Çoktan Seçmeli Test Sonuçlarından Elde Edilen Farklı Korelâsyon Türlerinin Birinci ve İkinci Sıralı Faktör Analizlerindeki Uyum İndekslerine Etkisi

Yıl 2007, Cilt: 6 Sayı: 1, 154 - 179, 26.06.2007

Halil Yurdugül

Öz

Bu çalışmada, ikili derecelendirilmiş çoktan seçmeli ölçme sonuçlarından elde edilen
kovaryans ve korelasyon matrislerinin birinci ve ikinci sıralı doğrulayıcı faktör analizlerindeki
sonuçların model uyumlarına etkisi araştırılmıştır. Bu nedenle; 553108 öğrencinin katıldığı
Ortaöğretim Kurumları Öğrenci Seçme ve Yerleştirme Sınavı (2001)’nda yer alan matematik ve
fen bilimleri alt testi ele alınmıştır. Madde puanlarından elde edilen veriler Pearson, Goodman ve
tetrakorik korelasyon katsayıları ve maddeler arası kovaryans terimleri ile birinci sıralı ve ikinci
sıralı modellerin doğrulayıcı faktör çözümlemesi yapılmıştır. Elde edilen sonuçlara göre ikinci
sıralı faktör yükleri (birinci sıralı korelasyonlar) eşit olduğunda Pearson korelasyon katsayısına
dayalı çözümler en iyi uyumu vermiştir. İkinci sıralı faktör yükleri (birinci sıralı korelasyonlar)
eşit olmadığında ise tetrakorik koreslayona dayalı çözümler en büyük uyum değerlerini vermiştir.

Anahtar Kelimeler

Doğrulayıcı faktör analizi, hiyerarşik faktör analizi, korelasyon, kovaryans, uyum indeksleri

The Effects of Different Correlation Types on Goodness-of-Fit Indices in First Order and Second Order Factor Analysis for Multiple Choice Test Data

Öz

This study explores the effects of different correlation types (covariance and
correlation matrix, obtained from Pearson, Goodman, and Tetrachoric) on goodness-of-fit indices
in first order and second order factor analysis. The data included Math and Science subsets in
Student Selection and Placement Examination for Secondary Education test administered in 2001
with the participation of 553108 students. A first-order and second-order confirmatory factor
analyses were performed on the matrix from item scores obtained from several correlation
coefficients. The findings indicate that when second order factor loadings (first order correlations)
were equal, solutions with Pearson correlation coefficients yielded the most satisfactory goodnessof-fit.
When second order factor loadings (first order correlations) were not equal, solutions with
tetrachoric correlations yielded the most satisfactory goodness-of-fit

Anahtar Kelimeler

Confirmatory factor analysis, hierarchical factor analysis, correlation, covariance, fit indexes

