Percentage of Nonoverlapping Data
Also known as: PND, Percent Nonoverlapping Data, Nonoverlap of Data Points, Scruggs-Mastropieri PND
The Percentage of Nonoverlapping Data (PND) is a simple effect-size index for single-case research that summarizes how strongly a treatment phase departs from baseline by counting the share of treatment data points that lie beyond the most extreme baseline point. Introduced by Thomas Scruggs, Margo Mastropieri, and Glendon Casto in 1987 to allow quantitative synthesis of single-subject studies, it produces a single 0–100% number that complements visual analysis and can be aggregated across cases in a meta-analysis of single-case designs.
Key highlights
- Extremely simple to compute and explain — it requires only counting points relative to one baseline value.
- Maps closely onto how clinicians already read single-case graphs, aiding communication.
- Bounded on a 0–100% scale with established descriptive benchmarks, making cross-study comparison easy.
- Was the first widely used quantitative summary enabling meta-analysis of single-subject research.
Intuition
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How it works
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When to use it
Use PND when you want a quick, transparent effect-size summary of an AB or multi-phase single-case contrast to supplement visual analysis or to combine many single-case results in a synthesis. It is most defensible when the baseline is stable and free of outliers and when the desired direction of change is clear. It is poorly suited to baselines with a strong trend, to data with floor or ceiling effects, or to noisy baselines containing an extreme point, because a single aberrant baseline value can cap PND artificially low. Newer indices such as NAP or Tau-U are generally preferred when an outlier-robust statistic is needed.
Strengths & limitations
- Extremely simple to compute and explain — it requires only counting points relative to one baseline value.
- Maps closely onto how clinicians already read single-case graphs, aiding communication.
- Bounded on a 0–100% scale with established descriptive benchmarks, making cross-study comparison easy.
- Was the first widely used quantitative summary enabling meta-analysis of single-subject research.
- Hinges entirely on a single baseline data point, so one outlier in baseline can drastically distort the result.
- Has no known sampling distribution, so it cannot yield confidence intervals or significance tests directly.
- Ignores baseline trend, treating a rising baseline the same as a flat one and confounding trend with treatment effect.
- Suffers a ceiling at 100% that cannot distinguish a strong effect from an even stronger one, reducing sensitivity at the top end.
Common pitfalls
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Applications
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Frequently asked
Why is PND so sensitive to baseline outliers?
Because the comparison threshold is the single most extreme baseline point, not a central tendency. If one baseline session happens to be unusually high (when improvement means an increase), that one point sets a very high bar, and even a strongly effective treatment may fail to exceed it, driving PND toward zero. This is the central criticism that motivated outlier-robust alternatives like NAP and Tau-U, which use all pairwise comparisons rather than one extreme value.
How does PND differ from NAP and Tau-U?
PND compares treatment points to one baseline value (the extreme), so it discards most baseline information and lacks a sampling distribution. NAP compares every treatment point to every baseline point, using all the data and yielding a statistic with known standard error and confidence intervals. Tau-U extends this further by also adjusting for baseline trend. Both newer indices are more robust and inferentially grounded, though PND remains simpler to interpret.
Can PND handle a treatment aimed at decreasing a behavior?
Yes. When the goal is to decrease the target, the relevant extreme baseline point is the lowest one, and you count treatment points that fall below it. The logic is identical, only the direction is reversed; what matters is defining the direction of desired change before selecting the extreme baseline point and counting nonoverlap.
Sources
- 1.Scruggs, T. E., Mastropieri, M. A., & Casto, G. (1987). The quantitative synthesis of single-subject research: Methodology and validation. Remedial and Special Education, 8(2), 24–33.
- 2.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.
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Cite this page
ScholarGate. (2026, June 22). Percentage of Nonoverlapping Data. ScholarGate. https://scholargate.app/social-work/percentage-nonoverlapping-data