This is the first study to show that FDA, SPM and SnPM t-tests provide consistent results when applied to sports biomechanics data. Though the results were similar, selection of one technique over another by applied researchers and practitioners should be based on the underlying parametric assumption of SPM, as well as contextual factors related to the type of waveform data to be analysed and the experimental research question of interest.

The proliferation of new biomechanical technology in laboratory and field settings facilitates the capture of data-sets consisting of complex time-series. An understanding of the appropriate statistical approaches for analysing and interpreting these data-sets is required and the functional data analysis (FDA) family of statistical techniques has emerged in the biomechanical literature. Given the use of FDA is currently in its infancy with biomechanical data, this paper will form the first of a two part series aiming to address practical issues surrounding the application of FDA techniques in biomechanics. This work focuses on functional principal components analysis (fPCA), which is explored using existing literature and sample data from an on-water rowing database. In particular methodological considerations for the implementation of fPCA such as temporal normalisation of data, removal of unwanted forms of variation in a data-set and documented methods for preserving the original temporal properties within a set of curves are explored in detail as a part of this review. Limitations and strengths of the technique are outlined and recommendations are provided to encourage the appropriate use of fPCA within the field of applied sports biomechanics.

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The graphical presentation of the propulsive force applied at the pin plotted relative to the horizontal angle of the oar has been used practically in on-water rowing for the qualitative assessment of skill. How the pattern is related to performance variables has not been well identified, particularly for highly trained sculling athletes. Bivariate functional principal components analysis (bfPCA) was used on force-angle data to identify the main modes of variance in curves representing twenty-seven female rowers of different competition levels (national level and international level), rowing at 32 strokes per minute in a single scull boat. Discriminant function analysis showed moderate classification of rowers using force-angle graphs across both sides of the boat, with rate of force development identified as a potentially important characteristic for international rowers. Additionally for the bow-side, spending less time in the first half of the drive phase was also identified as an important feature for international rowers. Multiple linear regression of scores from the bfPCAs showed that a more pronounced front-peaked profile was associated with a higher average boat velocity. The results of this demonstrate that different characteristics of the force-angle graph may be associated with different metrics of performance.

Sporting performance is often investigated through graphical observation of key technical variables that are representative of whole movements. The presence of differences between athletes in such variables has led to terms such as movement signatures being used. These signatures can be multivariate (multiple time-series observed concurrently), and also be composed of variables measured relative to different scales. Analytical techniques from areas of statistics such as Functional Data Analysis (FDA) present a practical alternative for analysing multivariate signatures. When applied to concurrent bivariate time-series multivariate functional principal components analysis (referred to as bivariate fPCA or bfPCA in this paper) has demonstrated preliminary application in biomechanical contexts. Despite this, given the infancy of bfPCA in sports biomechanics there are still necessary considerations for its use with non-conventional or complex bivariate structures. This paper focuses on the application of bfPCA to the force-angle graph in on-water rowing, which is a bivariate structure composed of variables with different units. A normalisation approach is proposed to investigate and standardise differences in variability between the two variables. The results of bfPCA applied to the non-normalised data and normalised data are then compared. Considerations and recommendations for the application of bfPCA in this context are also provided.