Most methods in statistics are focused on the analysis of mean differences. Mean–difference questions, however, represent only a narrow range of the questions that can be posed. Focusing only on these questions can overlook important questions concerning change and variability. This chapter considers methods to model change and variability.
Most methods in statistics are focused on the analysis of mean differences. Methods such as the analysis of variance are frequently used to draw conclusions about the differences in the means of one or more groups. Applications of regression are used to model how the mean values of a dependent variable change as a function of one or more predictors. Such methods leave researchers familiar with, and well equipped, to asked mean–difference questions. Mean–difference questions, however, represent only a narrow range of the questions that can be posed. Focusing only on these questions can overlook important questions concerning change and variability.
The distinctive feature of many constructs may not be in mean differences, but rather in the fluctuations that comprise intraindividual variability: the ebb and flow of depressive or anxiety symptomatology; the waxing and waning of chronic pain; and transitions between confusion and clarity in severe dementia. These seemingly complex changes betray dynamics that are not likely to be adequately understood if one considers only mean differences. In many of these cases it is not only desirable to try to understand, and eventually control, mean levels of the construct but also the variation around mean levels. Two patients with similar mean levels of depression might exhibit different etiology and treatment response if one patient has relatively minor variations in affect while the other shows dramatic variation between extreme states. In many cases, fluctuations around a mean level of a variable may be as important, or even more important, than the value of the mean level itself.
Deboeck, P. R. & Boker, S. M. (2015). Analysis of Dynamic Systems: The Modeling of Change and Variability. In S. J. Henly (Ed.) Routledge International Handbook of Advanced Quantitative Methods in Nursing Research, pp. 170–186. Abingdon, UK: Routledge/Taylor & Francis.