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Örneklem Büyüklüğü, Korelasyon Tekniği ve Faktör Çıkarma Yönteminin Güvenirlik Katsayılarına Etkisi

Year 2018, Volume: 26 Issue: 3, 697 - 706, 15.05.2018
https://doi.org/10.24106/kefdergi.413303

Abstract

Bu araştırmanın amacı, güvenirlik katsayılarını örneklem
büyüklüğüne (250, 500, 1000, 2500, 5000 ve 9773), EFA faktör çıkarma yöntemine
(PCA, PA, ULS, WLS ve MLE); CFA kestirim yöntemine (UL, ML ve GL) ve korelasyon
matrisine (Pearson, phi ve tetrakorik) göre karşılaştırmaktır. Bu amaçla temel
araştırma yöntemine başvurulmuştur. Araştırma gerçek verilerle yürütülmüş olup
araştırma verileri, 2014 yılında uygulanan Temel Eğitimden Ortaöğretime Geçiş
sınavları Türkçe alt testine cevap veren öğrenci cevaplarından oluşturulmuştur.
Araştırmada McDonald ω, McDonald ωh, Maximal güvenirlik, Armor Ɵ,
Heise ve Bohrnstedt Ω, Revelle β ve Standartlaştırılmış Alfa katsayıları
karşılaştırılmıştır. Araştırma sonucunda aynı korelasyon matrisi için örneklem
büyüklüğünün çok değişikliğe neden olmadığı gözlenmiştir. Tetrakorik
korelasyonla hesaplanan McDonald ωh ve Revelle β katsayılarının
1’den büyük olduğu bazı koşulların bulunduğu araştırmanın bir diğer bulgusudur.
Araştırma sonuçlarına göre bu katsayıların konjerik tek faktörlü yapılar için
phi korelasyonuyla hesaplanmasını önerilmiştir. Diğer bulgular literatür
eşliğinde tartışılmış ve önerilerde bulunulmuştur.

References

  • AERA, APA, NCME, American Educational Research Association (AERA), American Psychological Association (APA), & National Council on Measurement In Education (NCME). (2014). Standards for educational and psychological testing. Washington, DC: American Educational Research Association.
  • Allen, M. J., & Yen, W. M. (1979). Introduction to measurement theory. Monterey: Brooks/Cole Publishing Company.
  • Armor, D. J. (1974). Theta reliability and factor scaling. Sociological Methodology, 5, 17–50.
  • Carmines, E. G., & Zeller, R. A. (1987). Reliability and validity assessment (9th ed.). Beverly Hills, California: SAGE.
  • Chou, C. P., & Bentler, P. M. (1995). Estimates and tests in structural equation modeling. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications. Thousand Oaks, CA: SAGE.
  • Comrey, A. L. (1988). Factor-analytic methods of scale development in personality and clinical psychology. Journal of Consulting and Clinical Psychology, 56(5), 754–761. https://doi.org/10.1037/0022-006X.56.5.754
  • Crocker, L., & Algina, J. (2008). Introduction of classical and modern test theory. Ohio: Cengage Learning.
  • Curran, P. J., West, S. G., & Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1(1), 16–29. https://doi.org/10.1037/1082-989X.1.1.16
  • Ercan, I., Yazici, B., Sigirli, D., Ediz, B., & Kan, I. (2007). Examining Cronbach alpha, theta, omega reliability coefficients according to sample size. Journal of Modern Applied Statistical Methods, 6(1), 291–303. Retrieved from http://digitalcommons.wayne.edu/jmasm/vol6/iss1/27
  • Fox, J. (2016). polycor: Polychoric and polyserial correlations. Retrieved from https://cran.r-project.org/package=polycor
  • Fraenkel, J. R., Wallen, N. E., & Huyn, H. H. (2012). How to design and evaluate research in education (8th ed.). New York: McGraw-Hill.
  • Gay, L. R., Mills, G. E., & Airasian, P. (2012). Educational research: Competencies for analysis and applications (10th ed.). New Jersey: Pearson.
  • Gorsuch, R. L. (1974). Factor Analysis (1st ed.). Toronto: W. B. Saunders Company.
  • Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74(1), 155–167. https://doi.org/10.1007/s11336-008-9099-3
  • Guadagnoli, E., & Velicer, W. F. (1988). Relation of sample size to the stability of component patterns. Psychological Bulletin, 103(2), 265–275.
  • Gulliksen, H. (1950). Theory of mental tests. New York: Wiley.
  • Hancock, G. R., & Mueller, R. O. (2001). Rethinking construct reliability within latent variable systems. In Structural Equation Modeling: Present and Future: A Festschrift in Honor of Karl Jöreskog (pp. 195–216).
  • Hancock, G. R., & Mueller, R. O. (2013). Structural equating modelling: A second course. B. G. Tabachnick & L. S. Fidell (Orgs.), Using multivariate statistics (2nd ed.). Charlotte, NC: Information Age Publishing.
  • Heise, D. R., & Bohrnstedt, G. W. (1970). Validity, invalidity, and reliability. In E. F. Borgatta & G. W. Bohrnstedt (Eds.), Sociological Methodology (pp. 104–129). San Francisco: Jossey-Bass.
  • McDonald, R. P. (1999). Test theory: A unified treatment. Mahwah, NJ: LEA Publisher.
  • Meyer, J. P. (2010). Reliability. New York: Oxford University Press.
  • Osburn, H. G. (2000). Coefficient alpha and related internal consistency reliability coefficients. Psychological Methods, 5(3), 343–355. https://doi.org/10.1037/1082-989X.5.3.343
  • Price, L. R. (2017). Psychometric methods: Theory and practice. New York, NY: The Guilford Press.
  • R Core Team. (2017). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from https://www.r-project.org/.
  • Revelle, W. (1979). Hierarchical cluster analysis and the internal structure of tests. Multivariate Behavioral Research, 14, 57–74. https://doi.org/10.1207/s15327906mbr1401_4
  • Revelle, W. (2016). psych: Procedures for Psychological, Psychometric, and Personality Research. Evanston, Illinois. Retrieved from https://cran.r-project.org/package=psych
  • Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modelling: Multilevel, longitudinal, and structural equation models. New York: Chapman & Hall.
  • Streiner, D. L. (1994). Figuring out factors: the use and misuse of factor analysis. Canadian Journal of Psychiatry, 39(3), 135–140.
  • Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach’s, α Revelle’s β and McDonald’s ω H: Their relations with each other and two alternative conceptualizations of reliability. Psychometrika, 70(1), 123–133. https://doi.org/10.1007/s11336-003-0974-7

