Interpreting graphed data

Behavior analysts rarely run statistical tests on a single client's data. Instead, you look at the graph and ask a short list of questions in the same order every time. That routine, called visual analysis, is how you decide whether behavior changed, how much, and whether to keep, adjust, or drop an intervention.

Why it matters

Every treatment decision you make as a BCBA rests on a graph: continue the program, change it, fade it, or start over. A careless read can keep a client in an ineffective program for weeks or end a helpful one too early. Visual analysis is also conservative: it reliably detects large, clear effects and tends to miss small ones. Many analysts see that as a strength, because small effects that only show up statistically are often not socially meaningful.

Practice items often describe a graph in words ("baseline data are 14, 12, 10, 8") and ask what the pattern shows, what decision follows, or which feature of the data matters most.

Key ideas

Within a phase, look at three things.

• Level: where the data sit on the vertical axis. Summarize it with the phase mean or median, and notice whether the last few points (the local level) differ from the phase as a whole.
• Trend: the overall direction of the data path. Describe its direction (increasing, decreasing, or zero), how steep it is, and how tightly the points cluster around it.
• Variability: how much the data bounce from point to point. The more variable the data, the more data points you need before you can trust a statement about level or trend.

Between adjacent phases, look at three more.

• Immediacy of effect: compare the last few points of one phase with the first few of the next. A quick change in level is more convincing than a slow drift.
• Overlap: how many data points in one phase fall within the range of the other. Less overlap means a clearer difference.
• Consistency: whether similar phases (for example, two baseline phases in a reversal design) show similar patterns.

Stability comes first. You need a predictable baseline before you introduce a change. A baseline already moving in the direction you hope treatment will produce is a problem, because further improvement could just be the old trend continuing. A trend in the opposite direction is less of a problem, since an effect would have to reverse it.

Check the graph itself. Read the axis labels and scale before the data. A vertical axis that starts at 40 instead of 0, or stretches a tiny range across the whole height, can make small changes look dramatic.

Definitions

• Visual analysis: judging behavior change by systematically inspecting graphed data rather than by statistical tests.
• Level: the value on the vertical axis around which a set of data points converges.
• Trend: the overall direction and steepness of a data path over time.
• Variability: the frequency and size of changes from one data point to the next.
• Split-middle line of progress: a trend line built by splitting a phase in half, marking the median session and median value of each half, and connecting those points (the quarter-intersect line). The line is then shifted, staying parallel, until equal numbers of points fall above and below it.
• Cumulative record: a graph in which each new count is added to the running total. The slope shows the response rate, a flat segment means no responses, and the line can never go down.
• Semilogarithmic chart: a graph with a logarithmic vertical axis, such as the Standard Celeration Chart, where equal vertical distances show equal proportional changes.

Examples from a session

• A stable baseline. Rosa, age 4, attends a clinic program. Her percentage of independent hand washing across five baseline sessions is 20, 25, 20, 22, 21. The level is low, the trend is flat, and variability is small, so her BCBA has a clear prediction to test against.
• A trend in the wrong place. In a middle school, Mr. Osei records Malik's call-outs per hour across baseline: 16, 13, 11, 9, 7. Call-outs are already falling. His BCBA keeps collecting baseline until the data level off, so that a later drop can be credited to the intervention rather than to the existing trend.
• Non-example of "no effect": high variability hiding behind a mean. At home, Grace, age 30, has a self-care routine with an average of 6 prompts per session in both phases. In treatment, though, the counts swing between 1 and 12. The means match, but the graph tells a different story, and her BCBA looks for what differs between the good and the hard days, such as sleep or staffing.
• Reading a cumulative record. Teo's cumulative record of spontaneous requests climbs steeply Monday and Tuesday, runs flat on Wednesday, and climbs again Thursday. The flat stretch means zero requests on Wednesday; a slower but steady rate would still slope upward.

Common mistakes / exam traps

• Reading only the mean. Equal means can hide very different patterns. Always describe level, trend, and variability together.
• Starting treatment on a therapeutic baseline trend. Improvement during treatment may simply continue a trend that was already there.
• Trusting a trend drawn from two or three points. Short, variable phases can suggest a direction that is not really there.
• Ignoring the axes. A truncated or uneven scale changes how big an effect looks.

Quick check

Related topics

• Graphing data: line graphs, bar graphs, and cumulative records (C.10)
• Measuring occurrence: count, rate, and percentage (C.3)
• Critiquing and interpreting single-case data (D.6)
• Reversal, multiple-baseline, multielement, and changing-criterion designs (D.7)
• Data-based decisions about effectiveness and when to modify (H.7)