A Bayesian Rate Ratio Effect Size to Quantify Intervention Effects for Count Data in Single Case Experimental Research

Abstract

Single case experimental design (SCED) is an indispensable methodology when evaluating intervention efficacy. Despite long-standing success with using visual analyses to evaluate SCED data, this method has limited utility for conducting meta-analyses. This is critical because meta-analyses should drive practice and policy in behavioral disorders more than evidence derived from individual SCEDs. Even when analyzing data from individual studies, there is merit to using multiple analytic methods since statistical analyses in SCED can be challenging given small sample sizes and autocorrelated data. These complexities are exacerbated when using count data, which are common in SCEDs. Bayesian methods can be used to develop new statistical procedures that may address these challenges. The purpose of the present study was to formulate a within-subject Bayesian rate ratio effect size (BRR) for autocorrelated count data that would obviate the need for small sample corrections. This effect size is the first step toward building a between-subject rate ratio that can be used for meta-analyses. We illustrate this within-subject effect size using real data for an ABAB design and provide codes for practitioners who may want to compute BRR.