Linear trend in single-case visual and quantitative analyses

Abstract

The frequently used visual analysis of single-case data focuses on data aspects such as level, trend, variability, overlap, immediacy of effect, and consistency of data patterns; most of these aspects are also commonly quantified besides inspecting them visually. The present text focuses on trend, because even linear trend can be operatively defined in several different ways, while there are also different approaches for controlling for baseline trend. We recommend using a quantitative criterion for choosing a trend line fitting technique and comparing baseline and intervention slopes, instead of detrending. We implement our proposal in a free web-based application created specifically for following the What Works Clearinghouse Standards recommendations for visual analysis. This application is especially destined to applied researchers and provides graphical representation of the data, visual aids, and quantifications of the difference between phases in terms of level, trend, and overlap, as well as two quantifications of the immediate effect. An evaluation of the consistency of effects across replications of the AB sequence is also provided. For methodologists and statisticians, we include formulas and examples of the different straight line fitting and detrending techniques to improve the reproducibility of results and simulations.