10th Anniversary Special IssueView this Special Issue
D. J. Best, J. C. W. Rayner, O. Thas, "Nonparametric analysis of blocked ordered categories data: some examples revisited", Advances in Decision Sciences, vol. 2006, Article ID 031089, 9 pages, 2006. https://doi.org/10.1155/JAMDS/2006/31089
Nonparametric analysis of blocked ordered categories data: some examples revisited
Nonparametric analysis for general block designs can be given by using the Cochran-Mantel-Haenszel (CMH) statistics. We demonstrate this with four examples and note that several well-known nonparametric statistics are special cases of CMH statistics.
- A. Agresti, Categorical Data Analysis, Wiley Series in Probability and Statistics, John Wiley & Sons, New York, 2nd edition, 2002.
- M. Alvo and P. Cabilio, “Testing ordered alternatives in the presence of incomplete data,” Journal of the American Statistical Association, vol. 90, no. 431, pp. 1015–1024, 1995.
- R. L. Anderson, “Use of contingency tables in the analysis of consumer preference studies,” Biometrics, vol. 15, pp. 582–590, 1959.
- J. V. Bradley, Distribution-Free Statistical Tests, Prentice-Hall, New Jersey, 1968.
- W. G. Cochran, “Some methods for strengthening the common tests,” Biometrics, vol. 10, pp. 417–451, 1954.
- C. S. Davis, Statistical Methods for the Analysis of Repeated Measurements, Springer Texts in Statistics, Springer, New York, 2002.
- M. M. Desu and D. Raghavarao, Nonparametric Statistical Methods for Complete and Censored Data, Chapman & Hall/CRC, Florida, 2004.
- M. Friedman, “The use of ranks to avoid the assumption of normality implicit in the analysis of variance,” Journal of the American Statistical Association, vol. 32, no. 200, pp. 675–701, 1937.
- IMSL, “IMSL User's Guide-Mathematical & Statistical Functions,” Houston: Visual Numerics. 1995.
- W. H. Kruskal and W. A. Wallis, “Use of ranks in one-criterion analysis of variance,” Journal of the American Statistical Association, vol. 47, no. 260, pp. 583–621, 1952.
- N. Mantel and W. Haenszel, “Statistical aspects of the analysis of data from retrospective studies of disease,” Journal of the National Cancer Institute, vol. 22, pp. 719–748, 1959.
- Q. McNemar, “Note on the sampling error of the difference between correlated proportions or percentages,” Psychometrika, vol. 12, no. 2, pp. 153–157, 1947.
- M. Meilgaard, G. V. Civille, and B. T. Carr, Sensory Evaluation Techniques, CRC Press, Florida, 3rd edition, 1999.
- E. B. Page, “Ordered hypotheses for multiple treatments: a significance test for linear ranks,” Journal of the American Statistical Association, vol. 58, no. 301, pp. 216–230, 1963.
- S. C. Pearce, “Supplemented balance,” Biometrika, vol. 47, no. 3-4, pp. 263–271, 1960.
- J. C. W. Rayner and D. J. Best, A Contingency Table Approach to Nonparametric Testing, Chapman & Hall/CRC, Florida, 2001.
- J. C. W. Rayner, D. J. Best, P. B. Brockhoff, and G. D. Rayner, Nonparametrics for Sensory Science: A More Informative Approach, Blackwell, Iowa, 2005.
- A. Stuart, “A test for homogeneity of the marginal distributions in a two-way classification,” Biometrika, vol. 42, no. 3-4, pp. 412–416, 1955.
- F. Yates, “The analysis of contingency tables with groupings based on quantitative characters,” Biometrika, vol. 35, no. 1-2, pp. 176–181, 1948.
Copyright © 2006 D. J. Best et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.