A Nonparametric Multivariate Test for a Monotone Trend among k Samples

- Journal title : Korean Journal of Applied Statistics
- Volume 22, Issue 5, 2009, pp.1047-1057
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2009.22.5.1047

Title & Authors

A Nonparametric Multivariate Test for a Monotone Trend among k Samples

Hyun, Noo-Rie; Song, Hae-Hiang;

Hyun, Noo-Rie; Song, Hae-Hiang;

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

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

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

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

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

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

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

11.

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

12.

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

13.

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

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