Browse > Article
http://dx.doi.org/10.5351/KJAS.2013.26.4.595

Developing of Exact Tests for Order-Restrictions in Categorical Data  

Nam, Jusun (Department of Statistics, Ewha Womans University, Biologics Division, NIFDS)
Kang, Seung-Ho (Department of Applied Statistics, Yonsei University)
Publication Information
The Korean Journal of Applied Statistics / v.26, no.4, 2013 , pp. 595-610 More about this Journal
Abstract
Testing of order-restricted alternative hypothesis in $2{\times}k$ contingency tables can be applied to various fields of medicine, sociology, and business administration. Most testing methods have been developed based on a large sample theory. In the case of a small sample size or unbalanced sample size, the Type I error rate of the testing method (based on a large sample theory) is very different from the target point of 5%. In this paper, the exact testing method is introduced in regards to the testing of an order-restricted alternative hypothesis in categorical data (particularly if a small sample size or extreme unbalanced data). Power and exact p-value are calculated, respectively.
Keywords
Exact test; categorical data; order-restricted alternative hypothesis;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Robertson, T., Wright, F. T. and Dykstra, R. L. (1988). Order Restricted Statistical Inference, Wiley, New York.
2 Barlow, R. E., Bartholoew, D. J., Bremner, J. M. and Brunk, H. D. (1972). Statistical Inference under Order Restrictions, Wiley, New York.
3 Barnard, G. A. (1979). In Contradiction to J. Berkson"s Dispraise: Conditional tests can be more efficient, Journal of Statistical Planning and Inference, 3, 181-188.   DOI   ScienceOn
4 Bartholomew, D. J. (1959). A test of homogeneity for ordered alternatives, Biometrika, 46, 36-48.   DOI
5 Cytel (2006). StatXact, version 6.0, Software for Exact Nonparametric Statistical Inference with Continuous or Categorical Data. Cytel Software: Cambridge, MA
6 Kang, S. H. (2002). Investigation on exact tests, The Korean Journal of Applied Statistics, 15, 187-199.   과학기술학회마을   DOI   ScienceOn
7 Kang, S. H. and Ahn, C. (2008). Tests for the homogeneity of two binomial proportions in extremely unbalanced $2{\times}2$ contingency tables, Statistics in Medicine, 27, 2524-2535.   DOI   ScienceOn
8 Mehta, C. R. and Patel, N. R. (1983). A network algorithm for performing Fisher's exact test in $r{\times}c$ contingency tables, Journal of the American Statistical Association, 78, 427-434.
9 Mehta, C. R., Patel, N. R. and Gray, R. (1985). Computing an exact confidence intervals for the common odds ratio in several 2${\times}2$ contingency tables, Journal of the American Statistical Association, 80, 969-973.
10 Mehta, C. R., Patel, N. R. and Senchaudhuri, P. (1998). Exact power and sample size computations for the Cochran-Armitage trend tests, Biometrics, 54, 1615-1621.   DOI   ScienceOn