Illustrating How the Bayesian Unknown Change-Point Model Supplements Visual Analysis for Single Case Designs

• In Event: Bayesian Methods in Single-Case Experimental Designs

Abstract

The purpose of the present study is to highlight how the Bayesian change-point model can supplement visual analysis to analyze single case experimental design (SCED) data. Although establishing treatment effect using visual analysis is the most commonly used practice, this may not always be easy. Difficulties may arise when: (a) immediacy is not possible due to the nature of the treatment, (b) errors are autocorrelated, and (c) the experimental effect size is not striking. Statistical analyses of SCEDs face challenges such as small samples, autocorrelated errors, and count or ratio data. The Bayesian unknown change-point model (BUCP, Natesan & Hedges, in press) overcomes statistical challenges posed by SCED data. It can be used to investigate all analytic criteria that are needed to demonstrate causal evidence as prescribed by the what works clearinghouse (WWC; Kratochwill et al., 2010).
According to WWC, the criteria for demonstrating evidence of a causal relation between an independent variable and an outcome variable are: documenting the consistency of level, trend, and variability within each phase, documenting the immediacy of the effect, the proportion of overlap, the consistency of the data across phases in order to demonstrate an intervention effect, and comparing the observed and projected patterns of the outcome variable, and examining external factors and anomalies (e.g., a sudden change of level within a phase). For the first two steps we describe how BUCP analysis can be utilized to augment visual analysis. For illustrative purposes, these standards will be applied to a real data example. We will walk the audience through the visual and statistical analyses in an interactive session.
Data were obtained from a published study (Feldman & Matos, 2012) which used a multiple baseline design and showed that training paraprofessionals in social facilitation procedures resulted in increased reciprocal social behaviors of the children with autism with their peers. Three paraprofessionals received training in teaching techniques and social facilitation procedures to help children with autism in reciprocal social behavior with their peers. Three children with autism were each assigned one of the trained paraprofessionals for assistance with reciprocal social behavior. The dependent variable is the percent of intervals the child is engaged in reciprocal social behavior with their peers. Graphical descriptions of data for Phase A (baseline) and Phase B (intervention) for each child showed that in the baseline phase, before the paraprofessionals received training, the three children with autism rarely engaged in reciprocal social interactions with their peers. However, after paraprofessionals received the training, children’s social engagement improved considerably (Figure 1). Using WWC standards for visual analysis for causality, Feldman and Matos (2012) showed that the reciprocal social behavior of the children with autism increased rapidly. Tables 1 and 2 show the parameters of BUCP that correspond to the WWC criteria and the estimates. These will be expanded upon in the final paper.

Authors

• Ratna Nandakumar, University of Delaware

• Prathiba Natesan, University of North Texas

• Pragya Shrestha, University of Delaware