Statistical Power of Piecewise Regression Analyses of Single-Case Experimental Studies Addressing Behavior Problems

Abstract

In intervention research, single-case experimental designs are an important way to gain insights into the causes of individual changes that yield high internal validity. They are commonly applied to examine the effectiveness of classroom-based interventions to reduce problem behavior in schools. At the same time, there is no consensus on good design characteristics of single-case experimental designs when dealing with behavioral problems in schools. Moreover, specific challenges arise concerning appropriate approaches to analyzing behavioral data. Our study addresses the interplay between the test power of piecewise regression analysis and important design specifications of single-case research designs. Here, we focus on the influence of the following specifications of single-case research designs: number of measurement times, the initial frequency of the behavior, intervention effect, and data trend. We conducted a Monte-Carlo study. First, simulated datasets were created with specific design conditions based on reviews of published single-case intervention studies. Following, data were analyzed using piecewise Poisson-regression models, and the influence of specific design specifications on the test power was investigated. Our results indicate that piecewise regressions have a high potential of adequately identifying the effects of interventions for single-case studies. At the same time, test power is strongly related to the specific design specifications of the single-case study: Few measurement times, especially in phase A, and low initial frequencies of the behavior make it impossible to detect even large intervention effects. Research designs with a high number of measurement times show robust power. The insights gained are highly relevant for researchers in the field, as decisions during the early stage of conceptualizing and planning single-case experimental design studies may impact the chance to identify an existing intervention effect during the research process correctly.