Kaynakça

• Agresti A. (1984). Analysis of Ordinal Categorical Data. New York: Wiley. Béland, F. & Maheux, B. (1989). Construct validity and second-order factorial model: The secondorder factor model. Quality and Quantity, 23(2). 143-159. Berberoğlu, G., Kaptan, F. ve Kutlu, O. (2005). “Türkiye genelinde sekizinci sınıf öğrencilerinin fen bilgisi dersindeki üst düzey zihinsel becerilerinin incelenmesi”, 6–18 Eylül V. Ulusal Fen ve Matematik Eğitim Kongresi, ODTÜ, Ankara. Berstein, I. H. & Teng, G. (1989). Factoring items and factoring scales are different: Spurious evidencefor multidimensionality due to item categorization. Psychological Bulletin, 105(3), 467-477. Bonett, D. G. & Price, R. M. (2005). Inferential methods fort he tetrachoric correlation coefficient. Journal of Educational and Behavioral Statistics, 30(2), 213-225. Byrne, B.M. (1998) Structural Equation Modelling with LISREL, PRELIS, and SÍMPLIS: basic concepts, applications, and programming. Mahwah, NJ: L. Erlbaum. Cudeck, R. (1989). Anaylsis of correlation matrices using covariance structure models. Psychological Bulletin, 105(2), 317-327. Comrey, A. L. & Lee, H. B. (1992), A First course in factor analysis (2nd ed.), Hillsdale, NJ: Lawrence Erlbaum Associates. Cortina, J.M. (1993) What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78(1), 98-104 Cudeck, R. (1989). Analysis of correlation structures with covariance structure models. Psychological Bulletin, 105, 316-329. DeVellis, R. F. (1991). Scale development: Theory and applications. Newbury Park, CA: Sage Greer, T., Dunlap, W.P., & Beatty, G.O. (2003). A Monte Carlo evaluation of the tetrachoric correlation coefficient. Educational and Psychological Measurement 63(6), 931-950. Haddock, C. K., Rindskopf, D. & Shadish, W. R. (1998). Using odds ratios as effect sizes for metaanalysis of dichotomous data: A primer on methods and issues. Psychological Methods, 3(3), 339-353. Hair, J. F., Anderson R. E., Tatham, R. L. & Black, W. C. (1998). Multivariate data analysis (5th ed.). Englewood Cliffs, NJ: Prentice Hall. Hayduk, L. A. (1996). LISREL issues, debates, and strategies. Baltimore, MD: The Johns HopkinsUniversity Press. Hoelter, J. W. (1983). The analysis of covariance structures: Goodness of fit indices. Sociological Methods and Research, 11, 325-344. Jaccard, J. & Wan, C. K. W. (1996). LISREL approaches to interaction effects in multiple regression. Thousand Oaks, CA: Sage Publications. Jöreskog, K.G. (1971). Statistical analysis of sets of congeneric tests. Psychometrika, 34, 109-133. Jöreskog, K. G. (1974). Analyzing psychological data by structural analysis of covariance matrices. In R. C. Atkinson, D. H. Krantz, R. D. Luce, & P. Suppes (Eds.), Contemporary developments in mathematical psychology: Measurement, psychophysics, and neural information processing (Vol. 2, pp. 1–56). San Francisco: Freeman. Kline, R. B. (1998). Principles and practice of structural equation modeling. NY: Guilford Press. Lord, F. M., & Novick, R. (1968). Statistical theories of mental test scores. Reading MA: AddisonWesley. Lucke, J. F. (2005). “Rassling the hog”: the influence of correlated item error on internal consistency, classical reliability, and congeneric reliability. Applied Psychological Measurement, 29(1), 106–125. Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indexes in confirmatory factor analysis: The effect of sample size. Psychological Bulletin, 103, 391-410. McDonald, R. P. (1985). Factor analysis and related methods. Hillsdale, NJ: Erlbaum. McDonald, R. P. (1999). Test theory: a unified treatment. Mahwah NJ: Erlbaum. Millsap, R. E., & Everson, H. (1991). Confirmatory measurement model comparisons using latent means. Multivariate Behavioral Research, 26, 479–497. Mislevy, R. J. (1986). Recent developments in the factor analysis of categorical variables. Journal of Educational Statistics, 11, 3–31. Mulaik, S. A., James, L. R., Van Alstine, J., Bennett, N., Lind, S. & Stilwell, C. D. (1989). Evaluation of goodness-of-fit indices for structural equation models. Psychological Bulletin, 105, 430- 445. Ogasawara, H. (2001). Approximations to the distributions of fit indexes for misspecified structural equation models. Structural Equation Modeling, 8, 556–574. Pohlmann, J. T. (2004). Use and interpretation of factor analysis in The Journal of Educational Research: 1992-2002. The Journal of Educational Research, 98(1), 14-22. Raykov, T. (1997). Estimation of composite reliability for congeneric measures. Applied Psychological Measurement, 21, 173-184 Reise, S. P. & Widaman, K. F. (1999). Assessing the fit of measurement models at the individual level: A comparison of item response theory and covariance structure approaches. Psychological Methods, 4(1), 3-21. Rindskopf, D. & Rose, T. (1988). Second order factor analysis: Some theory and applications. Multivariate Behavioral Research, 23, 51–67. Schumacker, R. E. & Beyerlein, S. T. (2000). Confirmatory factor analysis with different correlation types and estimation methods. Structural Equatıon Modeling, 7(4), 629–636 Spearman, C. (1904). The proof and measurement of association between two things. American Journal of Psychology, 15, 72−101. Steiger, J. H. (1990). Structural model evaluation and modification: an interval estimation approach. Multivariate Behavioral Research, 25 (2), 173-80. Tabachnick, B. G. & Fidell, L. S. (1996). Using multivariate statistics (3 Ed.). New York: Harpercollins College Publishers. Thompson, B. & Daniel, L. G. (1996). Factor analytic evidence for the construct validity of scores: A historical overview and some guidelines. Educational and Psychological Measurement, 56, 197-208. Widaman, K. F. & Thompson, J. S. (2003). On specifying the null model for incremental fit indices in structural equaiton modeling. Psychological Methods, 8(1), 16-37. Yuan, K. (2005). Fit indices versus test statistics. Multivariate Behavioral Research, 40(1), 115-148. Yurdugül, H. (2005). Konjenerik test kuramı ve konjenerik madde analizi: Tek boyutlu çoktan seçmeli testler üzerine bir uygulama. A.Ü. Eğitim Bilimleri Fakültesi Dergisi 38(2), 21-47. Yurdugül, H ve Aşkar, P. (2004). Ortaöğretim Kurumları Öğrenci Seçme ve Yerleştirme Sınavı’nın cinsiyete göre madde yanlılığı açısından incelenmesi. Egitim Bilimleri ve Uygulama Dergisi, 3(5), 3-20. Zinbarg, R.E., Revelle, W., Yovel, I., & Li. W. (2005). Cronbach's Alpha, Revelle's Beta, McDonald's Omega: Their relations with each and two alternative conceptualizations of reliability. Psychometrika. 70, 123-133.