Goodness-of-fit tests for rating scale data: Applying the minimum chi-square method

Journal of Economic and Social Measurement

Volumn 27, Issue 1-2, 2001, Pages 25-39

  Zeis, Charles ^a   Regassa, Hailu ^a   Shah, Abhay ^a   Ahmadian, Ahmad ^a  

^a Malik and Seeme Hasan School of Business   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

STATISTICAL ANALYSIS;

EID: 0035786835     PISSN: 07479662     EISSN: None     Source Type: Journal    
DOI: 10.3233/jem-2001-0193     Document Type: Article

References (34)

1. A. Agresti, Categorical Data Analysis, John Wiley & Co, 1990.
2. T.W. Anderson and D.A. Darling, A Test of Goodness of Fit, Journal of the American Statistical Association 49 (1954), 765-769.
3. E. Babakus and E.F. Jr. Carl, On choosing the appropriate measure of association when analyzing rating scale data, Journal of the Academy of Marketing Science 16(1) (1988).
4. J. Berkson, Minimum chi-square, not maximum likelihood! (with discussion), Annals of Statistics 8 (1980), 457-487.
5. H. Chernoff and E.L. Lehmann, The Use of Maximum Likelihood Estimates in 2 Tests for Goodness of Fit, The Annals of Mathematical Statistics 25 (1954), 579-586.
6. W.G. Cochran, Some Methods for Strengthening the Common 2 Tests, Biometrics 10 (1954), 417.
7. N. Cressie and R.C.R. Timothy, Multinomial Goodness-of-fit Tests, J. R. Statist. Soc. B46(3) (1984), 440-464.
8. J. Gaito, Measurement Scales and Statistics: Resurgence of an Old Misconception, Psychological Bulletin 87 (1980), 564-567.
9. W.F. Gilley and G.E. Uhlig, Factor Analysis and Ordinal Data, Education 114(2) (1993), 258-275.
10. L.J. Gleser, Exact Power of Goodness-of-Fit Tests of Kolmogorov Type for Discontinous Distributions, Journal of the American Statistical Association 80(392) (1985), 954-958.
11. S.D. Horn, Goodness-of-Fit Tests for Discrete Data: A Review and an Application to a Health Impairment Scale, Biometrics 33 (1977), 237-248.
12. G.A. Hughes and N.E. Savin, Is the minimum chi-square estimator the winner in logit regression? Journal of Econometrics 61(2) (1994), 345-367.
13. W.C.M. Kallenberg, J. Oosterhoff and B.F. Schriever, The Number of Classes in Chi-Squared Goodness-of-Fit Tests, Journal of the American Statistical Association 80(392) (1985), 959-968.
14. M.G. Kendall and A. Stuart, The Advanced Theory of Statistics, (Vol. 1), Distribution Theory, (Vol. 2), Inference and Relationship, Hafner Publishing Co., New York, 1973.
15. T.R. Knapp, Treating ordinal scales as interval scales: An attempt to resolve the controversy, Nursing Research 39(2) (1990), 121-123.
16. A.M. Law and W. David Kelton, Simulation Modeling and Analysis, (Second ed.), McGraw-Hill Book Company, New York, 1991.
17. S.R. Lipsitz, Methods of estimation for parameters of a linear model for ordered categorical data, Biometrics 48(1) (1992), 271-282.
18. N.K. Malhotra, Marketing Research, an Applied Orientation, (Second ed.), Prentice-Hall, Upper Saddle River, NJ, 1996.
19. D.C. Miller, Handbook of Research Design and Social Measurement, (5th ed.), Sage Publications, Inc., Thousand Oaks, CA, 1991.
20. J. Neyman, Contribution to the theory of the chi-square test, Proc. Berkeley Symp. on Math. Statist. Prob., (First), 1949, pp. 239-273.
21. K. Pearson, On a criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling, Philos. Mag. 5(50), 157-175. Reprinted in Karl Pearson's Early Statistical Papers, E.S. Pearson, ed., Cambridge University Press, 1900.
22. A.N. Pettitt and M.A. Stephens, The Kolmogorov-Smirnov Goodness-of-Fit Statistic with Discrete and Grouped Data, Technometrics 19(2) (1977), 207-210.
23. C.R. Rao, Theory of estimation by minimum chi-square, Bull. Inst. Inter. Statist. 35 (1955), 25-32.
24. C.R. Rao, Criteria of estimation in large samples, Sankhya A25 (1963), 189-206.
25. T.R.C. Read and A.C.C. Noel, Goodness-of-Fit Statistics for Discrete Multivariate Data, Springer-Verlag, New York, NY, 1988.
26. K. Rosiah, R.R. Kantam and V.L. Narasimham, Optimum Class Limits for ML Estimation in Two-Parameter Gamma Distribution from a Grouped Data, Communications in Statistics: simulation and computation 20(4) (1991), 1173-1190.
27. S. Seo and B. Yum, Estimation Methods for the Mean of the Exponential Distribution Based on Grouped and Censored Data, IEEE Transactions on Reliability 42(1) (1993), 87-96.
28. S.S. Stevens, On the theory of scales of measurement, Science 103 (1946), 677-680.
29. J.C. Townsend and F.G. Ashby, Measurement scales and statistics: The misconception misconceived, Psychological Bulletin 96 (1984), 394-401.
30. P.F. Velleman and L. Wilkinson, Nominal, Ordinal, Interval, and Ratio Typologies Are Misleading. The American Statistician 47(1) (1993), 65-72.
31. Victoria-Feser, Maria-Pia and E. Ronchetti, Robust Estimation for Grouped Data, Journal of the American Statistical Association 92(437) (1997), 333-340.
32. C.L. Wood and N.M. Altavela, Large Sample Results for Kolmogorov-Smirnov Statistics for Discrete Distributions, Biometrika 65 (1978), 235-239.
33. C. Zeis and H. Regassa, Abhay Shah, and Ahmad Ahmadian, Implementing Goodness-of-Fit Tests for Rating Scale Data, The International Business Schools Computing Association 26th Annual Conference Proceedings, Denver, Colorado, July 9-11, 1998.
34. W.G. Zikmund, Business Research Methods. The Dryden Press, New York,