Split-middle trend line calculation divides an ordered phase into two time halves, locates a median time and median value for each half, and draws a line through those coordinate pairs. Some specifications add a vertical adjustment to balance points above and below. Declare the exact variant, odd-point rule, and adjustment before calculation, then retain the raw graph and linearity limits.

What a split-middle line can show

A split-middle line is a structured aid for describing within-phase trend. It reduces a phase to two median coordinate pairs and draws the straight line that connects them. The result can make direction and approximate rate of change easier to discuss, especially when raw points vary. It remains a descriptive overlay. It does not establish a functional relation or predict that the same trend will continue.

A split-middle trend line calculation is appropriate only after the time scale and phase membership have been verified.

Several split-middle variants exist. A reproducible worksheet must name the variant, the time scale, the rule for an odd number of points, the median-coordinate method, and any vertical-adjustment rule. Two analysts can follow reasonable but different conventions and obtain different lines from the same phase.

Prepare one valid phase

Keep observations in chronological order and define the phase before calculating. Record the target, unit, dates, measurement opportunities, setting, and condition. Check missing values, duplicate timestamps, late entries, and changes in measurement definition. Exclude a point only under a declared data-quality rule and retain its original state and reason.

Choose the horizontal scale deliberately. Session number is reasonable when observations are equally spaced and the question concerns change per session. Calendar time or elapsed days may be more faithful when gaps vary. A line based on session 1 through session 6 answers a different question from a line based on six visits spread across twelve weeks.

Very short phases provide weak trend summaries. If splitting leaves too little information to form meaningful halves, report that limitation and rely on the raw graph until more valid observations are available.

Declare the split and coordinate rules

For an even number of observations, divide the ordered phase into equal early and late halves. For an odd number, state whether the middle point is omitted, assigned to one half, or included in both halves under the chosen method. Do not decide after seeing which rule gives the preferred slope.

Within each half, calculate:

  • the median horizontal coordinate, using the declared time scale; and
  • the median observed value, retaining ties and the original point identifiers.

Call the early coordinate \((x1,y1)\) and the late coordinate \((x2,y2)\). The unadjusted slope is

\[m=(y2-y1)/(x2-x1).\]

The line equation is \(y=mx+b\), where \(b=y1-mx1\). Keep adequate precision during calculation and round only the reported result. If \(x1=x2\), the selected rule or time data are invalid for a finite slope and require review.

Worked example: Jasper's baseline

Jasper has six evenly spaced baseline points: (1,2), (2,3), (3,4), (4,5), (5,6), and (6,7). The worksheet uses session number as time and splits the phase into two groups of three.

The early-half time values are 1, 2, and 3, so their median is 2. The early values are 2, 3, and 4, so their median is 3. The first coordinate is \((2,3)\).

The late-half time values are 4, 5, and 6, with median 5. The late values are 5, 6, and 7, with median 6. The second coordinate is \((5,6)\).

The slope is \((6-3)/(5-2)=3/3=1\). Using the first coordinate, \(b=3-(1\times2)=1\). Jasper's unadjusted line is therefore \(y=x+1\). At time 7, the projected value is \(7+1=8\).

All six points fall on this line, so the declared balancing procedure produces no vertical adjustment. The worksheet retains that statement instead of silently omitting the step.

Handle vertical adjustment transparently

Some split-middle procedures shift the initial line vertically until the distribution of phase points above and below it meets a specified balance rule. If that variant is used, record the unadjusted coordinates and equation, how points on the line are treated, the amount and direction of the shift, and the final equation. Software output without those choices is not reproducible.

Adjustment changes the intercept, not the observed data. It should never be used to make an unfavorable slope appear favorable. When multiple shifts satisfy a balance criterion, the selected tie-breaking rule belongs in the report.

Graph and report the result

Draw the line over the original phase using the same horizontal scale used in calculation. Preserve every raw point, phase boundary, missing observation, and contextual annotation. Label whether the line is unadjusted or adjusted and avoid extending it into later phases unless projection is the stated analytic purpose.

A concise report could read:

Six equally spaced baseline observations were split into two groups of three. Median coordinates were (2,3) and (5,6), producing an unadjusted line of y = x + 1. No vertical shift was required under the declared balance rule. The line projects a value of 8 at session 7; this projection is descriptive and was interpreted with variability and phase context.

If observations are unevenly spaced, say whether the equation uses sessions or elapsed time. Report valid points over planned points, excluded data and reasons, the odd-point rule, coordinates, equation, adjustment, and projection range.

Check edge cases before interpretation

  • A single extreme point can change a half median, especially in a short phase.
  • Ties can create a flat half median even while the raw sequence changes.
  • Curvature, cycles, abrupt shifts, or a floor or ceiling can make a straight line a poor summary.
  • Missing observations near the phase edge can alter the second coordinate and any projection.
  • A changing observation schedule can make session-based slope appear stable while calendar-time slope changes.
  • Projecting far beyond the observed phase magnifies uncertainty and should be avoided in routine clinical review.

The line does not supply magnitude, immediacy, overlap, or replication across phase changes. The WWC Version 5.0 handbook places trend within a broader visual-analysis framework. The single-case methods review describes quantitative aids while preserving their assumptions and design limits.

Review the trend with Jasper

Show Jasper the raw graph first and describe the line as a summary of the baseline pattern. Use a communication mode he can access, including AAC or an interpreter when needed. Ask whether the target matters, whether the conditions were acceptable, and whether important events explain any points. Keep mobility support, breaks, food, water, bathroom access, prescribed care, and emergency help available.

Record Jasper's input, assent or dissent when applicable, and any requested change. A rising line may represent improvement, deterioration, or no meaningful change depending on the outcome and his priorities. The analyst must define direction before interpretation.

Clinician checklist and limits

Before releasing the calculation, verify the phase, target, valid-point coverage, time scale, split rule, median coordinates, equation, adjustment rule, graph overlay, rounding, projection range, client review, and calculation owner. Have another qualified reviewer reproduce the slope when the result informs a consequential decision.

The BACB ethics resources, CASP practice-guideline summary, and ASHA AAC guidance support qualified, person-centered review. A split-middle line cannot determine treatment effectiveness, medical necessity, authorization, safety, or causality. Reopen the analysis when the data, phase, method, access needs, health context, or goal changes.

Related resources

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