Nonoverlap of All Pairs
Also known as: NAP, Nonoverlap of All Pairs (NAP), Parker-Vannest NAP, All-Pairs Nonoverlap
Nonoverlap of All Pairs (NAP) is an effect-size index for single-case research that measures how completely a treatment phase separates from a baseline phase by examining every possible pairing of a baseline point with a treatment point. Introduced by Richard Parker and Kimberly Vannest in 2009 as an improvement on the Percentage of Nonoverlapping Data, NAP reports the proportion of those pairs in which the treatment point shows improvement, is mathematically equivalent to the area under a ROC curve and the Mann-Whitney statistic, and therefore carries a known sampling distribution that supports confidence intervals and significance testing.
Key highlights
- Uses all baseline-treatment pairs, so it is robust to any single baseline outlier, unlike PND.
- Equals the area under the ROC curve and the Mann-Whitney statistic, inheriting a known distribution, confidence intervals, and p-values.
- Bounded in a clear 0.5-to-1 effective range with an intuitive 'probability of superiority' interpretation.
- Easy to aggregate across cases for meta-analysis because it is a standardized nonparametric quantity.
Intuition
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How it works
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When to use it
Use NAP when you want a robust, inferentially grounded nonoverlap effect size for an AB single-case contrast and the baseline is reasonably free of trend. It is preferable to PND whenever baseline outliers are a concern, and it provides confidence intervals for reporting and synthesis. It is less appropriate when the baseline has a meaningful trend that should be removed — Tau-U is then preferred — or when phases are so short that the U distribution is poorly approximated, in which case exact methods or model-based approaches are safer.
Strengths & limitations
- Uses all baseline-treatment pairs, so it is robust to any single baseline outlier, unlike PND.
- Equals the area under the ROC curve and the Mann-Whitney statistic, inheriting a known distribution, confidence intervals, and p-values.
- Bounded in a clear 0.5-to-1 effective range with an intuitive 'probability of superiority' interpretation.
- Easy to aggregate across cases for meta-analysis because it is a standardized nonparametric quantity.
- Does not account for baseline trend, so a pre-existing improving baseline inflates the apparent effect (Tau-U addresses this).
- As a rank-based measure it captures direction of difference, not magnitude, so a small consistent gain and a large one can yield similar NAP.
- Subject to a ceiling at 1.0 that cannot distinguish a strong effect from an extremely strong one.
- The normal approximation to its sampling distribution can be inaccurate when phases are very short.
Common pitfalls
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Applications
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Frequently asked
What does a NAP of, say, 0.85 mean in plain language?
It means that if you randomly picked one baseline observation and one treatment observation, there is an 85% chance the treatment observation would show improvement over the baseline one (counting ties as half). This 'probability of superiority' reading is one of NAP's strengths: it expresses the effect as an intuitive likelihood rather than an abstract index, and 0.5 corresponds to complete overlap or no effect.
Why is NAP considered better than PND?
PND compares the treatment phase to a single extreme baseline point, discarding the rest of the baseline and making it acutely sensitive to outliers, and it has no sampling distribution. NAP compares every baseline-treatment pair, so it uses all the data and no single point can dominate, and it equals the Mann-Whitney/AUC statistic, which supplies confidence intervals and significance tests. It is more robust and inferentially complete while remaining easy to interpret.
Should I use NAP or Tau-U?
Use NAP when the baseline is stable, because it is the simpler pure-nonoverlap statistic. Use Tau-U when the baseline shows a trend you need to remove, since Tau-U adds a Kendall trend component and an optional baseline-trend correction on top of the same all-pairs logic. NAP is the special case of the contrast without trend adjustment, so they are members of the same family.
Sources
- 1.Parker, R. I., & Vannest, K. J. (2009). An improved effect size for single-case research: Nonoverlap of all pairs. Behavior Therapy, 40(4), 357–367.
- 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). Nonoverlap of All Pairs. ScholarGate. https://scholargate.app/social-work/nap-nonoverlap-all-pairs