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Augmenting Analysis of Single-Case Math Interventions with Bayesian Multilevel Models: Examining Effect Visualization and Magnitude Uncertainty

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Title: Augmenting Analysis of Single-Case Math Interventions with Bayesian Multilevel Models: Examining Effect Visualization and Magnitude Uncertainty
Language: English
Authors: Garret J. Hall (ORCID 0000-0002-8285-3239), Wilhelmina van Dijk (ORCID 0000-0001-9195-8772), Jenny Root, Kaitlin Bundock
Source: School Psychology. 2026 41(2):219-232.
Availability: American Psychological Association. Journals Department, 750 First Street NE, Washington, DC 20002. Tel: 800-374-2721; Tel: 202-336-5510; Fax: 202-336-5502; e-mail: order@apa.org; Web site: http://www.apa.org
Peer Reviewed: Y
Page Count: 14
Publication Date: 2026
Sponsoring Agency: Department of Education (ED)
Contract Number: H325D140074
Document Type: Journal Articles
Reports - Research
Education Level: Secondary Education
Descriptors: Research Design, Bayesian Statistics, Hierarchical Linear Modeling, Mathematics, Intervention, Mathematics Education, Secondary School Students, Visualization, Effect Size
DOI: 10.1037/spq0000711
ISSN: 2578-4218
2578-4226
Abstract: 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.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1507928
Database: ERIC
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  Data: 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.
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      – SubjectFull: Effect Size
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