A general statistical approach to study measurement error (reliability) of quantitative data is proposed, including graphical analyses. The three probability models by Shrout and Fleiss (1979) are used and illustrated with sports data (psychology, biomechanics). By using the models parameters, several measurement indexes of error can be defined: intraclass correlation coefficient, standard error of measurement, coefficient of variation, limits of agreement. The three probability models are special cases of the linear mixed-effects model whose parameters can be estimated through restricted maximum likelihood. The main advantages of this approach are its theoretical and computing coherency, that datasets with missing values could nevertheless be analysed and confidence intervals computed.
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