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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. These elements of single-case math intervention analysis necessitate greater continuity in visual and quantitative analysis of intervention impacts in addition to methods to quantify uncertainty in these forms of intervention impact analysis. In the current 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, but these methods also help understand the degree of uncertainty in effect magnitude. This uncertainty quantification is especially important when considering the variety of ways effects may emerge in math interventions, and one form of analysis alone may not adequately characterize intervention impacts. We discuss limitations and future directions of the alignment of Bayesian modeling with visual analysis procedures for single-case math interventions and beyond.
Hall et al. (Mon,) studied this question.