Comparing N = 1 effect size indices in presence of autocorrelation.
Use PND or SMD—skip regression indices—when your single-case data are short and autocorrelated.
01Research in Context
What this study did
Rumen et al. (2008) ran computer simulations to test six common ways of measuring change in single-case data. They wanted to know which indices stay honest when data points bounce up and down together, a problem called autocorrelation.
They created short data series, added autocorrelation, and watched which indices gave the clearest picture of a real effect.
What they found
Percentage of non-overlapping data (PND) and standardized mean difference (SMD) stayed the least warped. Regression-based indices, like the slope test, were pulled off course the most.
For short series, PND and SMD kept their shape even when autocorrelation was strong.
How this fits with other research
Moeyaert et al. (2022) picked up the same simulation torch but asked a new question: how many single cases do you need for a powerful HLM analysis? Their PowerSCED app now lets you check sample size before you start, building on Rumen’s call for careful planning.
MacNaul et al. (2021) and Echeverria et al. (2024) both sifted piles of single-case studies. Their reviews assume you will need a clean effect size; Rumen tells you which one to trust when the data wiggle.
No direct clash appears—each paper tackles a different corner of the same assessment playground.
Why it matters
Next time you graph a client’s data across five or ten sessions, skip fancy regression lines. Compute PND or SMD instead. These simple metrics survive the autocorrelation that lives in most day-to-day behavior data, so your clinical story stays clear and defensible.
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02At a glance
03Original abstract
Generalization from single-case designs can be achieved by replicating individual studies across different experimental units and settings. When replications are available, their findings can be summarized using effect size measurements and integrated through meta-analyses. Several procedures are available for quantifying the magnitude of treatment effect in N = 1 designs, and some of them are studied in this article. Monte Carlo simulations were used to generate different data patterns (trend, level change, and slope change). The experimental conditions simulated were defined by the degrees of serial dependence and phase length. Out of all the effect size indices studied, the percentage of nonoverlapping data and standardized mean difference proved to be less affected by autocorrelation and to perform better for shorter data series. The regression-based procedures proposed specifically for single-case designs did not differentiate between data patterns as well as did simpler indices.
Behavior modification, 2008 · doi:10.1177/0145445508318866