW. H.TanurJ. M. (Eds.), International encyclopedia of statistics (Vol. 1, pp. 174-180). New York, NY: Free Press.
8.
BoomsmaA. (1983). On the robustness of LISREL (maximum likelihood estimation) against small sample size and nonnormality. Amsterdam, Netherlands: Sociometric Research Foundation. (Unpublished doctoral dissertation, University of Groningen, Netherlands)
9.
BrowneM. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.
10.
DixonW. J. (1950). Analysis of extreme values. Annals of Mathematical Statistics, 21, 488-506.
11.
FergusonC. J. (2009). An effect size primer: A guide for clinicians and researchers. Professional Psychology: Research and Practice, 40, 532-538.
12.
GolubG. H.Van LoanC. F. (1993). Matrix computation. Baltimore, MD: Johns Hopkins University Press.
13.
GorsuchR. L. (1983). Factor analysis (2nd ed.). Hillsdale, NJ: Erlbaum.
14.
HambletonR. K.MerendaP. F.SpielbergerC. D. (2005). Adapting educational and psychological tests for cross-cultural assessment. Mahwah, NJ: Erlbaum.
15.
HarmanH. H. (1976). Modern factor analysis. Chicago, IL: University of Chicago Press.
16.
HolzingerK. J.SwinefordF. (1939). A study in factor analysis: The stability of a bi-factor solution (Supplementary Educational Monographs, No. 48). Chicago, IL: University of Chicago.
17.
HubbardR.AllenS. J. (1987). An empirical comparison of alternative methods for principal components extraction. Journal of Business Research, 15, 173-190.
18.
HuberP. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35, 73-101.
19.
HuberP. J. (1981). Robust statistics. New York, NY: Wiley.
20.
KaiserH. F.DickmanK. (1962). Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika, 27, 179-182.
21.
LiuY.ZumboB. D. (2007). The impact of outliers on Cronbach’s coefficient alpha estimate of reliability: Visual analogue scales. Educational and Psychological Measurement, 67, 620-634.
22.
LiuY.ZumboB. D.WuA. D. (in press). A demonstration of the impact of outliers on the decisions about the number of factors in exploratory factor analysis. Educational and Psychological Measurement.
23.
MostellerF.TukeyJ. W. (1968). Data analysis, including statistics. In LindzeyG.AronsonE. (Eds.), Handbook of social psychology (2nd ed., Vol. 2, pp. 80-203). Reading, MA: Addison-Wesley.
PenaD.PrietoF. J. (2001). Multivariate outlier detection and robust covariance matrix estimation. Technometrics, 43, 286-310.
26.
SPSS Inc. (2009). PASW STATISTICS 17.0 command syntax reference. Chicago, IL: Author.
27.
TukeyJ. W. (1962). The future of data analysis. Annals of Mathematical Statistics, 3, 1-67.
28.
VelicerW. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41, 321-327.
29.
WatkinsD. S. (2010). Fundamentals of matrix computations (3rd ed.). Pullman, MA: Wiley.
30.
WilcoxR. R. (2010). Fundamentals of modern statistical methods: Substantially improving power and accuracy (2nd ed.). New York, NY: Springer.
31.
WilcoxR. R. (in press). Modern statistics for the social and behavioral sciences: A practical introduction. New York, NY: Chapman & Hall/CRC Press.
32.
YuanK. H.MarshallL. L.BentlerP. M. (2002). A unified approach to exploratory factor analysis with missing data, nonnormal data, and in the presence of outliers. Psychometrika, 67, 95-122.
33.
ZumboB. D.JenningsM. (2002). The robustness of validity and efficiency of the related samples t-test in the presence of outliers. Psicologica, 23, 415-450.
34.
ZumboB. D.ZimmermanD. W. (1993). Is the selection of statistical methods governed by level of measurement?Canadian Psychology, 34, 390-400.
35.
ZwickW. R.VelicerW. F. (1986). Comparison of 5 rules for determining the number of components to retain. Psychological Bulletin, 99, 432-442.
