Percentage of nonoverlapping data calculation selects the most improved baseline value and counts intervention observations strictly beyond it in the predefined improvement direction. Divide that count by valid intervention observations. A tie with the baseline extreme overlaps under the usual strict rule. Report the raw phases, extreme, ties, missing states, baseline trend, and the metric's sensitivity to one baseline point.

What PND asks

Percentage of nonoverlapping data, or PND, asks how many intervention observations improve beyond the single best baseline observation. When higher values are preferred, the reference is the highest valid baseline value. When lower values are preferred, the reference is the lowest valid baseline value. Intervention observations must move strictly past that extreme under the rule used here.

A percentage of nonoverlapping data calculation is defensible only when the baseline extreme comes from a valid, comparable phase.

PND is easy to explain and audit, but its reference comes from one point. An unusual baseline extreme can dominate the result even when most intervention observations show a clear and meaningful shift. Keep the raw graph and broader single-case analysis primary.

Define the comparison before calculating

State the target, unit, desired direction, baseline and intervention boundaries, observation opportunity, and data-quality rules. Confirm that both phases measure the same construct in the same way. A count in baseline and a percentage in intervention cannot be compared until they are transformed to a common, clinically valid unit.

Review blank cells, missed visits, duplicate timestamps, late entries, and points collected under different conditions. A blank is not a zero. A structurally unavailable observation should retain that state. Report valid values over planned observations for both phases and keep all exclusions with reasons.

The denominator is every valid intervention observation. A value that overlaps the baseline range remains in the denominator. Missing intervention observations stay outside it, although the pattern of missingness still affects confidence in the result.

Calculate PND step by step

  1. Declare whether improvement means higher or lower values.
  2. Identify the improvement-direction baseline extreme.
  3. Compare each valid intervention value with that one reference.
  4. Count values strictly beyond the extreme as nonoverlapping improvements.
  5. Count ties and other overlapping values separately.
  6. Divide the nonoverlapping count by all valid intervention observations and multiply by 100.

The higher-is-better formula is:

\[PND=(B{above\ baseline\ maximum}/nB)\times100.\]

For lower-is-better outcomes, count values below the baseline minimum. Under the strict convention, an intervention value equal to the extreme overlaps and earns no numerator credit. Name that convention in the calculation record so a later reviewer does not silently apply another boundary rule.

Worked example: Luca's phases

Luca's baseline values are 2, 4, 4, 6, and 8. Higher values were defined as improvement. The baseline maximum is therefore 8.

Intervention values are 9, 8, 10, 7, 11, and 12. Values 9, 10, 11, and 12 strictly exceed 8. One intervention value ties the reference at 8, and one value, 7, remains below it. Four of the six valid intervention points are nonoverlapping improvements:

\[PND=(4/6)\times100=66.666\ldots\%=66.7\%.\]

The audit reconciliation is four improvements, one tie, and one other overlap, totaling six. The tied 8 stays in the denominator and outside the numerator. No observation was imputed or dropped.

This calculation says that 66.7% of Luca's observed intervention values were better than every observed baseline value. It does not mean the target improved by 66.7%, nor does it say how much the four values exceeded 8.

Graph and report the comparison

Show both raw phases in chronological order with a phase-change line. Add a horizontal reference at the baseline extreme and label it “baseline maximum = 8.” Preserve the tied point at 8 and the value at 7 so the reader can see why they overlap. A PND percentage belongs in an annotation or report, not on the outcome axis as another data point.

A reproducible report could say:

Baseline contained five valid observations with a maximum of 8. Four of six valid intervention observations were strictly above 8, one tied 8, and one was below it. PND was 66.7% under the declared strict tie rule. The result was interpreted with baseline trend, variability, immediacy, and the raw magnitude of change.

Also report planned observations, missing reasons, direction, numerator, denominator, rounding, and the calculation version. Avoid a universal label such as “effective” based on the percentage alone.

Examine sensitivity and edge cases

  • If the baseline maximum of 8 were a data-entry error, correcting it could change the reference and every classification.
  • A valid but rare baseline spike can yield low PND despite a stable improvement in most intervention values.
  • A very stable baseline makes the extreme more representative, but PND still ignores magnitude and chronology.
  • With six intervention points, one classification changes PND by 16.7 percentage points.
  • Many ties may reflect limited measurement resolution, a floor or ceiling, or genuine lack of separation.
  • Strong baseline trend can make the most extreme observation occur at the phase edge, reducing the usefulness of a fixed reference.
  • Missing observations during difficult conditions can inflate PND even when no arithmetic error exists.
  • Reversing the improvement direction after inspecting results invalidates the analysis.

Do not winsorize or remove an extreme merely to improve the percentage. Correct a value only when the source record shows an error or a prespecified validity rule applies. Preserve the original value, correction evidence, owner, and recomputation.

Interpret PND within the design

The single-case methods review describes PND as a common nonoverlap measure and documents its computational limits. Research on decision accuracy across overlap measures shows why phase size and data pattern matter and why universal percentage bands can mislead.

The WWC Version 5.0 handbook integrates level, trend, variability, immediacy, overlap, consistency, and repeated demonstrations. PND describes one form of overlap. It cannot establish immediacy, replication, treatment fidelity, maintenance, generalization, social importance, or causality.

Qualified clinicians should review the graph, magnitude, client experience, contextual changes, health factors within scope, other services, and possible adverse effects. PND cannot determine diagnosis, treatment selection, intensity, medical necessity, authorization, discharge, or safety.

Review the result with Luca

Use an accessible graph or tactile, spoken, or simplified summary that Luca can understand. Explain that four of six intervention points were higher than the highest baseline point. Ask whether the measured outcome matters, whether the differences are noticeable in daily life, and whether the intervention conditions are acceptable. Record Luca's communication, assent or dissent when applicable, and requested changes.

Keep AAC, interpreters, mobility supports, breaks, food, water, bathroom access, prescribed care, and emergency help available. ASHA's AAC guidance supports continued access to communication across assessment and clinical review.

Clinician release checklist

Before using PND, verify the phase definitions, stable measurement unit, improvement direction, valid-point coverage, missing and duplicate states, baseline extreme, strict tie rule, intervention classifications, numerator, denominator, rounding, raw graph, sensitivity to the extreme, client review, qualified interpretation, calculation owner, and next review date. Retain the worksheet under applicable privacy and access controls and reopen it whenever a source value, phase, goal, or method changes.

Related resources

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