Ties in single-case nonoverlap metrics follow the selected metric's rule. Under strict PEM and PND calculations, an intervention value equal to the baseline median or extreme stays outside the improvement numerator. In common NAP scoring, a tied baseline-intervention pair receives one-half credit. Declare rules before calculation, show tied counts, and keep the raw values and software specification.

Identify the reference

A PEM tie is with the baseline median; a PND tie is with the improvement-direction extreme; a NAP tie is within a value pair.

Apply the metric's rule

Use strict exceedance for the stated PEM and PND versions and half credit for the stated NAP version.

Show tied counts

Report how many intervention values or pairs tied. Small datasets can change materially with one tie.

Avoid post-result switching

Select and document the rule before reviewing the preferred outcome. A different variant should be labeled as a separate sensitivity analysis.

Build a tie ledger before calculating

Lock the baseline and intervention phases, improvement direction, valid values, and missing-state decisions. Record the reference used by each metric. For PND, identify the improvement-direction baseline extreme. For PEM, calculate the baseline median under a stated even-sample convention. For NAP, list or program every baseline-intervention pair.

Add a tie field beside each intervention value or pair. The ledger should show which observations are beyond the reference, tied, or on the nonimproved side. Keep the selected rule and software version with the output so another reviewer can reproduce the numerator.

Reproduce Nadia's pair counts

Nadia's three baseline values and four intervention values create 3 × 4 = 12 NAP pairs. Compare each intervention value with 2, 4, and 6 in the preferred higher direction. Eight pairs favor intervention, one pair ties at 6, and three favor baseline. Common NAP scoring gives 8 + 0.5 = 8.5 of 12, or 70.8% after rounding.

The ledger makes that numerator visible. Baseline 2 contributes four favorable pairs. Baseline 4 contributes three favorable pairs and one unfavorable pair. Baseline 6 contributes one favorable pair, one tie, and two unfavorable pairs. Those rows reconcile to 8 favorable, 1 tied, and 3 unfavorable comparisons.

Report ties as evidence, not cleanup

Show the reference value, total comparisons, strict improvements, ties, nonimprovements, tie score, and final result. A sensitivity row can display how another declared convention would change the result. Keep it secondary and label the alternate method.

Ties can be especially influential in small phases or rounded measures. Review the measurement precision and raw values before interpreting a high tie count. Do not add arbitrary decimal changes to break ties.

Frame one declared phase comparison

The nonoverlap tie ledger for Nadia identifies the phase labels, improvement direction, raw observations, missing-state rule, reference value or line, formula, tie rule, calculation owner, and review date before a supplemental result is interpreted.

Worked example: strict PND and pairwise NAP

Nadia uses baseline 2, 4, and 6 and intervention 3, 5, 6, and 8. PND counts only 8 beyond the baseline maximum 6, so it is 1 of 4, or 25%; the intervention value 6 ties. NAP has one tied pair and scores it 0.5, yielding 8.5 of 12, or 70.8%.

Audit every tie and comparison

Nadia's ledger identifies which values or pairs tie, the rule used for each metric, and the effect of changing a tie score. The final report names the exact metric version.

Protect client relevance

During Nadia's metric-specific tie treatment review, keep AAC, interpreters, mobility, food, water, bathroom use, prescribed care, health support, rest, relationships, and emergency help available. Use accessible communication to ask whether the measured outcome and magnitude matter to the person. A favorable statistic cannot repair an unwanted goal or inaccessible plan.

Use single-case evidence within scope

For Nadia's calculation, the BCBA Test Content Outline supplies examination scope for graphing, interpretation, experimental design, and data-based evaluation. The BACB ethics hub and CASP summary provide professional context. The WWC Version 5.0 handbook is an education-research evidence standard, not a clinical authorization rule. A single-case methods review documents PND, NAP, and extended-line formulas. Research on structured visual-analysis aids and decision accuracy across overlap measures supports using calculations as transparent supplements while retaining metric and design limits. ASHA supports continuous AAC access.

Close the analysis review

Review the nonoverlap tie ledger with Nadia and the responsible clinician. Preserve raw data, graph, phase definitions, calculation version, coverage, ties, limitations, client input, decision, owner, and next review date. Reopen the analysis when data, context, access, health, goal, phase, or method changes.

Clinician review checklist

  • Are phase values, direction, missingness, and metric versions locked?
  • Is each PEM, PND, or NAP tie linked to the relevant value or pair?
  • Can an independent reviewer reproduce favorable, tied, and unfavorable counts?
  • Does the printed arithmetic agree with the raw values?
  • Are alternate tie conventions labeled as sensitivity analyses?
  • Is the metric presented beside the graph, phase context, and client feedback?
  • Are disputed calculations held until the source record is reconciled?

Related resources

Sources