Graph That Hides a Trend
A behavior analyst is evaluating a token economy for on-task behavior in a self-contained classroom of six students. The design is a multiple baseline across three pairs of students. Visual inspection of the graphed data shows an upward trend in on-task behavior for each pair after intervention onset, but the analyst notices that the y-axis on the second tier is scaled 0-50% while the first and third tiers are scaled 0-100%. The second tier also begins at a higher baseline level (about 45%). The teacher reports the intervention "works for everyone." The analyst must decide whether to claim a functional relation and how to present the data to the IEP team.
1. Evaluate the internal validity of the multiple baseline. What threats and design problems must be considered, and does the current graph support a functional relation?
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A functional relation in a multiple baseline requires that behavior change coincides with intervention onset in each tier while baselines remain stable in not-yet-treated tiers. Several problems must be checked before any claim is made.
First, inconsistent y-axis scaling across tiers distorts visual comparison. A 0-50% axis makes modest changes look large relative to a 0-100% axis. The graph should be redrawn with identical axes, or at minimum the scaling difference must be disclosed.
Second, the second tier's baseline is already at about 45%, creating a ceiling or floor issue depending on the measure, and leaving less room to demonstrate an effect. A change from 45% to 60% is not comparable to 10% to 60%.
Third, threats to internal validity: maturation and history (school-wide events, seasonal changes), instrumentation (observer drift, different observers per tier), and diffusion (students in one classroom may learn from peers whose intervention has started, which would contaminate untreated baselines). A multiple baseline across pairs in the same room is especially vulnerable to diffusion.
Fourth, verify baseline stability and the number of data points per phase; too few points weaken inference.
The honest conclusion: the design may support a functional relation if baselines were stable, axes are corrected, and diffusion is ruled out. The current graph alone does not justify the claim that it "works for everyone."
2. Draft the key points the analyst should present to the IEP team, balancing scientific caution with the team's need for a decision.
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The presentation should be accurate, plain-language, and decision-oriented.
- What the data show: on-task behavior increased after the token economy was introduced for each group, and the timing of changes generally followed the staggered introduction. That pattern is consistent with the intervention being responsible.
- What limits confidence: the graph's scales differ between groups, one group started higher, and students share a classroom so improvements in one group may influence others. These are reasons for caution, not reasons to discard the data.
- What was done to address it: redraw the graph on a common scale, confirm observer agreement, and check whether untreated students' behavior changed before their intervention started.
- What is still needed: continued data collection and, if feasible, a brief reversal or a probe of a not-yet-treated group to strengthen the inference.
- Recommendation: continue the token economy while monitoring, because the preponderance of evidence favors benefit, and commit to a review date with pre-specified criteria (for example, maintain at least 80% on-task for three consecutive weeks).
The analyst should avoid overclaiming ("proven effective for all") and avoid underclaiming ("we cannot say anything"). Stating the strength and limits of the evidence, with a concrete review plan, serves the team best and meets the obligation to base recommendations on data.