Multi-response permutation procedures for a priori classifications

Key Points

• To develop an exact permutation testing procedure and computationally efficient distributional approximations for analyzing multi-response data organized into predefined subgroups.
• Derived a test statistic based on the average Euclidean distance or generalized norm between multivariate points within a priori disjoint subgroups in r-dimensional space.
• Formulated alternative continuous approximation tests based on beta and normal distributions.
• Evaluated the exact and approximate procedures on two empirical social science datasets alongside simulations featuring extreme data configurations.
• The exact permutation procedure provides rigorous hypothesis testing for multivariate group separation without requiring conventional distributional assumptions.
• Beta and normal distribution approximations produce test statistics that align closely with exact permutation tests across standard applications.
• Evaluation under varied conditions demonstrates consistent and robust test behavior even when applied to extreme geometric configurations.