gms | German Medical Science

In many scientific fields, the most frequently used experimental or observational study designs rely on multivariate layouts. Such designs can have more than two possibly correlated response variables observed on each experimental unit and should allow comparisons across different treatment groups. Existing parametric tests in multivariate data analysis are based on the assumption that the observations follow multivariate normal distributions with equal covariance matrices across the groups. Such assumptions, however, are impossible to justify in real observations, e.g., for skewed data or ordered categorical data. In fact, existing methods that rely on the assumption of equal covariance matrices tend to be highly liberal or conservative when the covariance matrices of the different groups are actually different. In this study, we develop purely nonparametric multiple inference methods for general multivariate data that neither assume any specific data distribution nor identical covariance matrices across the treatment groups. Continuous, discrete, and even ordered categorical data could be analyzed with these procedures in a unified way. To test hypotheses formulated in terms of purely nonparametric treatment effects, we derive pseudo-rank based multiple contrast tests and simultaneous confidence intervals. Hereby, the simultaneous confidence intervals are compatible with multiple comparisons. The small-sample performance of the procedures is examined in a simulation study which indicates that the proposed procedures (i) control the family-wise error rate quite accurately and (ii) have a substantially higher power under non-normality than mean-based parametric competing methods. A real data example illustrates the application of the proposed tests.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.

This contribution has already been published: [1]