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ANALYSIS RESOURCES

The following list of resources provides an overview of key methods for analyzing single-case experimental designs. It includes:  

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  1. Reviews of Analysis Methods, 

  2. Statistical Techniques, 

  3. Effect Size Metrics, 

  4. Visual Analysis, 

  5. Key StatisticalConsiderations, and 

  6. Other Analysis Resources

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1. Reviews of Analysis Methods for Single-Case Designs 

 

These papers provide reviews of analysis methods for analysing single-case designs.

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  • Manolov, R., & Moeyaert, M. (2016). How can single-case data be analyzed? Software resources, tutorial, and reflections on analysis. Behaviour Modification, 41(2), 179-228. ​

  • Manolov, R., Gast, D. L., Perdices, M., & Evans, J. J. (2014). Single-case experimental designs: Reflections on conduct and analysis. Neuropsychological Rehabilitation, 24(3-4), 634-660. 

  • Mengersen, McGree & Schmid (2015). Statistical Analysis of N-of-1 Trials. In Nikles & Mitchell (Eds.) The Essential Guide to N-of-1 Trials in Health. Springer Netherlands. 

 

 

2. Statistical Techniques for Analysing Single-Case Data 

 

Statistical techniques are methods used to estimate the effect of an intervention while addressing complexities in the data (e.g. trend, autocorrelation, repeated measures).

 

2.1. Regression-Based Approaches

 

2.1.1. Dynamic Regression Modelling

 

Predictive modelling methods that analyse trends over time and handle covariates and time-dependent relationships

 

  • Vieira, R., McDonald, S., Araújo-Soares, V., Sniehotta, F. F., & Henderson, R. (2017). Dynamic modelling of n-of-1 data: powerful and flexible data analytics applied to individualised studies. Health Psychology Review, 11(3), 222-234. 

  • McDonald, S., Vieira, R., & Johnston, D. W. (2020). Analysing N-of-1 observational data in health psychology and behavioural medicine: a 10-step SPSS tutorial for beginners. Health Psychology and Behavioral Medicine, 8(1), 32-54.​ 

 

2.2. Time Series Approaches

 

2.2.1 Autoregressive Integrated Moving Average (ARIMA) Modelling 

 

Predictive modelling methods that analyse trends over time and identify patterns to predict future values. 

 

  • Lane-Brown, A., & Tate, R. (2010). Evaluation of an intervention for apathy after traumatic brain injury: a multiple-baseline, single-case experimental design. The Journal of head trauma rehabilitation, 25(6), 459-469.

 

2.3 Randomization Tests

 

Randomization tests refer to a family of statistical procedures where intervention effects are evaluated against a distribution generated by random reordering of data (i.e., resampling-based significance testing). In contrast to predictive modelling approaches, randomization tests assess experimental control rather than trends, testing whether observed effects occurred by chance. 

 

  • Bouwmeester, S., & Jongerling, J. (2020). Power of a randomization test in a single case multiple baseline AB design. PLoS One, 15(2), e0228355. 

  • Lall, V. F., & Levin, J. R. (2004). An empirical investigation of the statistical properties of generalized single-case randomization tests. Journal of School Psychology, 42(1), 61-86. 

 

2.4. Aggregation Methods

 

2.4.1 Bayesian Methods

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  • Blackston, J. W., Chapple, A. G., McGree, J. M., McDonald, S., & Nikles, J. (2019). Comparison of Aggregated N-of-1 Trials with Parallel and Crossover Randomized Controlled Trials Using Simulation Studies. MDPI Healthcare, 7(4), 137. 

 

2.4.2 Meta-Analysis 

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  • Marso & Shadish (2015). Software for meta-analysis of single-case designs: DHPSmacro

  • Mengersen, K., McGree, J. M., & Schmid, C. H. (2015). Systematic review and meta-analysis using N-of-1 trials. In J. Nikles & G. Mitchell (Eds.) The Essential Guide to N-of-1 Trials in Health (pp. 211-231). Springer. 

 

2.4.3 Multilevel Models 

 

  • Molenaar, P.C., Valsiner J. (2009). How generalization works through the single case: A simple idiographic process  analysis of an individual psychotherapy. YIS: Yearbook of idiographic science 1, 23-38. 

 

 

3. Effect Size Metrics for SCEDs 

 

Effect size refers to quantifying the magnitude of effect in a way that is interpretable and comparable across studies. This section provides an overview of the different effect size metrics used in SCEDs, categorised into overlap and non-overlap methods and standardised mean difference approaches.

 

3.1 Overview of Effect Size Metrics 

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  • Chen, L.T., Wu P.J., Peng C.Y. (2019). Accounting for baseline trends in intervention studies: Methods, effect sizes, and software. Cogent Psychology, 6(1), 1679941. 

 

3.2. Non-Overlap Methods 

 

Non-overlap indices measure how much the intervention phase data exceeds (or falls below) the baseline phase data. These methods are easy to calculate but can be sensitive to trends and data variability.

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  • Parker, R. I., Vannest, K. J., & Davis, J. L. (2011). Effect size in single-case research: A review of nine nonoverlap techniques. Behavior Modification, 35(4), 303-322.

 

3.2.1. Percentage of Non-Overlapping Data (PND)

 

PND measures the proportion of intervention-phase data points exceeding the highest baseline value. PND is simple but highly sensitive to baseline variability and outliers.

 

3.2.2. Percentage of All Non-Overlapping Data (PAND)

 

PAND considers all data points in both phases, providing a more comprehensive measure than PND.

