Nonoverlap of all pairs calculation compares every baseline value with every intervention value in the predefined improvement direction. Score each pair as improvement, deterioration, or tie; ties receive one-half credit in the common NAP formula. Divide improvement pairs plus half the ties by all pairs. Report phase sizes, pair counts, direction, missing states, and metric limits.

What NAP measures

Nonoverlap of all pairs, usually called NAP, compares every valid baseline observation with every valid intervention observation. Each pair is scored as improvement, deterioration, or tie in a direction defined before calculation. The common formula gives a tie one-half point.

A nonoverlap of all pairs calculation requires two clearly bounded phases measured on the same scale.

NAP describes rank separation between two phases. A result near 100% means intervention values tend to rank better than baseline values; a result near 50% indicates substantial mixing under the usual orientation. The metric does not measure how far apart values are, when change occurred, or whether the intervention caused it.

Build the two phase cohorts carefully

Define the baseline and intervention boundaries, target, unit, observation opportunity, and desired direction. Use only comparable measurements. If baseline records prompt level while intervention records percent independent, pairwise comparison has no coherent clinical meaning until the data are expressed under a valid shared definition.

Resolve blanks, missed sessions, duplicate timestamps, late entries, and measurement changes before creating pairs. A blank must not become zero. Preserve exclusions and reasons. Report coverage for both phases because the number of valid observations controls the number of pairs.

If baseline has \(nA\) valid values and intervention has \(nB\), the denominator is

\[N{pairs}=nA\times n_B.\]

Every valid observation appears in multiple pairs. This is intended in NAP, but the resulting comparisons are not independent clinical replications.

Score each pair with one rule

For higher-is-better outcomes, compare intervention value \(Bj\) with baseline value \(Ai\):

  • score 1 when \(Bj>Ai\);
  • score 0.5 when \(Bj=Ai\); and
  • score 0 when \(Bj<Ai\).

For lower-is-better outcomes, reverse the greater-than and less-than signs. Then calculate:

\[NAP=(I+0.5T)/(nA\times nB)\times100,\]

where \(I\) is the number of improvement pairs and \(T\) is the number of ties. Count deteriorations separately and verify that improvements, deteriorations, and ties sum to the pair denominator.

Lock the improvement direction and tie weight before scoring. Changing either after seeing the result makes the calculation outcome-driven rather than reproducible.

Worked example: Mae's pair table

Mae has baseline values 2, 4, and 6 and intervention values 3, 5, 6, and 8. Higher values were defined as improvement. Three baseline values times four intervention values produce 12 pairs.

Baseline valueIntervention 3Intervention 5Intervention 6Intervention 82ImprovementImprovementImprovementImprovement4DeteriorationImprovementImprovementImprovement6DeteriorationDeteriorationTieImprovement

The first row contributes four improvements. The second contributes three improvements and one deterioration. The third contributes one improvement, two deteriorations, and one tie. Totals are 8 improvements, 3 deteriorations, and 1 tie. They reconcile to 12.

Using half credit for the tie:

\[NAP=(8+0.5\times1)/12\times100=8.5/12\times100=70.833\ldots\%=70.8\%.\]

Mae's result means that a randomly selected intervention observation would receive improvement credit over a randomly selected baseline observation, with half credit for equality, in about 70.8% of these observed cross-phase comparisons. It does not mean the target improved by 70.8% in magnitude.

Audit arithmetic and missingness

The calculation sheet should retain both raw phase lists, valid and planned counts, direction, pair table, tie weight, cell totals, formula, rounding rule, software version if used, owner, and review date. For large phases, software can generate the matrix, but a reviewer should manually test representative improvement, deterioration, and tie cells.

If one baseline observation is missing, the denominator loses one pair for every valid intervention observation. If one intervention point is missing, it loses one pair for every baseline observation. Do not keep the original denominator after excluding data. Recompute the matrix and state why the point was unavailable.

Duplicate source observations can inflate their influence because each duplicate generates an entire row or column of pairs. Hold the result until source identity is resolved. Tied values remain separate valid observations when they came from distinct measurement opportunities.

Graph and report NAP accurately

Keep the raw chronological graph as the main display. NAP can appear in a caption or analytic panel with the pair counts. A pair table is helpful for audit but should not replace the graph because it removes chronology, phase-edge change, and within-phase pattern.

A concise report could say:

Three valid baseline observations and four valid intervention observations generated 12 cross-phase pairs. With higher values defined as improvement and ties weighted 0.5, the matrix contained 8 improvement pairs, 3 deterioration pairs, and 1 tie. NAP was 70.8%. The result was reviewed with raw level, trend, variability, immediacy, magnitude, and design replication.

Avoid writing “70.8% effective” or “70.8% of sessions improved.” Those phrases change the denominator and imply conclusions NAP cannot support.

Examine edge cases

  • Small phases create few pairs and unstable percentages. One corrected value can change several pair scores at once.
  • Many ties may reflect limited measurement resolution, a floor or ceiling, or genuine phase overlap.
  • NAP gives the same credit to an improvement of 0.1 and an improvement of 100 when each crosses the paired rank.
  • Strong baseline or intervention trend is hidden after values enter the pair matrix.
  • Delayed effects and immediate reversals can produce similar NAP values despite different clinical patterns.
  • Unequal phase sizes change how many pairs each observation generates and can affect sampling uncertainty.
  • Missingness related to difficult sessions can bias rank separation even when arithmetic is correct.
  • Combining repeated baselines or interventions without respecting design tiers can create a misleading pooled result.

Universal interpretation bands should be avoided. Research on decision accuracy across overlap and distance measures shows that performance depends on phase size and data pattern. A single-case methods review provides the common NAP formula and positions it as a supplement to design analysis.

Integrate the result with visual and causal analysis

The WWC Version 5.0 handbook considers level, trend, variability, immediacy, overlap, consistency across similar phases, and repeated demonstrations. NAP directly summarizes one cross-phase rank relationship. It cannot establish a replicated effect, rule out history or maturation, confirm implementation fidelity, or show maintenance and generalization.

Review the result alongside raw magnitude, adverse effects, contextual changes, other services, health variables within scope, and the client's experience. A qualified clinician retains decisions about goals and care. NAP cannot determine diagnosis, medical necessity, treatment intensity, authorization, discharge, or safety.

Review the comparison with Mae

Show Mae the original graph and explain the pair result in an accessible way, such as “when each intervention point was compared with each baseline point, most comparisons favored intervention.” Offer the pair table only if it helps. Ask whether the outcome matters, whether the size of change is noticeable, and whether the conditions were acceptable.

Record Mae'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 communication access during assessment and review.

Clinician release checklist

Verify phase membership, comparable measurement, direction, valid-point coverage, missing and duplicate states, pair denominator, cell scoring, tie weight, reconciliation, formula, rounding, raw graph, client review, qualified interpretation, causal limits, calculation owner, and next review date. Preserve the source data and matrix under applicable privacy controls and rerun NAP whenever a value, phase, or scoring rule changes.

Related resources

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