Celeration Line Analysis
Also known as: Celeration Line, Split-Middle Method, Trend Line Analysis (Single-Case), Celeration Approach
Celeration line analysis is a single-case method that fits a trend line to the baseline phase, projects that line forward into the intervention phase, and judges effect by how many intervention data points fall on the improvement side of the projected trend. Built on Owen White's split-middle technique from precision teaching and codified for social-work practice by Bloom, Fischer, and Orme, it directly addresses a weakness of level-only comparisons: it asks whether the client improved beyond the trajectory the baseline was already on, and pairs the count with a simple binomial test for statistical decision-making.
Key highlights
- Explicitly accounts for baseline trend, separating improvement caused by treatment from a pre-existing trajectory.
- The split-middle, median-based fit is robust to occasional baseline outliers.
- Couples a visual trend projection with a simple binomial significance test, aiding accountable decisions.
- Computable by hand on graph paper, making it usable in field practice without specialized software.
Intuition
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How it works
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When to use it
Use celeration line analysis when the baseline shows a trend that a simple level comparison would confound with treatment effect, and you want a transparent, projectable account of improvement beyond the baseline trajectory. It suits single-system practice evaluation with enough baseline points to estimate a stable trend (commonly five or more). It is less appropriate when the baseline is too short to define a trend, when the trend is curvilinear (the method assumes a straight line), or when autocorrelation is strong, since the binomial test assumes independent points and can overstate significance.
Strengths & limitations
- Explicitly accounts for baseline trend, separating improvement caused by treatment from a pre-existing trajectory.
- The split-middle, median-based fit is robust to occasional baseline outliers.
- Couples a visual trend projection with a simple binomial significance test, aiding accountable decisions.
- Computable by hand on graph paper, making it usable in field practice without specialized software.
- Assumes a linear baseline trend; curved or accelerating baselines are poorly summarized by a straight celeration line.
- The binomial test treats intervention points as independent, which autocorrelated time-series data typically violate, inflating significance.
- Sensitive to baseline length: too few points give an unstable, easily extrapolated-into-error trend line.
- Projecting a baseline trend far into a long intervention phase can yield implausible predicted values.
Common pitfalls
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Applications
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Frequently asked
What does 'celeration' mean?
Celeration is a term from precision teaching meaning the change in the rate of a behavior over time — acceleration if the behavior is speeding up and deceleration if it is slowing down. The celeration line is simply the trend line whose slope expresses that rate of change. In single-case practice evaluation the projected celeration line represents the trajectory the behavior was on during baseline, extended into the intervention period as a prediction.
Why use the split-middle method instead of ordinary least-squares regression?
The split-middle method estimates the trend from the medians of the two baseline halves, so a single extreme baseline point cannot pull the line the way it can pull a least-squares fit. It is also computable by hand on graph paper, which mattered for field practitioners. Ordinary regression is a defensible alternative when software is available and outliers are not a concern, but the median-based line is more robust for the short, noisy baselines common in practice.
Is the binomial test on celeration data trustworthy?
It is a useful decision aid but rests on the assumption that intervention points are independent and equally likely to fall above or below the projected line under the null. Single-case time-series data are usually autocorrelated, which violates independence and tends to make the test too liberal. Treat a significant binomial result as supportive evidence alongside visual analysis and nonoverlap statistics rather than as a definitive significance test.
Sources
- 1.Kazdin, A. E. (2011). Single-Case Research Designs: Methods for Clinical and Applied Settings (2nd ed.). Oxford University Press.ISBN 9780195341881
- 2.Bloom, M., Fischer, J., & Orme, J. G. (2009). Evaluating Practice: Guidelines for the Accountable Professional (6th ed.). Pearson/Allyn & Bacon.ISBN 9780205458066
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Cite this page
ScholarGate. (2026, June 22). Celeration Line Analysis. ScholarGate. https://scholargate.app/social-work/celeration-line-analysis