BRIEF EDITORIAL Single-Case Research Designs: Elegant Analyses

Dr. Marcia M. Ward and her associates (this issue) applied both traditional multivariate analytic procedures to their grouped data, and a time series analytic procedure (Box—Jenkins) to findings from each of their eight subjects separately. The latter method carried the day in its sensitivity and informative value in tracking the impact of laboratory stressors on the concentrations of catecholamines in plasma samples from their subjects. This approach to the analysis of repeated measures over time was a result of over a decade of collaborative research by Professor George E. P. Box at the University of Wisconsin and Professor Gwilym M. Jenkins at the University of Lancaster. Their work, sponsored by the Air Force Office of Scientific Research and the British Science Research Council, culminated in their classic volume Time Series Analysis: Forecasting and ControJ (1). Most of the problems to which the Box-Jenkins technique has traditionally been applied (in the fields of economics, business administration, agriculture, engineering, and the natural sciences) have been based upon grouped data. But the extension of this approach to data generated by single subjects, as exemplified in Ward's study, has been facilitated by the clear explication provided recently by Porter Home, Mark Yang, and William Ware (2). The Box-Jenkins model-building procedure begins with an effort to fit a traditional linear regression line to the data set. The departures from this regression line are computed and these residuals from this first approximation provide the basic data for the analysis. The remaining steps of the time series procedure are designed to generate a specific statistical model to summarize the interrelationships appearing among the consecutive data points. Broadly, these steps comprise identification techniques (to suggest what particular kind of model might be worth considering); fitting of specific values (to provide initial estimates of either the parameters of the model or Bayesian posterior distributions); and diagnostic checks (to detect any remaining model inadequacies). The procedures are iterative, to improve upon the successively more accurate summarization of the various contributions to the patterns of interrelationship found in a particular set of data. The model-building steps can be extended to the task of modeling the dynamic interplay, if any, between various measures (for example, epinephrine and norepinephrine determinations in the study of Ward and her colleagues). Obviously, these elaborate techniques demand sizable data sets, larger than most traditional single-subject research designs now generate (a minimum of 35 to 40 data points, according to Home et al.). Several statistical packages now contain the necessary computational components for the Box— Jenkins technique, most notably the revised Statistical Analysis System (SAS User's Guides: Basic and Statistical (both 1982) and SAS/ETS package (1980)). Home et al. (2) specify at least five parts of the needed set of software: data transformation; a least-squares program permitting the saving of the residuals; data