An ABA dual criteria calculator should show the projected mean, the projected baseline trend and each comparison point's relationship to both. This worksheet makes the dual-criteria and conservative-dual-criteria views reproducible while keeping them separate from complete visual analysis, design review and clinical judgment.

Clinicians & ABA Professionals / Data, Outcomes and Clinical Decision-Making.

The narrow question this worksheet answers

The dual-criteria method projects two summaries from baseline into the comparison phase: the baseline mean and a baseline trend line. A comparison point qualifies only when it is beyond both projected criteria in the prespecified preferred direction. For higher values preferred, it must be strictly above both. For lower values preferred, it must be strictly below both.

The conservative dual-criteria view shifts both projected criteria by one quarter of the baseline standard deviation in the preferred direction before classifying the same comparison points. The shift makes the criterion more conservative, not more clinically meaningful by itself.

The output is a count against projected reference lines. It does not establish treatment effectiveness, clinical significance, replication, experimental control or a functional relation. A qualified reviewer must still inspect level, trend, variability, immediacy, overlap, consistency, phase-change logic and the person's experience.

The ABA dual criteria calculator is therefore a projection aid with an audit trail, not a substitute for the graph or the responsible clinical review.

Declare the method before building the lines

Different split-middle conventions can produce different slopes and vertical placement. Record the exact convention before inspecting the result. The worked example below uses consecutive session numbers, divides an even-length baseline into equal first and second halves, takes the median x and median y within each half, connects those coordinates, and shifts the line vertically by the median baseline residual so the final baseline points are balanced above and below it as closely as ties permit.

Do not silently apply that convention to an odd-length baseline, uneven timing or a protocol that requires a different median or balancing rule. If the implementation cannot honor the declared method, return not calculated and send the issue to methods review.

The analysis record should name:

  • the outcome, operational definition, unit and opportunity or exposure base;
  • ordered observations, actual time coordinates, phase labels and boundaries;
  • the prespecified preferred direction and focal review question;
  • the mean and sample-standard-deviation conventions;
  • the exact split-middle, median-coordinate and vertical-balancing rules;
  • the slope, intercept and precision retained for every projection;
  • missing, invalid, late, corrected and disputed records;
  • strict or inclusive comparison rules and how ties are displayed;
  • the DC and CDC point classifications in separate columns;
  • any reference table, probability model, phase length and alpha used;
  • calculation version, analyst, reviewer, client input and unresolved evidence.

Do not fill a missing observation with zero. Do not treat irregularly spaced dates as consecutive sessions if elapsed time is part of the question. Do not change the preferred direction or split rule after seeing which choice gives the larger count.

Copyable ordered input

PhaseOrderActual x or dateRaw valueUnit and denominatorStatusContext or correction noteA1valid / missing / invalid / late / disputedA2A3A4A5A6B1B2B3B4B5B6

Keep excluded records visible in the audit trail with their original values, reason, author and date. The graph should distinguish observed points from projected lines and should never connect a missing point as though it were observed.

Calculate the baseline mean and sample standard deviation

For n valid baseline values y1 through yn:

baseline mean = sum of baseline values / n

sample SD = square root of [sum of (y - baseline mean)^2 / (n - 1)]

This sheet uses sample standard deviation because that is the declared implementation. Label a different convention rather than silently substituting it. With fewer than two valid baseline values, sample SD is undefined. A zero SD produces a zero CDC shift; it does not show that the baseline is stable or sufficient.

Construct the declared split-middle line

For the even-length variant used here:

  1. Split the ordered baseline into equal first and second halves.
  2. Find the median x and median y in each half.
  3. Call those median coordinates (x1, y1) and (x2, y2).
  4. Calculate slope = (y2 - y1) / (x2 - x1).
  5. Calculate unbalanced intercept = y1 - slope * x1.
  6. Calculate each baseline residual as observed y - unbalanced predicted y; add the median residual to the intercept as the declared vertical-balancing shift.
  7. Project trend criterion at x = balanced intercept + slope * x through every comparison coordinate.

If x2 - x1 is zero, the slope is undefined. If actual observation timing is irregular, use the declared actual x variable rather than substituting row number. Preserve enough precision in the slope and intercept to reproduce each projected criterion; round only the display.

Classify dual-criteria points

For higher values preferred, a comparison point qualifies under DC only when:

observed B value > projected baseline mean and observed B value > projected trend value

For lower values preferred, replace both greater-than signs with less-than signs. A tie with either criterion is not beyond both under this worksheet's strict rule. Display the reason a point does not qualify instead of collapsing every result to yes or no.

The original DC and CDC paper introduced these projected criteria and evaluated them with simulated AB graphs. Its results do not turn a qualifying-point count into a complete analysis of causation.

Add the conservative sensitivity without overwriting DC

Calculate the declared shift:

CDC shift = 0.25 x baseline sample SD

For higher values preferred, add the shift to both the baseline mean and every projected trend criterion. For lower values preferred, subtract it from both. Then classify each comparison observation against both shifted criteria.

Keep the unshifted DC and shifted CDC results side by side. Do not replace the DC count with CDC, choose the larger count or describe CDC as a confidence interval. Stewart and colleagues evaluated the methods and instruction in their use; that work supports transparent construction, not automatic clinical conclusions.

