A new formulation of the coefficient of multiple correlation to assess the similarity of waveforms measured synchronously by different motion analysis protocols

Different 3D motion analysis protocols are currently available, but little is known regarding the level of similarity of their outcomes, e.g. whether a joint-angle waveform from one protocol can be interchanged with that measured by another protocol. Similarity assessments are therefore urgent to ease the comparison of results. In this context, a major issue is how to quantify the similarity between waveforms measured synchronously through different protocols, within each of many movement-cycles (e.g. gait-cycle), when the effect of protocols on waveforms similarity is the only of interest. For this purpose we developed a new formulation of the statistical index called coefficient of multiple correlation (CMC). The CMC measures the overall similarity of waveforms taking into account the concurrent effects of differences in offset, correlation, and gain. The within-day CMC originally proposed by Kadaba et al. [7], was firstly reinterpreted in terms of "excluded factors". Then, the new formulation was set to assess the inter-protocol similarity, removing the between-gait-cycle variability. An example showing the effectiveness of the new formulation is presented regarding the pelvis-trunk and ankle kinematics.