The Effects of Sample Size, Correlation Technique, and Factor Extraction Method on Reliability Coefficients

Year 2018, Volume: 26 Issue: 3, 697 - 706, 15.05.2018
https://doi.org/10.24106/kefdergi.413303

Abstract

This
study aims to compare reliability coefficients according to sample size (250,
500, 1,000, 2,500, 5,000, and 9,773), EFA factor extraction methods (PCA, PA,
ULS, WLS, and MLE), CFA estimation methods (UL, ML, and GL), and correlation
matrices (Pearson, phi, and tetrachoric). Therefore, it employs a basic research
method. The study was conducted 
with
real data, and the data were collected from students’ answers to a Turkish
sub-test in the Test for Transition from Basic Education into Secondary
Education administered in 2014. Within the scope of the study, McDonald ω,
McDonald ω
h, maximal reliability, Armor Ɵ, Heise and Bohrnstedt Ω,
Revelle β, and standardized alpha coefficients were compared. Consequently, it
was found that sample size in the same correlation matrices did not lead to
serious changes. It was also found that McDonald ω
h and Revelle β
coefficients calculated with a tetrachoric correlation were bigger than 1 in some
conditions. It was recommended in consequence that those coefficients should be
calculated through phi correlations for congeric one-factor structures. Other
findings obtained support the literature, and necessary suggestions are made. 

