Hypothesis Testing of Multivariate Biomechanical Responses using Statistical Parametric Mapping and Arc-Length Re-Parameterization

Abstract

Detection of differences between experimental biomechanical data sets is critical to quantify effects and their significance. Many forms of biomechanical data are continuous and multivariate in nature, yet contemporary statistical analysis and hypothesis testing most often utilize single-value scalar metrics. However, reducing continuous responses to single-value scalar metrics can introduce bias and eliminate much of the physical context of a response. This study proposes a methodology to perform hypothesis testing directly on continuous multivariate experimental data sets. The methodology couples arc-length re-parameterization with statistical parametric mapping (SPM) to provide a general framework that can be applied to many of the response types found in biomechanics, including sets of responses that do not terminate at a common coordinate or are hysteretic, such as load-unload data. The arc-length-based SPM methodology was applied to three literature data sets representing a cross-section of the types of responses encountered in biomechanics. In each case, the arc-length-based SPM methodology produced results that agreed with contemporary statistical techniques while providing quantification and identification of statistically significant differences between the data sets. The proposed method provided important contextual information and a deeper understanding of the underlying behaviour of a dataset that would otherwise be missed using contemporary single-value scalar metric statistical techniques, such as highlighting specific response features that drive differences between datasets.