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Statistical analyses of repeated measures in physiological research: a tutorial

¹ August Krogh Institute, University of Copenhagen
² Department of Epidemiology and Biostatistics, National Institute of Public Health, DK-2100 Copenhagen Ø, Denmark

Address for reprint requests and other correspondence: T. Hansen, Dept. of Epidemiology and Biostatistics, National Institute of Public Health, Svanemøllevej 25, DK-2100 Copenhagen Ø, Denmark (E-mail: THa{at}niph.dk)

Abstract

Experimental designs involving repeated measurements on experimental units are widely used in physiological research. Often, relatively many consecutive observations on each experimental unit are involved and the data may be quite nonlinear. Yet evidently, one of the most commonly used statistical methods for dealing with such data sets in physiological research is the repeated-measurements ANOVA model. The problem herewith is that it is not well suited for data sets with many consecutive measurements; it does not deal with nonlinear features of the data, and the interpretability of the model may be low. The use of inappropriate statistical models increases the likelihood of drawing wrong conclusions. The aim of this article is to illustrate, for a reasonably typical repeated-measurements data set, how fundamental assumptions of the repeated-measurements ANOVA model are inappropriate and how researchers may benefit from adopting different modeling approaches using a variety of different kinds of models. We emphasize intuitive ideas rather than mathematical rigor. We illustrate how such models represent alternatives that 1) can have much higher interpretability, 2) are more likely to meet underlying assumptions, 3) provide better fitted models, and 4) are readily implemented in widely distributed software products.

Key words: experimental design; longitudinal data; analysis of variance; nonlinear mixed effects models

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