References

  • AERA, APA, NCME, American Educational Research Association (AERA), American Psychological Association (APA), & National Council on Measurement In Education (NCME). (2014). Standards for educational and psychological testing. Washington, DC: American Educational Research Association.
  • Allen, M. J., & Yen, W. M. (1979). Introduction to measurement theory. Monterey: Brooks/Cole Publishing Company.
  • Armor, D. J. (1974). Theta reliability and factor scaling. Sociological Methodology, 5, 17–50.
  • Carmines, E. G., & Zeller, R. A. (1987). Reliability and validity assessment (9th ed.). Beverly Hills, California: SAGE.
  • Chou, C. P., & Bentler, P. M. (1995). Estimates and tests in structural equation modeling. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications. Thousand Oaks, CA: SAGE.
  • Comrey, A. L. (1988). Factor-analytic methods of scale development in personality and clinical psychology. Journal of Consulting and Clinical Psychology, 56(5), 754–761. https://doi.org/10.1037/0022-006X.56.5.754
  • Crocker, L., & Algina, J. (2008). Introduction of classical and modern test theory. Ohio: Cengage Learning.
  • Curran, P. J., West, S. G., & Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1(1), 16–29. https://doi.org/10.1037/1082-989X.1.1.16
  • Ercan, I., Yazici, B., Sigirli, D., Ediz, B., & Kan, I. (2007). Examining Cronbach alpha, theta, omega reliability coefficients according to sample size. Journal of Modern Applied Statistical Methods, 6(1), 291–303. Retrieved from http://digitalcommons.wayne.edu/jmasm/vol6/iss1/27
  • Fox, J. (2016). polycor: Polychoric and polyserial correlations. Retrieved from https://cran.r-project.org/package=polycor
  • Fraenkel, J. R., Wallen, N. E., & Huyn, H. H. (2012). How to design and evaluate research in education (8th ed.). New York: McGraw-Hill.
  • Gay, L. R., Mills, G. E., & Airasian, P. (2012). Educational research: Competencies for analysis and applications (10th ed.). New Jersey: Pearson.
  • Gorsuch, R. L. (1974). Factor Analysis (1st ed.). Toronto: W. B. Saunders Company.
  • Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74(1), 155–167. https://doi.org/10.1007/s11336-008-9099-3
  • Guadagnoli, E., & Velicer, W. F. (1988). Relation of sample size to the stability of component patterns. Psychological Bulletin, 103(2), 265–275.
  • Gulliksen, H. (1950). Theory of mental tests. New York: Wiley.
  • Hancock, G. R., & Mueller, R. O. (2001). Rethinking construct reliability within latent variable systems. In Structural Equation Modeling: Present and Future: A Festschrift in Honor of Karl Jöreskog (pp. 195–216).
  • Hancock, G. R., & Mueller, R. O. (2013). Structural equating modelling: A second course. B. G. Tabachnick & L. S. Fidell (Orgs.), Using multivariate statistics (2nd ed.). Charlotte, NC: Information Age Publishing.
  • Heise, D. R., & Bohrnstedt, G. W. (1970). Validity, invalidity, and reliability. In E. F. Borgatta & G. W. Bohrnstedt (Eds.), Sociological Methodology (pp. 104–129). San Francisco: Jossey-Bass.
  • McDonald, R. P. (1999). Test theory: A unified treatment. Mahwah, NJ: LEA Publisher.
  • Meyer, J. P. (2010). Reliability. New York: Oxford University Press.
  • Osburn, H. G. (2000). Coefficient alpha and related internal consistency reliability coefficients. Psychological Methods, 5(3), 343–355. https://doi.org/10.1037/1082-989X.5.3.343
  • Price, L. R. (2017). Psychometric methods: Theory and practice. New York, NY: The Guilford Press.
  • R Core Team. (2017). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from https://www.r-project.org/.
  • Revelle, W. (1979). Hierarchical cluster analysis and the internal structure of tests. Multivariate Behavioral Research, 14, 57–74. https://doi.org/10.1207/s15327906mbr1401_4
  • Revelle, W. (2016). psych: Procedures for Psychological, Psychometric, and Personality Research. Evanston, Illinois. Retrieved from https://cran.r-project.org/package=psych
  • Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modelling: Multilevel, longitudinal, and structural equation models. New York: Chapman & Hall.
  • Streiner, D. L. (1994). Figuring out factors: the use and misuse of factor analysis. Canadian Journal of Psychiatry, 39(3), 135–140.
  • Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach’s, α Revelle’s β and McDonald’s ω H: Their relations with each other and two alternative conceptualizations of reliability. Psychometrika, 70(1), 123–133. https://doi.org/10.1007/s11336-003-0974-7
There are 29 citations in total.

Details

Primary Language English
Subjects Studies on Education
Journal Section Review Article
Authors

Nuri Doğan This is me

Abdullah Faruk Kılıç

Publication Date May 15, 2018
Acceptance Date August 25, 2017
Published in Issue Year 2018 Volume: 26 Issue: 3

Cite

APA Doğan, N., & Kılıç, A. F. (2018). The Effects of Sample Size, Correlation Technique, and Factor Extraction Method on Reliability Coefficients. Kastamonu Education Journal, 26(3), 697-706. https://doi.org/10.24106/kefdergi.413303

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