The effect of alternative scoring methods on the analysis of rank order categorical data

References

• Abelson , R.P. and Tukey , J.W. 1963 . “Efficient Utilization of Nonnumerical Information in Quantitative Analysis: General Theory, The Case of Simple Rank Order” . Annals of Mathematical Statistics , 4 December : 1347 – 1369 .
   Google Scholar
• Bechtel , Gordon G. 1985 . “Generalizing The Rasch Model for Consumer Rating Scales,” . Marketing Science, , 4 Winter : 62 – 73 .
   Google Scholar
• Bertrand , William , Brockett , Patrick and Levine , Arnold . 1979 . “A Methodology for Determining High Risk Components in Urban Environments,” . International Journal of Epidemiology, , 8 June : 161 – 166 .
   Google Scholar
• Berenson , Mark L. , Levine , David M. and Goldstein , Matthew . 1983 . Intermediate Statistical Methods and Applications, , Englewood Cliffs, New Jersey : Prentice‐Hall, Inc. .
   Google Scholar
• Borgatta , E.F. 1968 . “My Student, The Purist: A Lament,” . Sociological Quarterly, , 9 Winter : 29 – 34 .
   Web of Science ®Google Scholar
• _____ and Bohrnstedt , G.W. 1980 . “Level of Measurement: Once Over Again,” . Sociological Methods and Research, , 9 November : 147 – 160 .
   Google Scholar
• Brockett , Patrick . 1981 . “A Note on the Numerical Assignment of Scores to Ranked Categorical Data,” . Journal of Mathematical Sociology , 8 : 91 – 101 .
   Web of Science ®Google Scholar
• _____ and Levine , Arnold . 1977 . “On A Characterization of Ridits,” . Annals of Statistics, , 5 November : 1245 – 1248 .
   Google Scholar
• _____ and Levine , Arnold . 1980 . “High‐Low Discrete Discrimination Using Unclassified Initial Samples,” , Technical Report #71 Department of Statistics, University of California at Riverside .
   Google Scholar
• Broffit , J.D. , Randies , R.H. and Hogg , R.V. 1976 . “Distribution‐Free Partial Discriminant Analysis,” . Journal of the American Statistical Association, , 71 December : 934 – 939 .
   Google Scholar
• Bross , Irwin . 1958 . “How to Use Ridit Analysis,” . Biometrics, , 14 March : 18 – 38 .
   Web of Science ®Google Scholar
• Chang , Y. , Lachenbruch , P.A. and Clarke , W. “Discrimination with Categorical Data,” . paper presented at the Biometric Society Meeting . March , Charleston, South Carolina.
   Google Scholar
• Conover , J. and Iman , R. 1978 . “The Rank Transformation As A Method of Discrimination with Some Examples,” . In Resarch Report SAND‐0533 , Sandia Laboratories .
   Google Scholar
• David , F.N. , Barton , D.E. , Ganeshalingam , S. , Harter , H.L. , Kim , P.J. , Merrington , M. and Walley , D. 1968 . Normal Centroids, Medians and Scores for Ordinal Data, , Cambridge, , England : University Press .
   Google Scholar
• Didow , Nicholas L. Jr. , Keller , KevIn L. , Barksdale , Hiram C. Jr. and Franke , George R. 1985 . “Improving Measure Quality by Alternating Least Squares Optimal Scaling,” . Journal of Marketing Research, , 22 February : 30 – 40 .
   Web of Science ®Google Scholar
• Dillon , William R. , Goldstein , Matthew and Schiffman , Leon . 1978 . “On the Appropriateness of Linear Discriminant and Multinomial Classification Analysis in Marketing Research,” . Journal of Marketing Research, , 15 February : 103 – 112 .
   Google Scholar
• _____ and Westin , Stewart . 1982 . “Scoring Frequency Data for Discriminant Analysis: Perhaps Discrete Procedures Can be Avoided,” . Journal of Marketing Research, , 19 February : 44 – 56 .
   Google Scholar
• Dixon , W.J. , Brown , M.B. , Engelman , L. , Frane , J.W. , Hill , M.A. , Jennrich , R.I. and Toporek , J.D. 1981 . BMDP Statistical Software, , Berkeley : University of California Press .
   Google Scholar
• Goldstein , Matthew and Dillon , William R. 1978 . Discrete Discriminant Analysis, , New York : John Wiley and Sons .
   Google Scholar
• Goodman , L.A. 1978 . Analyzing Quantitative/Categorical Data, , Cambridge, Mass. : Abt Books .
   Google Scholar
• Heise , D.R. 1975 . Causal Analysis, , New York : John Wiley Press .
