Estimating slope and level change in N = 1 designs.
Use these new formulas to split slope from level change in your single-case data, but guard against shaky estimates when scores flip-flop.
01Research in Context
What this study did
Antonio and colleagues built new math formulas. These formulas pull apart two things in your AB design data.
They separate the steady slope from the sudden level change.
Computer simulations tested the formulas on fake datasets to see if they give honest answers.
What they found
The new formulas hit the bull’s-eye on average. They do not tilt the slope or level change up or down.
But watch out for negative autocorrelation. When one high score is followed by a low score, the level-change estimate can swing wildly.
How this fits with other research
Manolov (2026) now gives you free websites that run these exact formulas. You just upload your file and click.
Manolov et al. (2022) uses the same slope and level numbers to judge if a later client shows the same effect.
Lanovaz et al. (2017) adds a simple rule: collect at least 3 points in A and 5 in B. This keeps false alarms low when you use the new estimators.
Jacobs (2019) offers a different path. Randomization tests give p-values without assuming normal data. You can pair the two methods for stronger proof.
Why it matters
You can now get clean slope and level numbers from any AB chart. Use the free web tools to save time. If your data bounce up and down a lot, collect extra points or combine with randomization tests for safer decisions.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Upload your last AB graph to the free Manolov (2026) site and compare the printed slope and level-change values to your visual inspection.
02At a glance
03Original abstract
The current study proposes a new procedure for separately estimating slope change and level change between two adjacent phases in single-case designs. The procedure eliminates baseline trend from the whole data series before assessing treatment effectiveness. The steps necessary to obtain the estimates are presented in detail, explained, and illustrated. A simulation study is carried out to explore the bias and precision of the estimators and compare them to an analytical procedure matching the data simulation model. The experimental conditions include 2 data generation models, several degrees of serial dependence, trend, and level and/or slope change. The results suggest that the level and slope change estimates provided by the procedure are unbiased for all levels of serial dependence tested and trend is effectively controlled for. The efficiency of the slope change estimator is acceptable, whereas the variance of the level change estimator may be problematic for highly negatively autocorrelated data series.
Behavior modification, 2010 · doi:10.1177/0145445510363306