Abstract
This paper reviewed the current state of the literature on the appropriateness of various correlation measures when data are ordinal. Emphasis was on the use of these measures as input to multivariate analysis. Based on the review, four correlation indexes were further studied via a simulation design. The simulation results indicated that the polychoric correlation outperformed product-moment, Spearman’s rho and Kendall’s tau-b measures on the basis of bias and squared error criteria. The present study suggests that the chapter investigating pairwise correlations may be closed and attention may now be directed towards non-normal data and actual multivariate analysis with correlation matrices.
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References
Allan, G. J. Borris. 1976. “Ordinal-scaled variables and multi-variate analysis: comment on Hawkes.”American Journal of Sociology 81:1498–1500.
Borgatta, E. F. and G. F. Bohrnstedt. 1981. “Levels of Measurement: Once Over Again.” InSocial Measurement: Current Issues. Ed. G. W. Bohrnstedt and E. F. Borgatta, eds., Beverly Hills: Sage.
Burke, C. J. 1970. “Measurement Scales and Statistical Models.” InScaling: A Sourcebook for Behavioral Scientists, Chicago: Aldine: 42–55.
Carroll, John B. 1961. “The Nature of Data, or How to Choose a Correlation Coefficient.”Psychometrika 26: 347–372.
Cattell, Raymond B. 1978.The Scientific use of Factor Analysis in Behavioral and Life Sciences. New York: Plenum Press.
Clark, M. Louise. 1984. “Robustness of One Way Analysis of Variance for Ordinal Data.” Unpublished Doctoral Dissertation. The University of Alabama.
Costner, H. L. 1965. “Criteria for Measures of Association,” American Sociological Review 30: 341,353.
Gaito, J. 1980. “Measurement Scales and Statistics: Resurgence of an Old Misconception.”Psychological Bulletin 87: 564–567.
Gibbons, J. D. 1971.Nonparametric Statistical Inference. New York: McGraw-Hill.
— 1976.Nonparametric Methods for Quantitative Analysis. New York. Holt, Rinehart, and Winston.
Goodman, Leo A. and William H. Kruskal. 1954. “Measurement of Association for Cross Classifications.”Journal of the American Statistical Association 49:723–764.
Guttman, L. 1955. “The Determinancy of Factor Score Matrices with Implications for Five Other Basic Problems of Common Factor Theory.”The British Journal of Statistical Psychology 8: 65–81.
— 1981. “What is not What in Statistics.” InMultidimensional Data Representations: When and Why. Ed. I. Borg. Ann Arbor, Michigan: Mathesis: 20–46.
Havlicek, Larry L. and Nancy L. Peterson. 1977. “Effect of Violation of Assumptions Upon Significance Levels of the Pearson r.”Psychological Bulletin: 373–377.
Hawkes, Ronald K. 1971. “The Multivariate Analysis of Ordinal Measures.”American Journal of Sociology 76: 908–926.
Hays, William L. 1981.Statistics. New York: Holt, Rinehart and Winston. Third Edition.
Henry, Frank. 1982. “Multivariate Analysis and Ordinal Data.”American Sociological Review 47: 299–307.
Horst, Paul. 1965.Factor Analysis of Data Matrices. New York: Holt, Rinehart and Winston.
IMSL. 1981.International Mathematical and Statistical Libraries. Houston: IMSL, Inc.
Janson, S. and J. Vegelius. 1982. “Correlation Coefficients for More Than on Scale Type.”Multivariate Behavioral Research 17: 274–284.
Jöreskog, K. G. 1979. “A General Approach to Confirmatory Maximum Likelihood Factor Analysis with Addendum.” InAdvances in Factor Analysis and Structural Equation Models. Ed. Jay Madigson. Cambridge: Abt: 21–43.
— and Dag Sörbom. 1981.LISREL: Analysis of Linear Structural Relationships by the Method of Maximum Likelihood (Version V). Chicago: National Educational Resources, Inc.
Kendall, Maurice G. 1955.Rank Correlation Methods, Second edition. New York: Hafner.
Kim, Jae On. 1975. “Multivariate Analysis of Ordinal Variables.”American Journal of Sociology 81: 261–298.
—. 1978. “Multivariate Analysis of Ordinal Variables Revisited.”American Journal of Sociology 84: 448–456.
Kruskal, William H. 1958. “Ordinal Measures of Association.”Journal of the American Statistical Association 53: 814–861.