 

3.2.3. Non-Overlap of All Pairs (NAP)

 

NAP compares every baseline point to every intervention point, reporting the proportion of non-overlapping pairs. NAP is more robust than PND and PAND.

 

  • Parker, R.I. & Vannest, K. (2009). An improved effect size for single-case research: Nonoverlap of all pairs. Behavior Therapy. 2009 Dec 1;40(4):357-67. 

 

3.2.4. Tau-U 

 

Tau-U adjusts for baseline trend while measuring non-overlap. Tau-U is more advanced than NAP and PND, making it useful for detecting intervention effects when baseline trends exist.

 

  • Brossart, D. F., Laird, V. C., & Armstrong, T. W. (2018). Interpreting Kendall’s Tau and Tau-U for single-case experimental designs. Cogent Psychology, 5(1), 1518687. 

  • Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011). Combining nonoverlap and trend for single-case research: Tau-U. Behavior Therapy, 42(2), 284-299. 

  • Tarlow, K. R. (2017). An improved rank correlation effect size statistic for single-case designs: Baseline corrected Tau. Behavior Modification, 41(4), 427-467. 

 

Online Tau-U calculators:

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3.3. Standardised Mean Difference (SMD) Approaches

 

Expresses the effect size in standard deviation units. 

 

3.3.1. D Statistic

 

The D statistic expresses the effect of an intervention in standard deviation units, making it comparable to traditional between-group effect sizes. It is derived using regression modelling and accounts for autocorrelation in SCEDs. It is specifically designed for within-case comparisons but can also be used in meta-analysis of SCEDs.

 

  • Shadish, W. R., Hedges, L. V., Pustejovsky, J. E., Boyajian, J. G., Sullivan, K. J., Andrade, A., & Barrientos, J. L. (2014). A d-statistic for single-case designs that is equivalent to the usual between-groups d-statistic. Neuropsychological Rehabilitation, 24(3-4), 528-553. 

  • Shadish (2015). A manual on SPSS® macros to calculate d for both WRDs and multiple baseline designs.

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3.3.2. Between Case Standardised Mean Difference 

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  • Odom, S. L., Barton, E. E., Reichow, B., Swaminathan, H., & Pustejovsky, J. E. (2018). Between-case standardized effect size analysis of single case designs: Examination of the two methods. Research in Developmental Disabilities, 79, 88-96. 

 

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4. Visual Analysis

 

Visual analysis is a fundamental method for interpreting single-case experimental design (SCED) data, allowing researchers to identify patterns, trends, and variability across phases. However, relying solely on visual inspection can lead to subjective interpretations and may miss important statistical trends or small but meaningful intervention effects. To improve the robustness of findings, visual analysis should be complemented with statistical methods.

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  • Lane, J. D., & Gast, D. L. (2014). Visual analysis in single case experimental design studies: Brief review and guideline. Neuropsychological Rehabilitation, 24(3-4), 445-463. 

  • Gast, D. (2014). Visual analysis of graphic data. In D. Gast & J.R. Ledford (Eds.) Single Case Research Methodology. Applications in Special Education and Behavioral Sciences (2nd ed). pp. 176-210. Routledge. 

 

 

5. Key Statistical Considerations 

 

Several factors must be considered when analyzing single-case experimental designs (SCEDs) to ensure valid and reliable results. Sample size considerations are critical for determining the strength and generalisability of findings, particularly in N-of-1 trials. Missing data can introduce bias, and appropriate handling techniques, such as imputation or model-based approaches, help maintain data integrity. 

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5.1. Sample Size Considerations

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  • Senn, S. (2019). Sample size considerations for n-of-1 trials. Statistical Methods in Medical Research, 28(2), 372-383. 

 

5.2. Missing Data

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  • Chen, L. T., Feng, Y., Wu, P. J., & Peng, C. Y. J. (2020). Dealing with missing data by EM in single-case studies. Behavior Research Methods, 52, 131-150. 

  • De, T. K., Michiels, B., Tanious, R., & Onghena, P. (2020). Handling missing data in randomization tests for single-case experiments: A simulation study. Behavior Research Methods, 52, 1355-1370. 

  • Aydin, O. (2024). A Description of Missing Data in Single-Case Experimental Designs Studies and an Evaluation of Single Imputation Methods. Behavior Modification, 48(3), 312-359.

 

5.3. Causal Analysis

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  • Daza (2018) Causal Analysis of Self-tracked Time Series Data Using a Counterfactual Framework for N-of-1 Trials. Methods of Information in Medicine, 57(S01), e10-e21. 

 

 

6. Other analysis resources

 

This section provides additional tools and references to support SCED analysis, including tutorials, effect size calculators, data simulation resources, and curated repositories for analytical software and datasets.

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6.1. Statistical tutorials

 

  • McDonald, S., Vieira, R., & Johnston, D. W. (2020). Analysing N-of-1 observational data in health psychology and behavioural medicine: a 10-step SPSS tutorial for beginners. Health Psychology and Behavioral Medicine, 8(1), 32-54.​ 

  • Senn, S. (2024). The analysis of continuous data from n-of-1 trials using paired cycles: a simple tutorial. Trials, 25(1), 128.

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6.2. Effect Size Calculators 

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  • Vannest, K.J., Parker, R.I., Gonen, O., & Adiguzel, T. (2016). Single Case Research: web based calculators for SCR analysis (Version 2.0). 

 

6.3. Simulating Mock Data from a Single Case Design

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  • Pustejovsky, JE (2018). Easily simulate thousands of single-case designs. 

 

6.4. Websites

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  • Manolov, R. (2019). List of single-case data analysis software tools. A collection of analysis resources for SCEDs on the Open Science Framework. 

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