Bayesian Unknown Change-Point Models to Investigate Immediacy in Single Case Designs

Prathiba Natesan*, Larry V. Hedges

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Although immediacy is one of the necessary criteria to show strong evidence of a causal relation in single case designs (SCDs), no inferential statistical tool is currently used to demonstrate it. We propose a Bayesian unknown change-point model to investigate and quantify immediacy in SCD analysis. Unlike visual analysis that considers only 3-5 observations in consecutive phases to investigate immediacy, this model considers all data points. Immediacy is indicated when the posterior distribution of the unknown change-point is narrow around the true value of the change-point. This model can accommodate delayed effects. Monte Carlo simulation for a 2-phase design shows that the posterior standard deviations of the change-points decrease with increase in standardized mean difference between phases and decrease in test length. This method is illustrated with real data.

Original languageEnglish (US)
Pages (from-to)743-759
Number of pages17
JournalPsychological methods
Issue number4
StatePublished - Dec 2017


  • Bayesian estimation
  • Markov Chain Monte Carlo
  • n-of-1 designs
  • single case designs

ASJC Scopus subject areas

  • Psychology (miscellaneous)


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