Labovitz, S. 1967. “Some Observations on Measurement and Statistics.”Social Forces 46:151–160.
— 1970. “The Assignment of Numbers Rank Order Categories.”American Sociological Review 35: 515–524.
Lawley, D. N. and A. E. Maxwell. 1971.Factor Analysis as a Statistical Method. London: Butterworths.
Lord, F. M. 1953. “On the Statistical Treatment of Football Numbers.”American Psychologist 8: 750–51.
Martilla, John A. and Davis W. Carvey. 1975. “Four Subtle Sins in Marketing Research.”Journal of Marketing 39: 8–15.
Martin, Warren S. 1973. “The Effects of Scaling on the Correlation Coefficients: A Test of Validity.”Journal of Marketing Research 10: 326–318.
— 1978. “Effects of Scaling on the Correlation Coefficients: Additional Considerations.”Journal of Marketing Research 15: 304–308.
Morrison, Donald G. and Normal E. Toy. 1982. “The Effect of Grouping Continuous Variables on Correlation Coefficients.”Marketing Science 1: 379–389.
Nunnally, J. C. 1970.Introduction to Psychological Measurement. New York: McGraw-Hill.
O’Brien, R. M. 1979. “The Use of Pearson’s r With Ordinal Data.”American Sociological Review 36: 519–20.
— 1981. “Using Rank Category Variables to Represent Continuous Variables: Defects of Common Practice.”Social Forces 59: 1149–1162.
Olsson, Ulf. 1979. “Maximum Likelihood Estimation of the Polychoric Correlation Coefficient.”Psychometrika 44: 443–460.
—. 1980. “Measuring Correlation in Ordered Two-Way Contingency Tables.”Journal of Marketing Research 17 (August): 391–394.
Peters, C. C. and W. R. Van Voorhis. 1940.Statistical Procedures and Their Mathematical Bases. New York: McGraw-Hill.
Peterson, Robert A. and Subhash Sharma. 1977. “Adjusting Correlation Coefficients for the Effects of Scaling,” InProceedings of the Business and Economics Statistics Section of the American Statistical Association.
Ploch, D. H. 1974. “Ordinal Measures of Association and General Linear Model.” InMeasurement in the Social Sciences, Ed. H. M. Blalock, Jr. Chicago: Aldine: 343–368.
Reynolds, Henry. 1973. “On The Multivariate Analysis of Ordinal Measures.”American Journal of Sociology 78: 1513–1516.
Roskam, Edward E. 1979. “Data Theory and Mathematical Models.” InGeometric Representations of Relational Data. Ed. J. C. Lingoes at al. Ann Arbor, Michigan: Mathesis: 149–235.
Smith, Robert B. 1971. “Neighborhood Context and College Plans: An Ordinal Path Analysis.”Social Forces 51: 199–217.
Somers, Robert H. 1974. “Analysis of Partial Rank Correlation Measures Based on the Product-Moment Model: Part One.”Social Forces 53: 229–246.
SPSSX. 1983.Statistical Package for the Social Sciences: User Guide. New York: McGraw-Hill.
SSP. 1968.Scientific Subroutine Package. Version III, Fourth Edition. IBM Corporation.
Stevens, S. S. 1951. “Mathematics, Measurement, and Psychophysics.” InHandbook of Experimental Psychology. Ed. S. S. Stevens. New York: Wiley: 1–49.
— 1968. “Measurement, Statistics, and the Schemaphiric View.”Science 161: 849–856.
Wainer Howard and David Thissen. 1976. “Three Steps Towards Robust Regression.”Psychometrika 41: 9–34.
Wilson, T. P. 1969. “A Proportional-Reduction-In-Error Interpretation for Kendall’s tau-b.”Social Forces 47: 340–342.
— 1971. “Critique of Ordinal Variables.”Social Forces 49: 432–444.
— 1974a. “On Ordinal Path Analysis: Reply to Smith’s Neighborhood Context and College Plans’”Social Forces 53: 120–123.
— 1974b. “Reply to Somers and Smith”.Social Forces 53: 247–251.
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Babakus, E., Ferguson, C.E. On choosing the appropriate measure of association when analyzing rating scale data. JAMS 16, 95–102 (1988). https://doi.org/10.1007/BF02723328
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DOI: https://doi.org/10.1007/BF02723328