Augmenting analysis of single-case math interventions with Bayesian multilevel models: Examining effect visualization and magnitude uncertainty.

Different types of math interventions and outcomes naturally yield quantitatively and qualitatively different impacts: Some interventions may produce rapid change whereas others may promote the gradual accumulation of skills. Visual and quantitative analyses require greater continuity to understand the different nuances across types of intervention impacts that may emerge. In the present study, we use data from two separate math interventions among secondary students to examine how Bayesian multilevel models can more effectively integrate both visual and quantitative analysis of single-case designs to quantify and visualize uncertainty. We demonstrate that Bayesian models can augment the analysis of single-case designs without compromising the technical sophistication of quantitative analyses or the interpretive ease of visual analysis. These methods also help understand the degree of uncertainty in effect magnitude, which is especially important when considering the variety of ways effects may emerge in math interventions. We discuss limitations and future directions of the alignment of Bayesian modeling with visual analysis procedures for single-case math interventions and beyond. (PsycInfo Database Record (c) 2025 APA, all rights reserved).