What Is a Cumulative Record?
A cumulative record is a type of graph that plots the running total of responses over time. Unlike a standard line graph where individual data points represent the count or rate for a single session, a cumulative record adds each new response to the total of all previous responses. This means the line can only go up or remain flat; it never decreases.
Cumulative records were developed by B.F. Skinner and became one of the defining tools of the experimental analysis of behavior. They provide an elegant visual representation of response rate and allow trained observers to detect subtle changes in responding that might not be visible in other graph formats.
How to Read a Cumulative Record
Slope Equals Rate
The most important principle for reading cumulative records is that the slope of the line represents the rate of responding. A steeper slope indicates a higher rate of responding (more responses per unit of time). A flatter slope indicates a lower rate. A completely flat (horizontal) line indicates that no responding is occurring.
This relationship between slope and rate is the key to interpreting all cumulative record patterns. When the line suddenly becomes steeper, the organism has begun responding at a higher rate. When it flattens, responding has slowed or stopped.
Constant Rate
When an organism responds at a constant rate, the cumulative record shows a straight line with a consistent slope. The steeper the line, the higher the constant rate. A gradual, consistent slope indicates steady, moderate responding. A very steep line indicates rapid, consistent responding.
Acceleration and Deceleration
When the response rate increases over time (acceleration), the cumulative record shows a curve that becomes progressively steeper. When the rate decreases (deceleration), the curve becomes progressively flatter. These curved patterns are often seen during the transition between conditions or at the beginning of new schedules of reinforcement.
Breakpoints
A breakpoint (sometimes called a "break and run" pattern) appears as an abrupt change in the slope of the cumulative record. The line may be flat for a period (no responding), then suddenly shift to a steep slope (rapid responding). This pattern is characteristic of fixed-ratio schedule performance, where the organism pauses after reinforcement and then engages in a burst of responding to complete the next ratio.
The duration of the pause and the rate of the subsequent responding can both be read directly from the cumulative record. Longer pauses appear as longer flat segments, and faster responding appears as steeper climbs.
Schedule Effects Visible in Cumulative Records
Fixed-Ratio (FR) Schedules
Fixed-ratio schedules produce a distinctive "break and run" pattern. After each reinforcer delivery, there is a post-reinforcement pause followed by a high, constant rate of responding until the next reinforcer is earned. The cumulative record shows a stair-step pattern: flat segments (pauses) alternating with steep segments (responding).
Higher ratio requirements tend to produce longer post-reinforcement pauses. This is visible in the cumulative record as longer flat segments between the steep response bursts.
Variable-Ratio (VR) Schedules
Variable-ratio schedules produce a high, relatively constant rate of responding with little or no post-reinforcement pausing. The cumulative record shows a steep, steady line with only minor fluctuations. VR schedules produce the highest rates of responding among the four basic intermittent schedules.
Fixed-Interval (FI) Schedules
Fixed-interval schedules produce a distinctive "scallop" pattern. After reinforcement, the organism pauses or responds at a low rate. As the interval progresses and the time for the next reinforcer approaches, the response rate gradually increases. The cumulative record shows a characteristic curved acceleration pattern that resets after each reinforcement.
The FI scallop is one of the most recognizable patterns in the experimental analysis of behavior. On the BCBA exam, being able to identify this pattern in a cumulative record is an important skill.
Variable-Interval (VI) Schedules
Variable-interval schedules produce a moderate, relatively constant rate of responding. The cumulative record shows a steady line with a moderate slope. There are few or no pauses because the next interval could end at any time, making pausing unproductive.
Skinner's Contributions
B.F. Skinner developed the cumulative recorder as a mechanical device in his laboratory. The original device used a paper drum that moved at a constant speed while a pen moved upward with each response. The result was a continuous, real-time record of responding that allowed Skinner to observe the effects of different schedules of reinforcement with remarkable precision.
Skinner's use of cumulative records led to many of the foundational discoveries in the experimental analysis of behavior, including the characteristic patterns produced by different schedules of reinforcement. His work demonstrated that behavior could be understood as lawful and orderly, and cumulative records provided the visual evidence for this claim.
While modern data collection has largely moved to digital systems, cumulative records remain important for understanding the principles of behavioral science and for certain clinical applications, particularly in precision teaching and fluency-based instruction.
Clinical Applications
In applied settings, cumulative records are used in several contexts. Precision teaching uses cumulative records (called "Standard Celeration Charts" in that context) to track learning rates. Fluency-based instruction monitors response rates using cumulative-style data displays. Research on schedule effects in applied populations often uses cumulative records to display results.
BCBA Exam Preparation
For the exam, practice identifying the following patterns in cumulative records: high steady rate (steep line), low steady rate (gradual line), no responding (flat line), acceleration (curving upward), deceleration (curving toward flat), post-reinforcement pause followed by responding (break and run), and the FI scallop (curved acceleration within each interval).
Remember the core principle: slope equals rate. If you can read the slope, you can read the cumulative record.