Extended celeration line calculation projects a documented baseline median-trend line into the intervention phase, then counts intervention observations beyond the projected line in the improvement direction. Divide by valid intervention observations. Preserve the line-construction variant, equation, time scale, ties, missing points, and linearity assumption. The result supplements the full visual and design analysis.

Construct the baseline line first

Use a declared median-trend or split-middle specification and preserve the coordinates, adjustment, and equation.

Project on the actual time scale

Extend the line to each intervention time. Irregular spacing requires actual elapsed or session time under the chosen graph.

Score each intervention point

Mark beyond, tied with, or on the nonimproved side of the projection. Apply the declared tie rule.

Retain the linearity assumption

A straight projection may fit baseline poorly. Review the raw graph, variability, level change, immediacy, and replications.

Build the line from a reproducible specification

Record the baseline observations, session or elapsed-time coordinates, improvement direction, and exact trend-line method before projection. If the method divides baseline into halves, state how an odd number of points is handled and how the fitted line is vertically adjusted. Preserve the resulting coordinates and equation with the worksheet.

The time axis matters. Session numbers can be acceptable when observations are evenly spaced and the question is session based. Calendar time or another actual interval may be necessary when gaps vary. A reviewer should be able to enter the stored coordinates and reproduce every projected value without estimating from a screenshot.

Compare projected and observed points row by row

Create one row per valid intervention observation with its time, projected baseline value, observed value, signed difference, beyond-line classification, and validity state. For a higher-is-better measure, a positive difference is beyond the line. Reverse the direction for a lower-is-better measure. A value on the line follows the declared tie rule and stays visible in the ledger.

Hold observations affected by duplicate timestamps, missing values, changed units, or unresolved phase labels. Report valid comparisons divided by all intervention observations due so excluded work does not disappear from coverage.

Apply extended celeration line calculation to one phase comparison

The extended celeration-line worksheet for Pia identifies the phase labels, improvement direction, raw observations, missing-state rule, reference value or line, formula, tie rule, calculation owner, and review date before a supplemental result is interpreted.

Work the single-case example for Pia

Pia's baseline line predicts 8, 9, 10, and 11 at intervention times 7 through 10. Her intervention values are 9, 8, 12, and 10. Two values are above their projections and two are below. With higher values preferred, the extended-line result is 2 of 4, or 50%.

The signed differences are +1, -1, +2, and -1. No point ties its projection. The same four-row ledger therefore supports the 2-of-4 numerator and confirms that all four scheduled intervention comparisons were valid. If a fifth point were missing, the report would show four valid comparisons out of five due and would not silently reduce the coverage denominator.

Audit reproducibility for Pia

Pia's worksheet retains the baseline coordinates, equation, projected values, actual intervention values, direction, and point-by-point comparison. No value ties its projection in this example.

Interpret the result beside the graph

The 50% result says that half of Pia's valid intervention observations fall beyond the projected baseline line in the preferred direction. It does not show how far beyond the line they are, whether the baseline trend is stable, whether change was immediate, or whether the pattern replicates. Inspect those features directly on the time-series graph.

Projection can also be fragile when baseline is short, curved, highly variable, or shaped by a changing context. Report that limitation instead of treating a precise percentage as a precise causal estimate. If another reasonable line specification materially changes the result, show it as a labeled sensitivity analysis and retain the predeclared primary method.

Protect client relevance for Pia

During Pia's intervention points beyond projected baseline trend review, keep AAC, interpreters, mobility, food, water, bathroom use, prescribed care, health support, rest, relationships, and emergency help available. Use accessible communication to ask whether the measured outcome and magnitude matter to the person. A favorable statistic cannot repair an unwanted goal or inaccessible plan.

Use current single-case evidence for Pia

For Pia's calculation, the BCBA Test Content Outline supplies examination scope for graphing, interpretation, experimental design, and data-based evaluation. The BACB ethics hub and CASP summary provide professional context. The WWC Version 5.0 handbook is an education-research evidence standard, not a clinical authorization rule. A single-case methods review documents PND, NAP, and extended-line formulas. Research on structured visual-analysis aids and decision accuracy across overlap measures supports using calculations as transparent supplements while retaining metric and design limits. ASHA supports continuous AAC access.

Close Pia's analysis review

Review the extended celeration-line worksheet with Pia and the responsible clinician. Preserve raw data, graph, phase definitions, calculation version, coverage, ties, limitations, client input, decision, owner, and next review date. Reopen the analysis when data, context, access, health, goal, phase, or method changes.

Clinician review checklist

  • Is the improvement direction defined in observable terms?
  • Can another reviewer reconstruct the baseline line from stored coordinates and the named method?
  • Does the projection use the intended time scale and preserve irregular gaps?
  • Are observed values, projected values, signed differences, ties, and invalid states shown row by row?
  • Does the numerator reconcile to the row classifications and the denominator to valid intervention points?
  • Are coverage, sensitivity to line construction, and any baseline nonlinearity reported?
  • Is the percentage interpreted with the graph, design replications, context, and Pia's priorities?

Related resources

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