Educational Sciences: Theory & Practice

ISSN: 2630-5984

The Effect of Sample Size on Parametric and Nonparametric Factor Analytical Methods

Ömür Kaya Kalkan
Hacettepe ASO 1.OSB Vocational School, Hacettepe University, 1. Organize Sanayi Bölgesi, ASORA Ticaret Merkezi, Ayaş yolu 25. Km. Ankara 06935 Turkey
Hülya Kelecioğlu
Department of Educational Measurement and Evaluation, Faculty of Educational Sciences, Hacettepe University, Ankara Turkey.


Linear factor analysis models used to examine constructs underlying the responses are not very suitable for dichotomous or polytomous response formats. The associated problems cannot be eliminated by polychoric or tetrachoric correlations in place of the Pearson correlation. Therefore, we considered parameters obtained from the NOHARM and FACTOR programs (which use parametric methods) and from the DETECT and DIMTEST programs (which use nonparametric methods) for different sample sizes of a real large dataset (50, 80, 100, 160, 200, 300, 500, 1000, 3000, 5000). A parallel analysis (PA) based on the tetrachoric correlation with the FACTOR program produced inconsistent results among the sampling sizes. However, the analyses based on the Pearson correlation could not adequately determine the dimension numbers. Although DETECT and NOHARM determined the multidimensionality at acceptable level for the 50 sample size, they yielded the most consistent results at sample sizes of 1000 and above.

Test dimensionality, Sample size effect, Nonlinear item factor analysis, Exploratory nonparametric dimension assessment, Conditional item pair covariance.