An ABA PND PEM NAP calculator should make three different reference rules visible, not flatten them into one claim about treatment success. This worksheet locks the same baseline values, comparison values and preferred direction, then shows how percentage of nonoverlapping data, percentage exceeding the median and nonoverlap of all pairs respond to those inputs. It keeps the raw graph, ties, denominators and a documented sensitivity scenario beside every result.

Clinicians & ABA Professionals / Data, Outcomes and Clinical Decision-Making.

One dataset, three questions

PND, PEM and NAP can produce different percentages from the same phase contrast because they do not ask the same mathematical question. This ABA PND PEM NAP calculator keeps those separate questions visible throughout the review.

  • PND asks how many comparison-phase values move strictly beyond the most favorable baseline value.
  • PEM asks how many comparison-phase values move strictly beyond the baseline median.
  • NAP asks how every comparison-phase value ranks against every baseline value, assigning half credit to ties under the rule used here.

The three results are supplemental descriptions. None is the percentage a person improved. None establishes treatment effectiveness, clinical importance, replication or causation. A larger number is not automatically the better analysis, and agreement among the three metrics does not repair weak measurement or design.

The locked analysis record

Before calculating, freeze the inputs and the review question. Keep the chronological graph open beside the sheet. The record should contain:

  • the outcome, operational definition, unit and opportunity or exposure denominator;
  • ordered baseline and comparison values with phase labels and dates or sequence positions;
  • the prespecified direction in which values would represent improvement for this question;
  • valid, missing, invalid, late, corrected and disputed states;
  • the baseline median and improvement-direction extreme;
  • the PND and PEM reference and tie rules;
  • the full NAP favorable, tied and unfavorable pair counts;
  • phase length, trend, variability, immediacy, overlap and consistency across similar phases;
  • measurement, intervention, staffing, support, health and context changes;
  • calculation version, precision, owner, reviewer and date;
  • client and stakeholder input, unresolved evidence and the qualified decision owner.

Do not reverse the preferred direction after looking at the results. Do not silently remove a baseline extreme because it lowers PND. If a source value is corrected or a late record arrives, preserve the original calculation and display a versioned sensitivity rerun with the validity decision still visible.

Copyable input table

SeriesOrderRaw valueUnit and denominatorStatusSource or correction noteBaseline A1valid / missing / invalid / late / disputedBaseline A2Baseline A3Baseline A4Comparison B1Comparison B2Comparison B3Comparison B4Comparison B5

Record the analysis direction as higher values preferred or lower values preferred before scoring. If direction is not clinically or logically meaningful, do not force a directional nonoverlap calculation.

PND calculation

For higher values preferred, the PND reference is the highest valid baseline value. Count comparison values strictly greater than that reference. For lower values preferred, use the lowest valid baseline value and count comparison values strictly lower than it.

PND = comparison values strictly beyond the baseline extreme / valid comparison values x 100

A comparison value tied with the baseline extreme does not move strictly beyond it under this rule. State a different tie rule if a governing protocol requires one. Because PND depends on one baseline extreme, one valid correction or late observation can change the reference and every comparison classification.

PEM calculation

Find the median of the valid baseline values. For higher values preferred, count comparison values strictly above that median. For lower values preferred, count values strictly below it.

PEM = comparison values strictly beyond the baseline median / valid comparison values x 100

The declared rule here does not count a comparison value tied with the median. PEM uses a more central reference than PND, but it still discards chronology, distance and most of the baseline distribution after the median is found.

NAP calculation

Compare every valid baseline value with every valid comparison value. With higher values preferred, score a comparison value above the baseline value as 1, a tie as 0.5 and a lower value as 0. With lower values preferred, reverse the favorable and unfavorable comparisons while retaining half credit for ties.

NAP pairs = valid baseline n x valid comparison n

NAP score = favorable pairs + 0.5 x tied pairs

NAP = NAP score / all cross-phase pairs x 100

The What Works Clearinghouse Version 5.0 handbook describes this all-pairs scoring rule. NAP summarizes the ordering of values across the two series. It does not show how far apart values are or when they occurred.

Blank result and reconciliation panel

FieldPrimary locked calculationVersioned sensitivity calculationBaseline valid nComparison valid nBaseline medianBaseline preferred-direction extremePND numerator / denominatorPNDPEM numerator / denominatorPEMNAP favorable pairsNAP tied pairsNAP unfavorable pairsNAP score / all pairsNAPIncluded or excluded recordnoneValidity rationale and approver

Require favorable + tied + unfavorable = all pairs. Require all pairs = baseline n x comparison n. An undefined denominator returns not calculated, not zero. Retain sufficient precision to reproduce the arithmetic, then state the rounding rule used for display.

Theo's fictional locked comparison

Theo is fictional. The measure is the number of client-selected completed steps during matched opportunities, with higher values preferred for the example. The locked baseline values are 4, 6, 5 and 7. The comparison values are 6, 8, 5, 9 and 7. No value represents a real person or clinical record.