   Google Scholar
• Hull , C. Hadlai and Nie , Norman H. 1981 . SPSS Update 7–9, , New York : McGraw‐Hill Book Company .
   Google Scholar
• Inman , R.L. and Conover , W. J. 1979 . “The Use of the Rank Transformation in Regression,” . Technometrics, , 21 November : 499 – 510 .
   Google Scholar
• Labovitz , S. 1967 . “Some Observations on Measurement and Statistics.” . Social Forces, , 46 December : 151 – 160 .
   Web of Science ®Google Scholar
• _____ . 1968 . “Reply to Champion and Morris,” . Social Forces, , 46 June : 543 – 544 .
   Google Scholar
• _____ . 1970 . “The Assignment of Numbers to Rank Order Categories,” . American Sociological Review, , 35 June : 515 – 524 .
   Google Scholar
• _____ . 1971 . “In Defense of Assigning Numbers to Ranks,” . American Sociological Review, , 36 June : 521 – 522 .
   Google Scholar
• _____ . 1972 . “Statistical Usage in Sociology: Sacred Cows and Rituals,” . Sociological Methods and Research, , 1 August : 13 – 37 .
   Google Scholar
• _____ . 1975 . “Comment on Henkel's Paper: The Interplay Between Measurement and Statistics,” . Pacific Sociological Review, , 18 January : 27 – 35 .
   Google Scholar
• Lachenbruch , Peter A. 1975 . Discriminant Analysis, , New York : Hafner Press .
   Google Scholar
• Malkovich , J.F. and Afifi , A.A. 1973 . “On Tests for Multivariate Normality,” . Journal of the American Statistical Association, , 68 March : 176 – 179 .
   Web of Science ®Google Scholar
• Martin , W.S. 1978 . “Effects of Scaling on the Correlation Coefficient: Additional Considerations,” . Journal of Marketing Research, , 15 May : 304 – 308 .
   Web of Science ®Google Scholar
• McCullagh , P. 1980 . “Regression Models for Ordinal Data,” . Journal of the Royal Statistical Society , B42 ( 2 ) : 109 – 127 .
   Google Scholar
• Mohberg , N.R. , Ghosh , M. and Grizzle , J.E. 1978 . “Linear Models Analysis of Small Samples of Categorized Ordinal Response Data,” . Journal of Statistical Computation and Simulation, , 7 : 237 – 251 .
   Google Scholar
• Morrison , Donald G. and Toy , Norman E. 1982 . “The Effect of Grouping Continuous Variables on Correlation Coefficients,” . Marketing Science, , 1 Fall : 379 – 389 .
   Google Scholar
• Namboodiri , N. , Carter , L.F. and Blalock , H.M. Jr. 1975 . Applied Multivariate Analysis and Experimental Designs, , New York : McGraw‐Hill .
   Google Scholar
• Nie , Norman H. , Hull , C. Hadlai , Jenkins , Jean G. , Steinbrenner , Karin and Bent , Dale H. 1975 . Statistical Package for the Social Sciences, , Second Edition , New York : McGraw‐Hill Book Company .
   Google Scholar
• O'Brien , R.M. 1979 . “The Use of Pearson's r with Ordinal Data,” . American Sociological Review, , 44 October : 851 – 857 .
   Web of Science ®Google Scholar
• Perreault , William D. and Young , Forrest W. 1980 . “Alternating Least Squares Optimal Scaling: Analysis of Nonmetric Data in Marketing Research,” . Journal of Marketing Research, , 17 February : 1 – 13 .
   Google Scholar
• Prentice , R.L. 1976 . “A Generalization of the Probit and Logit Methods for Dose Response Curves,” . Biometrics, , 32 December : 761 – 768 .
   PubMed Web of Science ®Google Scholar
• Randies , R.H. , Broffit , J.D. and Hogg , R.V. 1978 . “Discriminant Analysis Based on Ranks,” . Journal of the American Statistical Association, , 73 June : 379 – 384 .
   Web of Science ®Google Scholar
• 1982 . SAS User's Guide , Cary, North Carolina : SAS Institute, Inc. .
   Google Scholar
• Tufte , E.R. 1969 . “Improving Data Analysis in Political Science,” . World Politics, , 21 July : 641 – 654 .
   Web of Science ®Google Scholar
• Wolf , C. and Brockett , P.L. “Transformations of Discrete Data for Use with Fisher's Linear Discriminant Function,” . Proceedings of the Business and Economics Section of the American Statistical Association . pp. 569 – 573 .
   Google Scholar
• Linda L. Golden is Professor of Marketing and Patrick L. Brockett is Professor of Finance. Both are at the University of Texas at Austin. We thank the anonymous referrees for their helpful comments.
   Google Scholar