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Related Experiment Video

Updated: Jul 20, 2025

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The Permutation Distancing Test for dependent single-case observational AB-phase design data: A Monte Carlo

Anouk Vroegindeweij1, Linde N Nijhof2, Patrick Onghena3

  • 1Department of Pediatric Rheumatology/Immunology, Wilhelmina Children's Hospital, University Medical Center Utrecht, Utrecht University, Utrecht, Netherlands.

Behavior Research Methods
|August 1, 2023
PubMed
Summary
This summary is machine-generated.

The Permutation Distancing Test (PDT) effectively evaluates treatment effects in single-case observational data, showing high power and reliable error rates, especially with more observations and higher autocorrelation.

Keywords:
AutocorrelationMonte Carlo simulationPermutationPermutation distancing testSingle-case observational design

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Area of Science:

  • Statistics
  • Behavioral Science
  • Single-Case Research Design

Background:

  • Evaluating treatment effects in single-case observational design (SCOD) data with dependencies is challenging.
  • Existing methods like the Single-Case Randomization Test (SCRT) and traditional permutation tests have limitations in power and error control, especially with autocorrelation.

Purpose of the Study:

  • To introduce and evaluate the Permutation Distancing Test (PDT) for analyzing dependent SCOD AB-phase data.
  • To compare the statistical power and type I error rate of the PDT against SCRT and traditional permutation tests.

Main Methods:

  • Monte Carlo simulations were employed to estimate PDT power and type I error rates.
  • Data were simulated across various treatment effect levels, autocorrelation levels, and observation numbers (30, 60, 90, 120).
  • Comparisons were made with the Single-Case Randomization Test (SCRT) and traditional permutation tests.

Main Results:

  • The PDT demonstrated sufficient power (≥ 80%) to detect medium treatment effects with 30 observations up to autocorrelation ≤ .45.
  • With 60 observations, the PDT achieved sufficient power regardless of autocorrelation; with ≥ 90 observations, it detected small effects up to autocorrelation ≤ .30.
  • The PDT maintained acceptable type I error rates (≤ 5% with ≥ 60 observations and autocorrelation < .60) and outperformed SCRT in power and traditional permutation tests in error control.

Conclusions:

  • The Permutation Distancing Test (PDT) is a robust nonparametric method for analyzing dependent SCOD AB-phase data without linear trends.
  • The PDT offers improved power and type I error control compared to existing methods, particularly in the presence of autocorrelation and with fewer observations.