The baseline median is 5.5, and the higher-is-preferred baseline extreme is 7.

MetricNumerator and denominatorResultPNDValues 8 and 9 are strictly above 7: 2 / 540.0%PEMValues 6, 8, 9 and 7 are strictly above 5.5: 4 / 580.0%NAP14 favorable + half of 3 ties = 15.5 points; 15.5 / 2077.5%

The NAP pair ledger reconciles to 14 favorable, 3 tied and 3 unfavorable comparisons. There are 4 x 5 = 20 pairs. The three classifications sum to 20, and the weighted score is 14 + 0.5(3) = 15.5.

The spread from 40.0% PND to 80.0% PEM is not a contradiction. PND uses the single baseline value 7 as its reference. PEM uses the baseline median 5.5. NAP uses all 20 cross-phase comparisons. The display should explain those mechanics rather than selecting the largest result.

Sensitivity to a late baseline value

Suppose a baseline value of 9 arrives late. The team has not yet decided whether it is valid and belongs in the phase. The primary locked result stays intact. A separate sensitivity column shows what the formulas would return if 9 were included.

The alternative baseline is 4, 6, 5, 7 and 9. Its median is 6, and its preferred-direction extreme is 9.

MetricSensitivity arithmeticResultPNDNo comparison value is strictly above 9: 0 / 50.0%PEMValues 8, 9 and 7 are strictly above 6: 3 / 560.0%NAP14 favorable + half of 4 ties = 16 points; 16 / 2564.0%

The added baseline row creates five new NAP comparisons: zero favorable, one tied and four unfavorable. The new ledger therefore contains 14 favorable, 4 tied and 7 unfavorable pairs, totaling 25. The weighted score is 14 + 0.5(4) = 16.

These are alternative arithmetic results, not evidence that the late value should be accepted or rejected. Resolve identity, timing, measurement conditions and the documented eligibility rule through the responsible process. Never pick the version that produces the preferred percentage.

Why the three metrics can move differently

PND can fall sharply when one valid baseline extreme moves in the preferred direction. PEM is less controlled by that extreme, yet one change can move the median in a short phase. NAP spreads influence across all cross-phase pairs, but duplicated or erroneous observations create entire rows or columns of comparisons. All three metrics can be distorted when missingness, phase membership or measurement changes are mishandled.

The size of a favorable rank difference is invisible to these formulas. A comparison value barely beyond a baseline value receives the same favorable NAP score as a much larger difference. Chronology also disappears in PND, PEM and the NAP matrix. Two series with different trends or delayed changes can produce the same nonoverlap percentage.

For those reasons, do not attach universal labels such as weak, effective or highly effective. Report raw values, graph, formulas, pair counts, phase lengths and uncertainty. A metric should answer a predeclared supplemental question, not become a target selected after the result is known.

Research boundaries for nonoverlap summaries

Parker and Vannest's original NAP paper demonstrates the all-pairs measure and compares it with PND, PEM and other indices. Their later review with Davis describes conceptual and computational differences among nine nonoverlap techniques. These papers support showing different reference rules. They do not establish that one number is universally appropriate for clinical decisions.

Manolov and colleagues used simulated data to examine how trend, serial dependence and changing variability affect quantitative techniques and emphasized visual inspection. Parker and colleagues' Tau-U paper illustrates that trend-aware extensions require additional definitions. This calculator does not calculate Tau-U or correct baseline trend automatically.

Research on decision accuracy across overlap and distance measures shows that phase length and data pattern matter. This worksheet therefore does not provide universal bands and keeps the chronological graph central.

Visual analysis, replication and clinical meaning

The WWC handbook treats NAP within a defined education-research review process. It also retains review of level, trend, variability, immediacy, overlap and consistency and the need for an eligible design with repeated demonstrations. A single A-to-B contrast cannot establish a functional relation merely because its PND, PEM or NAP is favorable.

Review measurement validity, opportunity access, treatment integrity, concurrent changes, harms, burdens, adverse effects and the person's experience. Ask whether the outcome and magnitude matter to the client. Use accessible communication and preserve assent or dissent when applicable. A qualified professional remains responsible for case-specific interpretation and decisions within competence, licensure, supervision, payer and setting requirements.

The BACB ethics materials are the current professional source for certificants. They do not approve this calculator, supply its formulas or turn a reproducible percentage into ethical or clinical compliance.

Data governance and correction history

Minimize identifiers to what the legitimate review needs. Store source data and calculation files in approved systems, grant access by role, keep an auditable correction history, and follow the organization's retention and incident procedures. HHS summarizes federal obligations for regulated entities in its Privacy Rule overview, while the companion Security Rule overview addresses safeguards for electronic protected health information. These summaries are starting points, not complete compliance instructions or a determination that a particular person or workflow is covered.

Finish by recording the selected analysis version, reasons for any inclusion or exclusion, metric-specific results, raw graph, client input, qualified interpretation, unresolved evidence and next review date. Reopen the review when a value, phase boundary, direction, formula, context or decision question changes.

Related resources

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