Nonparametric directional testing for multivariate problems in conjunction with a closed testing principle.

It is common in a number of disciplines such as economics, sociology, psychology and clinical trials that researchers are interested to test treatment effects among several of the outcomes in the same direction. Such tests can be performed by using equi-directional test statistics for multivariate data. If on the other hand, treatment effects with respect to one or more of the outcomes differ in direction, the power of equi-directional tests is compromised. Thus, we interchanged the signs of different outcomes by multiplying the values with - 1 and made the anticipated direction similar. Following this, we employed a recently proposed test statistic which handles equi-directional alternatives since the direction of treatment effects is made uniform through interchanging the signs. Once monotonic trend, that is, monotonic increasing for some of the outcomes and monotonic decreasing for others is demonstrated through the global test statistic, an investigator may be further interested in which specific outcomes or sets of outcomes actually these trends are observed. To address this issue, we adapted a closed testing principle. The whole procedure is illustrated by data sets from a toxicology study carried out by the National Toxicology Program, and a cost of transporting milk from farms to dairy plants per mile by different trucks. [ABSTRACT FROM AUTHOR]