Nonparametric analysis of the two-period two-treatment crossover design

Abstract

The paper describes a nonparametric model for the analysis of the two-treatment, two-period, four-sequence crossover design. Tests for the equality of treatment effects and for the absence of carryover effects are provided. Some relevant asymptotic results of the proposed tests are obtained and compared with the existing nonparametric and parametric competitors via simulation. It is shown that the proposed tests are comparable to or better than the competitors in terms of type I error and power.

Keywords:

• asymptotic power
• asymptotic distribution
• asymptotically distribution free
• Balaam's design
• crossover design
• exactly distribution free
• step-down procedure
• U-statistic

AMS 2000 Subject Classifications::

• Primary: 62L05
• Secondary: 62G10

Acknowledgements

We thank the referees, the corresponding Associate Editor and the Editor for their comments and suggestions that have led to greatly improving the paper. We are also grateful to Professor Manisha Pal, Department of Statistics, University of Calcutta, for careful reading of the manuscript.

Funding

The work of Suryasish Chatterjee is supported by a research grant from the Council for Scientific and Industrial Research, India [sanction No. 09/028(0840)/2011-EMR-I].