Impact of within-case variability on Tau-U indices and the hierarchical linear modeling approach for multiple-baseline design data: A Monte Carlo simulation study
Abstract
This study focuses on two different measures to quantify intervention effectiveness for multiple-baseline design data. The influence of 216 design conditions on the estimate of the Tau-U index (with three different variants) and the regression-based effect size is empirically investigated through a Monte Carlo simulation study. Results demonstrate that the magnitude of the within-case variance influences the Tau-U indices the most when the true intervention effect is small relative to large within-case variance. The within-case variance does not systematically influence the regression-based effect size measure. The Critical Tau-U is introduced to help determine if Tau-U estimates indicate evidence in support of an intervention effect and address underlying issues with currently used benchmarks.
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PEM-T was selected over other overlap indices that also control for trend due to limitations of these methods in controlling trend with few data points and their reduced accuracy with significant within-case variability.
“PEM-T was selected over other overlap indices that also control for trend (i.e Tau-U) due to limitations of these methods in controlling trend with few data points and their reduced accuracy with significant within-case variability (Fingerhut et al., 2021).”
From A single-case experimental evaluation of a new group-based intervention to enhance adjustment to life with acquired brain injury: VaLiANT (valued living after neurological trauma) (2022) · cites this paper as Fingerhut et al., 2021
Cites
Combining nonoverlap and trend for single-case research: Tau-U
Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011) · Behavior Therapy · doi:10.1016/j.beth.2010.08.006 · Cited by 1,468 · see citing works
An improved effect size for single-case research: nonoverlap of all pairs.
Parker, R. I., & Vannest, K. (2009) · Behavior Therapy · doi:10.1016/j.beth.2008.10.006 · Cited by 1,126 · see citing works
Evaluating Intervention Effects in Single‐Case Research Designs
Vannest, K. J., & Ninci, J. (2015) · Journal of Counseling & Development · doi:10.1002/jcad.12038 · Cited by 665 · cited 4× · see citing works
“In the past, researchers have used benchmarks to determine if an intervention effect is present (e.g. Parker & Vannest, 2009; Vannest & Ninci, 2015).”
BackgroundInfluentialSingle-case experimental designs: a systematic review of published research and current standards
Smith, J. D. (2012) · Psychological Methods · doi:10.1037/a0029312 · Cited by 630 · cited 2× · see citing works
“This study focused on MBD data across cases because MBDs are internally and externally valid and commonly used in practice (see Jamshidi et al., 2021 in this issue; Smith, 2012); however, Tau-U is not capable of modeling between-case variance.”
MethodInterpreting Kendall’s Tau and Tau- <i>U</i> for single-case experimental designs
Brossart, D. F., Laird, V. C., & Armstrong, T. W. (2018) · Cogent Psychology · doi:10.1080/23311908.2018.1518687 · Cited by 210 · see citing works
The Aggregation of single-case results using hierarchical linear models
Van den Noortgate, W., & Onghena, P. (2007) · The Behavior Analyst Today · doi:10.1037/h0100613 · Cited by 86 · see citing works
Results reporting in single case experiments and single case meta-analysis
Vannest, K. J., Peltier, C., & Haas, A. (2018) · Research in Developmental Disabilities · doi:10.1016/j.ridd.2018.04.029 · Cited by 51 · see citing works
Fingerhut, J., Xu, X., & Moeyaert, M. (2021) · Evidence-Based Communication Assessment and Intervention · doi:10.1080/17489539.2021.1937851 · Cited by 43 · cited 1× · see citing works
“This flowchart along with an empirical demonstration can be seen in Fingerhut et al. (2021), within this same special issue.”
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Sathananthan, N., Dimech-Betancourt, B., Morris, E., Vicendese, D., Knox, L., Gillanders, D., Das Nair, R., & Wong, D. (2022) · Neuropsychological Rehabilitation · doi:10.1080/09602011.2021.1971094 · Cited by 31 · see citing works
“PEM-T was selected over other overlap indices that also control for trend (i.e., Tau-U ) due to limitations of these methods in controlling trends in phases with few data points and their reduced accuracy with significant within-case variability (Fingerhut et al., 2021).”
Method
- Authors
- Fingerhut, J., Xu, X., & Moeyaert, M.
- Affiliations
- University at Albany, State University of New York (US)
- Corresponding author
- Fingerhut, Joelle
- Venue
- Evidence-Based Communication Assessment and Intervention
- Publisher
- Informa UK Limited
- Published
- 2021-07-03
- Volume
- 15
- Issue
- 3
- Pages
- 115-141
- ISSN
- 1748-9539 (ISSN-L)
- 1748-9547
- OpenAlex
- W3180006176
- Cited by
- 12
- References
- 8
- Citations by year
- 2025: 1 · 2024: 4 · 2023: 4 · 2022: 2 · 2021: 1
- FWCI
- 1.60
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Evidence-Based Communication Assessment and Intervention (publishedVersion)
- Funders
- Institute of Education Sciences, U.S. Department of Education (R305D190022)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Management Science and Operations Research › Evaluation and Performance Assessment
- Keywords
- multiple baseline design, intervention effectiveness, effect size, single-case experimental design, intervention effect estimation
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