Statistical analyses of repeated measures in physiological research: a tutorial

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.

Lack of efficacy of music to improve sleep: A polysomnographic and quantitative EEG analysis

“…To test for differences between experimental nights, a linear mixed-effects model was used (Pinheiro and Bates, 2000;Kristensen and Hansen, 2004). The FFT data were positively skewed and were therefore log 10 transformed to normalise the residuals; graphs display the untransformed data.…”

Membrane proteins involved in potassium shifts during muscle activity and fatigue

“…Forces measured during electrical stimulation are expressed as a percentage of the initial force measured at the start of the experiments (t ϭ 0). Results from the K ATP channel experiment (see RESULTS) were published previously as an example to explain the use of different statistical models (27).…”

“…Usually, this model includes three fixed effects: time, treatment, and the interaction between time and treatment. Normally, however, one would not be interested in either the treatment effect or the interaction effect per se (27). Instead the most interesting-and easily interpretable-hypothesis would be to test whether the 12 pairwise differences between the 2 treatments (1 for each time point measurement) would all be the same (i.e., zero).…”

Blunted Hormone Responses to Ipsapirone are Associated with Trait Impulsivity in Personality Disorder Patients

“…We then conducted a series of stepwise multiple regression analyses to evaluate the association of both dimensional (trait) and categorical (diagnostic) measures as independent variables, each first with baseline measures and then with responses to ipsapirone. We have chosen the present analytic approach for several reasons: (1) with repeated-measures ANOVA, the variance is typically misestimated due to the variable correlations between repeated measures typically found in physiology research (Kristensen and Hansen, 2004); (2) change scores are also commonly utilized in longitudinal treatment response designs in psychiatry (Ekstrom et al, 1990), and, as summary measures, have an advantage of ease of interpretability (Hennen, 2003); and (3) stepwise regression allows for an 'omnibus' test of association of a number of predictor variables that are hypothetically related to the dependent variable, which we are compelled to consider given the extensive diagnostic comorbidity inherent in this personality disorder sample. This approach also allows for the simultaneous evaluation of diagnostic and trait/symptom measures, and estimates of the relative portion of the variance accounted for in the dependent variables by these clinical measures.…”