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Sports Biomech. 2019 Oct 3:1-22. doi: 10.1080/14763141.2019.1655089. [Epub ahead of print]

Test-retest reliability measures for curve data: an overview with recommendations and supplementary code.

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Department of Statistics, Umeå School of Business, Economics and Statistics, Umeå University , Umeå , Sweden.
Department of Statistical Sciences, Catholic University of the Sacred Heart , Milan , Italy.
Department of Community Medicine and Rehabilitation, Physiotherapy, Umeå University , Umeå , Sweden.


The purpose of this paper is to provide an overview of available methods for reliability investigations when the outcome of interest is a curve. Curve data, or functional data, is commonly collected in biomechanical research in order to better understand different aspects of human movement. Using recent statistical developments, curve data can be analysed in its most detailed form, as functions. However, an overview of appropriate statistical methods for assessing reliability of curve data is lacking. A review of contemporary literature of reliability measures for curve data within the fields of biomechanics and statistics identified the following methods: coefficient of multiple correlation, functional limits of agreement, measures of distance and similarity, and integrated pointwise indices (an extension of univariate reliability measures to curve data, inclusive of Pearson correlation, intraclass correlation, and standard error of measurement). These methods are briefly presented, implemented (R-code available as supplementary material) and evaluated on simulated data to highlight advantages and disadvantages of the methods. Among the identified methods, the integrated intraclass correlation and standard error of measurement are recommended. These methods are straightforward to implement, enable results over the domain, and consider variation between individuals, which the other methods partly neglect.


Agreement; functional data; kinematics; similarity

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