SOME OBSERVATIONS ON THE SCREE TEST, AND ON COEFFICIENT ALPHA

Authors

  • Larry R. Nelson

Keywords:

การวิเคราะห์การถดถอย, คณิตศาสตร์สถิติ, สหสัมพันธ์, Correlation, Regression analysis

Abstract

          The paper looks into the use of principal components from two perspectives. Regression lines are fitted to scree plots to see if they might assist with resolving the number of factors question. Then, the use of the principal eigenvalue and corresponding eigenvector from a classical components analysis is examined, with an eye to identifying best test items.  It was found that regression lines may be a useful addition when it comes to determining where an eigenvalue scree breaks. It was also found that the use of item loadings on the first principal component is more likely to identify best items than is the process of looking at item-test correlations.

References

Cattell, R.B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1, 245-76.

Dewber, T. (2004). An investigation of the robustness of Lord’s item difficulty and Discrimination formulas. Unpublished PhD dissertation, Centre for Research in Applied Measurement and Evaluation, University of Alberta.

Dawber, T., Rogers, W.T., & Carbonaro, M. (2004, April). Robustness of Lord’s formulas for Item difficulty and discrimination conversions between classical and item response theory models. Paper presented at the Annual Meeting of the American Educational Research Association, San Diego, California.

Hakstain, A.R. & Bay, K.S. (1972). User’s manual to accompany the Alberta general factor Analysis program. Edmonton, Alberta: Division of Educational Research Services, University of Alberta.

Hambleton, R.K., Swaminathan, H., & Rogers, H.J. (1991). Fundamentals of item response Theory. Newbury Park, California: Sage.

Hayton, J.C., Allen, D.G., & Scarpello, V. (2004). Factor retention decisions in exploratory Factor analysis: A tutorial on parallel analysis. Organizational Research Merthods, 7(2), 191-205.

Kehoe, J. (1995). Basic item analysis for multiple-choice tests. Washington, D.C.: ERIC Clearinghouse on Assessment and Evaluation, ERIC Identifier: ED398237.

Lord, F.M. (1958). Some relationships between Guttman’s principal components of scale analysis and other psychometric theory. Psychometrika, 23, 291-296.

Mulaik, S.A. (1972). The foundations of factor analysis. New York: McGraw-Hill.

Nandakamur, R. (1994). Assessing dimensionality of a set of item responses – comparison of different approaches. Journal of Educational Measurement, 31, 17-35.

Downloads

Published

2021-09-22