Line graph

A line graph shows change in sequence

An ABA line graph usually places successive sessions, dates, days, trials, or another ordered unit along the horizontal x-axis. The vertical y-axis shows the measured value. A marker represents one eligible observation, and a data path connects successive markers when the graph's rules call for a connection.

The current BACB BCBA Test Content Outline includes selecting data displays that communicate relevant quantitative relations and interpreting graphed data. It also covers single-case design features and data-based decisions. The outline identifies examination content; it does not prescribe one universal graph format.

The graph title should name the person or cohort, outcome, and relevant context without exposing unnecessary identifying information. Axis labels need units. “Communication” is too broad for a y-axis; “independent help messages per ten eligible opportunities” tells the reader what each point represents.

Read the measurement before the pattern

Locate the operational definition, observation unit, denominator, and recording method. A value of 60 could mean 60 seconds, 60 responses, 60 percent, or 60 responses per hour. Each supports a different interpretation.

Check whether observation duration and opportunity count stay comparable. If one session lasts 20 minutes and another lasts 60, raw counts may need a rate. If percentages use two opportunities on one day and twenty on another, show those denominators. A missing observation needs a reason; plotting zero would claim that measurement occurred and the outcome's value was zero.

Also check dates and elapsed time. Equally spaced session numbers can conceal a three-week gap. A companion table with date, raw numerator, denominator, condition, implementer, setting, and missing-data code makes the graph easier to audit.

Axes and scale shape what readers see

Use equal visual intervals for equal numeric changes on an equal-interval graph. Label any axis break or transformed scale. Keep scales comparable when readers are expected to compare panels.

A y-axis starting near the observed values can reveal small changes; it can also make a small difference look dramatic. A y-axis starting at zero gives broader context and may compress a clinically important pattern. There is no single best choice for every question. Display the range, tick values, and any alternate view clearly enough that scale cannot be mistaken for effect size.

Crowded dates, decorative smoothing, three-dimensional effects, and unexplained colors can obscure the data. Use accessible colors, distinct marker or line styles, readable labels, and text that communicates condition changes without relying on color alone.

Conditions and phase changes need evidence

Condition labels describe the environmental arrangement in effect for those observations. A vertical phase-change line marks the stated transition. Verify that the line matches the actual implementation date or session. Preserve data about procedural integrity, prompts, staff, setting, and concurrent changes.

A line can guide the eye without creating data between observations. A gap remains a gap. The graph should state whether paths stop at missing observations or condition boundaries and how multiple series are distinguished.

The What Works Clearinghouse single-case technical documentation organizes visual review around within-phase level, trend, and variability, followed by between-phase immediacy, overlap, and consistency. Design standards and replicated effects matter when the purpose is causal inference.

A fictional two-condition example

Suppose a graph reports independent help messages during ten defined opportunities per session. Baseline sessions 1 through 3 contain 2, 3, and 2 messages. The condition changes before session 4 after staff training and communication access are verified. Sessions 4 through 6 contain 5, 6, and 7.

The graph should show six markers, a labeled phase line between sessions 3 and 4, and separate data paths according to its stated convention. The reader sees a higher level beginning in the new condition and an upward trend across its first three sessions. There is no overlap between the two three-point ranges.

This six-point pattern supports a hypothesis of change. It provides one condition transition and no replication. History, practice, measurement drift, different opportunities, staff behavior, or another simultaneous event remain possible explanations. The team should report the raw 2/10, 3/10, 2/10, 5/10, 6/10, and 7/10 values, implementation evidence, and the person's view before acting.

Visual analysis follows a repeatable order

A single-case design analysis review separates within-phase inspection from between-phase comparisons and design-level experimental control. The authors of Systematic Protocols for Visual Analysis found meaningful differences among published protocols. Naming the sequence and decision rules helps another reviewer reproduce the judgment.

For each phase, examine level, direction and size of trend, and variability. Across phases, compare immediate boundary changes, overlap, and whether similar conditions produce consistent patterns. Then consider replication, expected latency, procedural integrity, measurement quality, clinical importance, client report, risk, and burden.

A line-graph review checklist

1. Read the outcome definition, unit, and denominator.
2. Verify the x-axis sequence, actual dates, and observation gaps.
3. Verify y-axis range, interval, transformation, and any break.
4. Match each marker and path to its condition and source record.
5. Confirm phase lines against actual implementation.
6. Examine level, trend, variability, immediacy, overlap, and consistency.
7. Pair the pattern with integrity, context, access, and client-relevant evidence.
8. Record the qualified interpretation and uncertainty.