A Vector Model of Single Case Design Data and Its Use in Analyzing Large Single Case Design Replication Series

Abstract

In this paper mathematical concepts from vector analysis are used to develop a vector model of single case design data. From this model several objective measures of change between single case design phases are developed. One, the Treatment Phase Effect Vector, is a multivariate index of change that indicates the change in level of a dependent variable at specific measurement points across treatment phase relative to baselme phase. A second, the Treatment Phase Effect, is a univariate index that represents the gross, overall change in a dependent variable that may have occurred between treatment and baseline phases. These, and other, conceptual tools have been developed for use in experimental studies of the effectiveness of a social work intervention in which methods from group comparison and single case design methodologies are used concomitantly. The use of these mathematical concepts in social work research is illustrated and discussed.