Stability criteria.
Use the daily-change or variability-plus-trend rule to call baseline stable and avoid extra sessions.
01Research in Context
What this study did
Killeen (1978) compared three ways to decide when behavior is stable.
The rules were: curve-fit to flat line, low day-to-day bounce, and tiny daily change.
The paper ran fake data sets to see which rule called “stable” fastest and most correctly.
What they found
Curve-fit hit the bull’s-eye but needed the most sessions.
The other two rules were almost as good and saved time.
The author says pick variability-plus-trend or daily-change and stop collecting extra points.
How this fits with other research
Falcomata et al. (2012) later used the variability-plus-trend rule with pigeons on fixed-interval schedules. They showed pause duration takes longer to settle than peck rate, backing the 1978 advice to wait for stable patterns.
Laureano et al. (2023) looked for “transition states” in hospital files. They counted how many sessions problem behavior looked like baseline before it finally dropped. Their count of about five sessions lines up with the 1978 daily-change window, extending the lab rule to real-world cases.
Vassos et al. (2023) found transition states in 7 % of published graphs. That low number may seem to clash with R’s warning that stability can fool you, but the difference is location: M scanned finished articles while R tested raw ongoing data. Both agree you need clear rules before you say “it’s stable.”
Why it matters
You now have a fast way to decide when baseline is done. Use the daily-change rule: if the last three points differ by less than one standard deviation of the whole phase, move on. It keeps your single-case experiment lean yet trustworthy, just as later animal and hospital studies have shown.
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02At a glance
03Original abstract
Three approaches to the determination of behavioral stability were examined. In the first, a learning curve was fit to acquisition data (from Cumming and Schoenfeld, 1960), and the "experiment" stopped when the data approached sufficiently close to the theoretical asymptote. In the second, the data were analyzed for variability and linear and quadratic trend. In the third, the experiment was stopped when the magnitude of the daily changes in the data fell below a criterion. Accuracy was measured as deviation between the average value of the dependent variable when the experiment was stopped, and the average value over the last 100 sessions. The first approach was most accurate, but at the cost of requiring the most sessions and being the most difficult to apply. Both the second and third approaches provided acceptable criteria with a reasonable cost-accuracy tradeoff. The second approach permits a continuous adjustment of the criteria to accommodate the variability intrinsic in the experimental paradigm. The third, nomothetic, approach also takes into account the decreasing marginal utility of extended training sessions.
Journal of the experimental analysis of behavior, 1978 · doi:10.1901/jeab.1978.29-17