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A Nonparametric Multivariate Test for a Monotone Trend among k Samples
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 Title & Authors
A Nonparametric Multivariate Test for a Monotone Trend among k Samples
Hyun, Noo-Rie; Song, Hae-Hiang;
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 Abstract
The nonparametric bivariate two-sample test of Bennett (1967) is extended to the multivariate k sample test. This test has been easily modified for a monotone trend among k samples. Often in applications it is important to consider a set of multivariate response variables simultaneously, rather than individually, and also important to consider testing k samples altogether. Different approaches of estimating the null covariance matrices of the test statistics resulted in the same limiting form. The multivariate k sample test is applied to the non-normal data of a randomized trial conducted for a period of four weeks in mental hospitals. The purpose of the trial is to compare the efficacy of three different interventions for a relief of the frequently occurring problems of constipation, caused as a side effect of antipsychotic drugs during hospitalization. The bowel movement status of patient for a week is summarized into a single severity score, and severity scores of four weeks comprise a four-dimensional multivariate variable. It is desirable with this trial data to consider a multivariate testing among k samples.
 Keywords
U statistics;multivariate test;nonparametric test;severity scores;
 Language
English
 Cited by
 References
1.
Bennett, B. M. (1967). On the bivariate generalization of the Wilcoxon two sample test and its relation to rank correlation theory, Review of the International Statistical Institute, 35, 30-33 crossref(new window)

2.
Dietz, E. J. (1989). Multivariate generalizations of Jonckheere's tests

3.
Dietz, E. J. and Kileen, T. J. (1981). A nonparametric multivariate test for monotone trend with pharmaceutical applications, Journal of the American Statistical Association, 76, 169-174 crossref(new window)

4.
Dietz, E. J. and Kileen, T. J. (1981). A nonparametric multivariate test for monotone trend with pharmaceutical applications, Communications in Statistics - Theory and Methods, 18, 3763-3783 crossref(new window)

5.
Elliot, D. L., Watts, W. J. and Girard, D. E. (1983). Constipation: Mechanism and management of a common clinical problem, Postgraduate Medicine, 74, 143-149

6.
Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution, Annals of Mathematical Statistics, 19, 293-325 crossref(new window)

7.
Hollander, M. and Wolfe, D. A. (1999). Nonparametric Statistical Methods, John Wiley & Sons, Inc., 2nd edition, 204

8.
Jonckheere, A. R. (1954). A distribution-free k-sample test against ordered alternatives, Biometrika, 41, 133-145 crossref(new window)

9.
Kendall, M. G. (1962). Rank Correlation Methods, Griffin & Co., 3rd edition, 135

10.
Mann, H. B. and Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other, Annals of Mathematical Statistics, 18, 50-60 crossref(new window)

11.
Oja, H. (1983). Descriptive statistics for multivariate distributions, Statistics and Probability Letters, 1, 327-332 crossref(new window)

12.
Oja, H. and Randles, R. H. (2004). Multivariate nonparametric tests, Statistical Science, 19, 598-605 crossref(new window)

13.
Randles, R. H. (2000). A simpler, affine-invariant, multivariate, distribution-free sign test, Journal of the American Statistical Association, 95, 1263-1268 crossref(new window)

14.
Randles, R. H. and Wolfe, D. A. (1979). Introduction to the Theory of Nonparametric Statistics, John Wiley & Sons, Inc.

15.
Yang, S. (1992). Effects of fluid intake, dietary fiber supplement and abdominal muscle exercises on antipsychotic drug-induced constipation in schizophrenics, Journal of Catholic Medical College, 45, 1501-1514