Troubleshooting
Problem
I'm using SPSS for data analysis on a set of variables with data that is measured on an ordinal scale.. I'd like to calculate an internal consistency reliability coefficient and the research I've conducted highlights some of the problems with using coefficient alpha for ordinal data. Which is the correct statistic to use in SPSS to calculate the reliability coefficitent for ordinal (rank based) data?
Resolving The Problem
Cohen's weighted kappa provides a measure of reliability for ordinal items (see Fleiss & Cohen, 1973; Fleiss, Levin, & Paik, 2003) . However, SPSS does not have a means of producing weighted kappa for more than 2 variables at a time. See Technote 1477357 for further discussion of weighted kappa and instructions for the SPSS MATRIX commands to compute it.
Fleiss, J.L., & Cohen, J. (1973). The equivalence of weighted kappa and the intraclass correlation coefficient as measures of reliability. Educational and Psychological Measurement, 33, 613-619.
Fleiss, J.L., Levin, B., & Paik, M.C. (2003). Statistical Methods for Rates and Proportions (3rd Ed.). New York: Wiley.
The SPSS Categories procedure CATPCA (Categorical Principal Components Analysis) provides an alpha measure for multiple ordinal items. CATPCA transforms the ordinal variables to maximize the largest eigenvalue and the alpha produced is for the transformed variables. There is a book chapter that discusses the Cronbach's alpha produced by CATPCA that you may find helpful. Three of the Categories module developers at Leiden University have published a book chapter on CATPCA which is available for free downloading from the publisher's web site (as one of 2 sample chapters). The chapter includes examples of CATPCA analysis and comparisons to related methods. The chapter is available at
http://www.sagepub.com/upm-data/5040_Kaplan_Final_Pages_Chapter_3.pdf
and the citation is:
Meulman, J.J., Van Der Kooij, A.J., & Heiser, W.J. (2004). Principal components analysis with nonlinear optimal scaling transformations for ordinal and nominal data. In D. Kaplan (Ed.) "The Sage Handbook of Quantitative Methodology for the Social Sciences". Thousand Oaks CA: Sage. (Chap. 3, pp 49-70).
See sections 3.3.3 and 3.4 in regard to the alpha produced by Categories.
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