Blank projection ledger

FieldDeclared value or rulePreferred directionBaseline valid nBaseline meanSample SDCDC shiftSplit-middle variantFirst-half median coordinateSecond-half median coordinateTrend slope and unitUnbalanced interceptVertical-balancing shiftBalanced interceptTie rulestrict beyond / other declared ruleCalculation version and precision

B order and xObserved valueMean criterionTrend criterionDC relationship to eachDC qualifiesShifted meanShifted trendCDC relationship to eachCDC qualifies123456

Reconcile qualifying + nonqualifying = valid comparison n for each view. A comparison point missing under the declared eligibility rule stays out of both denominators and remains visible as missing.

Mateo's fictional projection

Mateo is fictional. His team is reviewing client-selected completed steps per matched opportunity, with higher values prespecified as preferred. Baseline sessions 1 through 6 contain 4, 5, 4, 5, 5 and 6. Comparison sessions 7 through 12 contain 6.3, exactly 19/3, 7, 7.4, 7.5 and 8. The fraction at session 8 is used only to make the tie reproducible.

The baseline sum is 29, so the mean is 29 / 6 = 4.8333. The squared deviations sum to 2.8333. Using the declared sample formula, variance is 2.8333 / 5 = 0.5667, sample SD is 0.7528 and the CDC shift is 0.25 x 0.7528 = 0.1882.

The first baseline half has median coordinate (2, 4). The second has median coordinate (5, 5). The slope is (5 - 4) / (5 - 2) = 0.3333 units per session, and the unbalanced intercept is 4 - (0.3333 x 2) = 3.3333. The baseline residuals have median 0.3333, so the declared vertical-balancing step raises the line by 0.3333. The final balanced intercept is 3.6667 and the projected trend is y = 3.6667 + 0.3333x. Two baseline points are above the final line, two are below and two tie it.

SessionObserved BMeanTrendDCShifted meanShifted trendCDC76.34.83336.0000qualifies5.02156.1882qualifies819/34.83336.3333trend tie, no5.02156.5215no97.04.83336.6667qualifies5.02156.8549qualifies107.44.83337.0000qualifies5.02157.1882qualifies117.54.83337.3333qualifies5.02157.5215no128.04.83337.6667qualifies5.02157.8549qualifies

The DC view counts 5 of 6 points. The CDC view counts 4 of 6. Session 8 demonstrates the strict tie rule. Session 11 demonstrates why the 0.1882 shift must be applied to the projected trend as well as the mean.

The different counts are a sensitivity finding, not a dispute to erase. They show how one declared conservative shift changes the classification of a value close to the projected trend line. Neither count establishes that an intervention caused the pattern or that the observed difference matters to Mateo.

Reference counts and optional probability displays

Some implementations compare the qualifying count with a binomial reference. Do not import a critical count from a graph with a different comparison-phase length, direction, probability model or alpha. Record the exact table or calculation and preserve the number of valid B points.

For illustration only, under an explicitly declared one-sided binomial model with n = 6 and p = 0.5, the probability of at least five qualifying points is (6 + 1) / 64 = 0.109375. The probability of at least four is (15 + 6 + 1) / 64 = 0.34375. These values simply reproduce the stated count model. They are not automatic evidence thresholds, treatment decisions or substitutes for design-based inference.

If no reference rule was selected in advance, leave that field blank. Never search among alpha levels, phase lengths or variants for the most favorable label.

Why the graph can disagree with the count

A projected straight line can summarize a curved or highly variable baseline poorly. A single baseline extreme may affect both the mean and standard deviation. Missing observations, unequal opportunity bases or a measurement change can alter the projections without reflecting a true behavioral change. A delayed comparison effect may produce a lower count even when later values are visibly different.

The 2026 tutorial on visual inference and projection aids emphasizes choosing a focal feature in advance and retaining visual analysis and design features as primary. The WCER abstract on systematic visual analysis notes application across different single-case designs. This worksheet does not reconstruct methods unavailable in that abstract or pretend one AB projection supplies the replication of an ABAB or multiple-baseline design.

The official What Works Clearinghouse Version 5.0 handbook calls for examining six visual features: within-phase level, trend and variability, then between-phase immediacy, overlap and consistency. Its design and replication requirements remain separate from this projection sheet. Report the lines as supplemental evidence inside that wider review.

Client meaning and qualified judgment

Ask whether the outcome and visible magnitude matter to the person. Discuss burdens, harms, adverse effects, accessibility and tradeoffs through the person's preferred communication. Maintain the person's usual communication system and any mobility, sensory or access supports during observation and review. Record assent, dissent and requested changes where applicable.

The current BACB ethics materials remain the professional source for certificants. They do not certify this calculator. The SCRIBE 2016 Statement supports clear reporting of single-case work but does not make a favorable count proof of study quality or benefit. A professional with the relevant competence, authority and supervision remains accountable for case-specific interpretation under applicable licensure, consent, payer and organizational rules.

Privacy, security and the retained record

Training should use fictional or appropriately de-identified values whenever feasible. If a legitimate purpose requires identifiable health information, minimize the fields, work only in approved systems, restrict access and preserve corrections and calculation versions. HHS provides official summaries of the Privacy Rule and Security Rule. They do not determine whether a specific workflow is covered or certify one storage design.

The retained record should contain the raw graph, declared method, separate DC and CDC ledgers, any reference rule, review disagreements, the person's feedback, the accountable interpretation, open evidence questions and a follow-up date. Start a new version whenever source values, phase boundaries, timing, measurement, method settings or the clinical question change.

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