Data overlap

Overlap is one visual-analysis dimension

Imagine baseline points from 2 to 4 and intervention points from 3 to 6 for a skill expected to increase. Values 3 and 4 occupy the baseline range, while 5 and 6 lie beyond it. That visible mixing is overlap under a simple range description.

The current BACB BCBA Test Content Outline includes graphing and interpreting quantitative relations in Domain C and interpreting single-case experimental designs in Domain D. The outline identifies examination content. It leaves the operational definition and weighting of overlap to the analytic method and context.

The What Works Clearinghouse single-case technical documentation treats overlap as one of six visual features alongside level, trend, variability, immediacy, and consistency across similar phases. Its procedure uses all features collectively when reviewing a design.

Direction determines which points improve

For a skill expected to increase, higher intervention values generally count as favorable separation. For an outcome expected to decrease, lower values do. State the direction before inspection. A graph with changing goals, bidirectional targets, percentages near a ceiling, or values near zero may need a different summary.

Time order still matters. An intervention phase that begins inside the baseline range and then steadily rises has overlap plus a changing trend. Another phase may start with complete separation and drift back toward baseline. A single overlap percentage can assign similar values to these different patterns.

The graph should display raw observations, phase boundaries, condition labels, missing data, and a consistent scale. Inspect within-condition level, trend, and variability before comparing phase overlap.

Visual range overlap and PND use an extreme point

A common descriptive check counts intervention points inside the full baseline range. Percentage of nonoverlapping data, or PND, instead identifies the most favorable baseline point and counts intervention points that go beyond it in the desired direction. Ties at the baseline extreme do not exceed it.

PND is easy to calculate and easy to distort with one baseline outlier. A single unusually favorable baseline observation moves the threshold for every intervention point. Baseline trend and phase length can also change its meaning.

A review of single-case analysis methods describes PND, nonoverlap of all pairs (NAP), Tau-U, improvement rate difference, and other techniques. These methods use different rules. Their outputs should carry the metric name rather than the generic label “overlap score.”

NAP compares every cross-phase pair

NAP forms every baseline-to-intervention pair. For an expected increase, an intervention value above a baseline value is favorable, a tie receives half credit, and a lower intervention value is unfavorable. The favorable score is divided by the number of pairs.

Because NAP uses all pairs, it is less dependent on one extreme baseline point than PND. It still does not preserve the distance between values. A one-unit advantage and a hundred-unit advantage receive the same favorable-pair credit.

A study of overlap and distance-based decision measures explains that overlap statistics offer limited information about effect magnitude. The paper also shows why one critical value can behave differently as phase lengths and data structures change.

A worked comparison gives two answers

Suppose a fictional skill is expected to increase.

• Baseline A: 2, 3, 4, 3, 2
• Intervention B: 3, 4, 5, 6, 5

The baseline range is 2 through 4. Two of five B points, 3 and 4, fall inside that range, so simple range overlap is 2/5, or 40%. Three B points exceed the highest A value of 4, so PND is 3/5, or 60% nonoverlap.

NAP forms 5 × 5 = 25 pairs. Across the five B values, favorable scores are 3.0, 4.5, 5.0, 5.0, and 5.0 after ties receive half credit. The total is 22.5/25, or 90% favorable pairwise separation.

All three results describe the same ten observations. Forty percent range overlap, 60% PND, and 90% NAP are compatible because the methods ask different questions. Report the data, direction, formula, numerator, denominator, treatment of ties, phases, and software or calculation record.

A cutoff cannot replace the full graph

Low overlap may support a visible condition difference, yet causation also depends on repeated predicted changes, adequate phase timing, measurement quality, procedural integrity, and control of competing explanations. High overlap can occur with a clinically meaningful but gradual shift or a small change measured precisely. Context and risk determine whether that change matters.

The authors of Systematic Protocols for Visual Analysis use a structured set of questions across all six visual dimensions. A review of nine nonoverlap techniques likewise emphasizes that indices differ conceptually and computationally.

Avoid declaring success from a borrowed PND, NAP, or Tau-U cutoff. Record how the decision threshold was selected, examine contradictions among visual dimensions, and retain the client's outcome, side effects, burden, and preferences.

A practical overlap checklist

1. Verify the dependent variable, direction of improvement, graph scale, and phase labels.
2. Describe level, trend, variability, and outliers within each phase.
3. Inspect adjacent and repeated conditions visually.
4. Name the overlap or nonoverlap method and its handling of ties and trend.
5. Show the raw numerator, denominator, and calculation.
6. Integrate immediacy, consistency, replication, integrity, context, and social validity.

If two reviewers disagree, preserve both interpretations and identify the dimension or rule producing the difference. A structured discussion is more informative than averaging incompatible judgments.