Precursor target conditional probability ABA calculations need two directions. P(precursor | target) asks how often the precursor appeared before a target response. P(target | precursor) asks how often a precursor was followed by the target. Use fixed windows and separate denominators. Preserve precursor occurrences without the target, client communication, health signals, and safety limits.

Define precursor and target independently

Describe each event in observable terms with onset and offset rules. Preserve Esme’s recognizable communication, pain behavior, distress signal, request to stop, and other meaningful actions in their own terms. A clinical label such as “precursor” must not erase the person’s message or turn a request for help into a prediction problem.

State the use of the analysis. One question is coverage: how often did the candidate precursor appear before recorded targets? A second is predictive value: how often was a precursor followed by the target? Precursor target conditional probability ABA requires both directions because one can be high while the other is modest.

Set the sequence and matching rules

Choose target onset as the anchor and define a backward window, such as 30 seconds. State whether precursor onset or any overlap must fall inside it. For the reverse direction, specify the forward target window after precursor onset or offset. These two windows may share a joint sequence count only when the matching rules are constructed to do so.

Repeated precursors need one-to-one matching rules. Decide whether the closest precursor links to the target, whether one precursor can link to several targets, and how episodes are separated. Truncated windows at observation start or end remain incomplete. Timestamp precision must support the declared 30-second boundary.

Build the four evidence cells

Preserve target events with and without a precursor, and precursor events with and without a later target. The shared linked-sequence count belongs in both conditional numerators, but the denominator changes:

  • P(precursor | target) uses every valid target event.
  • The forward target-given-precursor calculation uses every valid precursor event.

Also report missed or truncated targets, unmatched precursor events, disputed matches, and observation coverage. Avoid calling an unmatched precursor a false alarm until the person’s communication and alternate outcomes have been reviewed.

Verify Esme’s arithmetic

Esme has 12 valid target events. The candidate precursor occurs inside the backward window before 9, so P(precursor | target) = 9 / 12 = 75%. Three targets have no matched precursor under the current rule.

The precursor occurs 20 times with complete forward windows, and 9 are followed by the target. Using those precursor exposures, 9 / 20 = 45%. Eleven precursor events are not followed by the target inside the window. The joint numerator is 9 in both calculations; denominator universes are 12 targets and 20 precursors.

The 75% result describes sensitivity to target events in this sample. The 45% result describes how often the candidate precursor predicts a target under the protocol. Reporting only 75% would make the sequence appear more reliable than it is for prospective support decisions.

Handle zero cells, gaps, and overlap

If no target events occur, P(precursor | target) is undefined because the target denominator is zero. If no precursor occurs, P(target | precursor) is undefined. A positive denominator with no linked sequences produces 0%. Keep these states distinct.

Observation gaps may hide target events, precursors, or the ends of windows. Report complete target anchors divided by all targets and complete precursor anchors divided by all precursors. When one precursor overlaps another or the target begins before the first window closes, use the predeclared episode rule and preserve the raw timeline.

Never extend observation or delay support to complete a dangerous sequence. A truncated record created by a safety response is still valuable evidence and should remain labeled as such.

Graph and report both directions

Use two paired displays: 9 of 12 targets with the precursor versus 3 without, and 9 of 20 precursors followed by the target versus 11 without. A timeline sample can show the 30-second rule and disputed matches. Include planned and valid observation coverage.

Suggested wording: “The candidate precursor occurred within 30 seconds before 9 of 12 target events (75%). The target followed 9 of 20 precursor events with complete windows (45%). Three targets had no matched precursor, and eleven precursors had no target inside the window. These descriptive estimates depend on event definitions, matching rules, coverage, and sampled context.”

Protect safety and clinical authority

Use naturally occurring, approved observation. Do not recreate a dangerous event, withhold assistance, block communication, or wait for the target after a meaningful precursor. Follow the individualized safety and medical plan. Urgent medical, safety, or reporting action takes priority over sequence completion.

The precursor study provides method context, not permission to induce risk. Lag-sequential work demonstrates the importance of timing, while comparative descriptive-method research cautions against treating association as experimental function.

Review meaning and access with Esme

Ask Esme, using her preferred communication, what the candidate precursor communicates and which supports should follow it. Keep AAC continuously available under ASHA guidance. Record assent, dissent, discomfort, pain, priorities, and corrections.

Maintain food, water, bathroom use, mobility, prescribed health care, rest, relationships, and emergency help throughout observation. The BACB ethics hub and CASP summary provide professional context. Medical, safety, privacy, payer, and legal decisions stay with qualified owners.

Keep interpretation bounded

Neither direction establishes behavioral function, causal sequence, or the safety of waiting after a precursor. The precursor may occur with alternate outcomes, and some targets may have different precursors. Both events may reflect pain, access failure, environmental change, or another correlated condition.

Predictor research and contingency-space analysis support careful denominator and timing comparisons. Use the result to plan a qualified, safe next step and to improve support at early signs, never as a reason to require target behavior.

Clinician checklist and limitations

Before using the sequence table, confirm:

  • precursor, target, anchor, backward and forward windows, episodes, and matching are defined;
  • target, precursor, linked, unlinked, truncated, missing, and disputed events reconcile;
  • 9/12 = 75% and 9/20 = 45% reproduce from source timestamps;
  • zero-event and zero-denominator results have accurate labels;
  • graphs show both directions, raw cells, coverage, and session distribution;
  • safety action and accessible communication never depend on completing a sequence; and
  • Esme’s input, limits, next support or assessment step, owner, and date are recorded.

The denominators are small. One changed match moves precursor-given-target by 8.3 points and target-given-precursor by 5 points. Window length, timestamp precision, event definitions, matching rules, and missingness can alter both values. Reopen the method after any relevant data, health, access, observer, context, or software change, preserving prior versions.

Related resources

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