Compound antecedents ABC data should preserve each component and the combination. Build mutually exclusive exposure cells such as A only, B only, both, and neither, then calculate response occurrence within each cell. Keep raw counts, windows, and coverage. A high response probability in the combined cell identifies a sampled pattern and does not isolate either component's effect.

Define components before combinations

Write observable definitions for noise, crowding, transition, and the response. Record each component independently in the source data, with onset, offset, intensity or other relevant dimensions, observer, setting, and source. Compound antecedents ABC data can then be regrouped without rewriting what was observed.

Set the sequence question and forward window. For example: “Among valid transition exposures, how often did the response begin within 20 seconds under noise only, crowding only, both, or neither?” Define how simultaneous onsets, a component already underway, repeated transitions, and truncated windows are handled.

Build mutually exclusive exposure cells

Derive four exclusive cells from the two component codes: noise only, crowding only, both, and neither. Every valid exposure belongs to exactly one. Prove that the cell denominators sum to the full exposure cohort. Keep missing, disputed, and truncated events outside the valid cells and report them separately.

Do not start with overlapping “noise present” and “crowding present” totals because the both cell would appear twice. Marginal views can be calculated later, with their overlap stated. Exclusive cells provide the clearest foundation for within-cell response probabilities.

Verify the table and arithmetic

Dario has 30 valid transitions:

Exposure cellTransitionsResponses in windowConditional probabilityNoise only1022 / 10 = 20%Crowding only411 / 4 = 25%Both866 / 8 = 75%Neither811 / 8 = 12.5%

The denominators reconcile: 10 + 4 + 8 + 8 = 30. Response cells total 2 + 1 + 6 + 1 = 10. The both-versus-neither difference is 75% − 12.5% = 62.5 percentage points; the descriptive ratio is 75 / 12.5 = 6.0. Keep the 6-of-8 and 1-of-8 fractions visible because each cell is small.

A marginal noise-present view combines noise only and both: 8 responses across 18 exposures, or 44.4%. A crowding-present view combines crowding only and both: 7 of 12, or 58.3%. These summaries answer broader exposure questions and share the both cell. They do not isolate either component’s effect.

Check coverage and correlated context

Report planned, observed, valid, missing, excluded, and truncated transitions. Stratify the four cells by routine, time, location, observer, communication access, and other predeclared contexts. If six of the eight both exposures occurred in one crowded arrival period, the 75% value may describe that period more than the component combination generally.

Retain noise intensity, crowd density, predictability, duration, task changes, people present, health information within scope, and client feedback as source-labeled context. Avoid adding post hoc categories only because they produce a stronger percentage. New hypotheses should be tested in a prospective review plan.

Handle zero, missing, and sparse cells

A cell with exposures and no responses has a calculable 0% result. A cell with zero exposures is undefined. Report “no valid exposure” instead of 0%. Never merge an empty both cell with a component-only cell merely to obtain a percentage.

An exposure whose forward window extends past observation end is truncated. An uncertain component code is disputed. Neither belongs in a valid exclusive denominator until resolved under the written rule. Show how many records occupy these states and whether missingness concentrates in high-noise or crowded situations.

Graph and report the pattern

Use four dots or bars with each raw fraction printed beside the percentage. A stacked count display can show responses and nonresponses within every exposure cell. Add cell-specific coverage and session distribution; do not graph the 62.5-point difference alone.

Suggested wording: “Across 30 valid transitions, the response occurred after 2 of 10 noise-only exposures (20%), 1 of 4 crowding-only exposures (25%), 6 of 8 combined exposures (75%), and 1 of 8 neither exposures (12.5%). The combined cell was 62.5 percentage points above the neither cell. Cell size, context concentration, and descriptive design limit interpretation.”

Keep interpretation noncausal

The pattern identifies a sampled combination for further review. It does not show that noise, crowding, or their interaction caused the response. The both cell may differ in routine, people, predictability, communication access, or health context. A larger conditional probability is not an experimental interaction effect.

Predictor research, contingency-space analysis, and lag-sequential work support careful event and timing comparisons. Comparative descriptive-method research cautions that observed associations have limited correspondence with experimental findings.

Include accessible client review

Ask Dario, through a usable communication method, about noise, crowding, pain, predictability, transitions, preferred supports, assent, and dissent. Keep AAC continuously available under ASHA guidance. Preserve access to food, water, bathroom use, mobility, prescribed health care, rest, relationships, and emergency help.

Observation must use naturally occurring, approved conditions and cannot justify creating distress or delaying support. The BACB ethics hub and CASP summary provide professional context. Medical, safety, privacy, payer, and legal questions remain with qualified owners.

Clinician checklist and explicit limits

Before using the table, confirm:

  • components, response, transition exposure, direction, and window are observable and fixed;
  • exclusive cells reconcile to all valid exposures without double counting;
  • 2/10, 1/4, 6/8, and 1/8 reproduce from source records;
  • zero-exposure, zero-response, missing, disputed, and truncated states are distinct;
  • routine, time, access, health, observer, and setting coverage are visible;
  • graphs retain raw cells and the report avoids causal or interaction claims; and
  • accessible client input, next assessment step, qualified owner, and review date are recorded.

Dario’s cell sizes are small, especially crowding only. One additional response would move that cell from 25% to 50%. Marginal summaries reuse compound exposures, and the combined cell may carry correlated context. Reopen the analysis when definitions, sampling, data, access, health, observer, or software changes, preserving all prior versions.

Related resources

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