Data from several response variables, potentially measured on different scales, occurrnnaturally in various practical settings such as clinical trials. Treatment differencesrnwith respect to these response variables are usually analyzed using parametric methodsrnunder the assumptions of multivariate normality and covariance homogeneity.rnIn many situations, however, these assumptions are not fulfilled, in particular whenrnthe response variables under consideration are ordered categorical. Thus, a rankbasedrn(nonparametric) approach which disregards the above assumptions is desirable.rnMore importantly, an investigator may be interested to test a global hypothesisrnof no treatment difference versus the alternative that treatment effects are monotonicallyrnincreasing (decreasing) with respect to all responses. A number of studiesrnhave been conducted to address the issue of testing directional alternatives in two orrnmore multivariate samples both in the parametric as well as nonparametric framework.rnGiven that the response variables are measured in a mix of metric and orderedrncategorical scales, the parametric methods are not suitable. In turn, most of therncontributions in the area of nonparametric statistics base their inferences on severalrnpairwise comparisons of treatments in such a way that the ranks are being computedrnpairwise only, that is, only between those two levels that are compared at each step.rnThis reduces the amount of available information and is well known to potentiallyrnlead to paradoxical situations. In order to incorporate more information from multivariaterndata for testing directional hypotheses which involve variables measuredrnrnboth in metric as well as ordered categorical scales in a unified manner we proposerna new rank-based test statistic. The statistic we have derived is a multivariate generalizationrnbased on a coordinate-wise approach of a univariate test statistic proposedrnby Bathke (2009) for alternative patterns within a nonparametric framework. Separaternranking for different variables is employed in order to ensure invariance underrnmonotone transformations of the responses as well as the weights describing alternativernpatters. Unlike most methods available in the literature, the newly introducedrntest handles data with ties, in particular, ordered categorical data as the underlyingrndistribution is not required to be continuous. The test statistic introduced inrnthis dissertation is proved to be accurate in detecting pre-specified equi-directionalrnalternative patterns across two or more multivariate samples trough extensive simulationrnstudies. A comparison is also made with that of the rank-sum type test forrndirectional multivariate problems proposed by Oâ€™Brien (1984) in which the newlyrndeveloped test is in par and sometimes better than the test by Oâ€™Brien. Applicationsrnto several datasets obtained from clinical trials are presented and potential extensionsrnin different directions are discussed.rnThe other more interesting practical issue in directional multivariate problems isrnto test conjectured alternative patterns in which treatments effects are monotonicallyrnincreasing for some of the responses and monotonically decreasing for others. Sornlong as treatment effects can be specified on a priori basis, we suggest interchangingrnthe signs of different responses and making the anticipated direction of treatmentrneffects similar. Following this, we employ the newly developed test statistic to testrntreatment effects in opposite directions in two or more multivariate samples. Furthermore,rnwe employ the closed testing principle in conjunction with the test wernhave proposed in order to identify on which specific responses or sets of responsesrnthe effects are actually observed. An application of this procedure is demonstratedrnby re-analyzing a dose-response dataset. In summary, the test developed in thisrndissertation can handle monotone trends based on a complete case multivariate data.rnDeveloping a test statistic which can handle umbrella alternatives, and/or incompleterncases is differed to future research.