Evaluating the Application of Multivariate Normality Tests in Ensuring Model Validity in Complex Data Analysis

Posted: Jan 14, 2006

• Brandon West
• Brian Butler
• Brianna Ramirez

Abstract

The proliferation of complex data analysis techniques across scientific and industrial domains has heightened the importance of rigorous model validation procedures. While statistical models frequently assume multivariate normality, practical applications often neglect comprehensive testing of this fundamental assumption. This oversight becomes particularly problematic in high-dimensional settings where the curse of dimensionality amplifies the consequences of distributional violations. Traditional model validation approaches typically focus on residual analysis and goodness-of-fit measures while paying insufficient attention to the underlying distributional assumptions that form the theoretical foundation of many statistical methods. Contemporary data analysis frequently involves datasets with intricate correlation structures and non-standard distributions, rendering conventional univariate normality tests inadequate for comprehensive model validation. The assumption of multivariate normality underpins numerous analytical techniques including linear discriminant analysis, multivariate analysis of variance, and various forms of regression modeling. When this assumption is violated, parameter estimates may become biased, hypothesis tests can lose validity, and prediction intervals may no longer provide accurate coverage. This research addresses a critical gap in current validation practices by developing and evaluating a systematic framework for incorporating multivariate normality testing into model validation workflows. Our approach recognizes that different multivariate normality tests possess varying sensitivities to specific types of distributional deviations, and that a combination of complementary tests provides more robust assessment than any single test in isolation. We investigate the performance of this framework across diverse data scenarios and demonstrate its practical utility through both simulation studies and real-world applications. The novelty of our contribution lies in the integration of multiple multivariate normality tests into a cohesive validation protocol that can be systematically applied across different analytical contexts. Rather than treating multivariate normality as a binary condition, our framework provides graduated assessment.