ABC contingency difference calculation subtracts P(consequence | no response) from P(consequence | response) using compatible observation units and timing rules. A positive value means the consequence appeared more often after the response in the sample; zero means equal sampled probabilities; a negative value means less often. Report both fractions, the difference, coverage, and descriptive limits.

State the comparison before opening the data

An ABC contingency difference compares the consequence's sampled probability in two states: response present and response absent. Write the direction in words first:

P(consequence | response) minus P(consequence | no response).

The response state, valid complement, consequence code, observation unit, and forward window must be fixed before counting. A positive result indicates higher consequence occurrence after response in this sample. A negative result indicates higher occurrence in the comparison state. Zero means the two calculated proportions are equal, although their raw counts and uncertainty may differ.

Only comparable units belong in the calculation. An inapplicable routine, lost observation, blocked AAC access, or window cut off by session end is not evidence of no response or no consequence. Keep these states in a coverage ledger.

Construct and reconcile the four cells

Build a row-level worklist, then total response-consequence, response-no consequence, no response-consequence, and no response-no consequence. For each row retain the time, setting, opportunity, response state, consequence state, window eligibility, observer, and resolution status. Count the two conditional denominators independently from those cells:

  • response denominator = response-consequence + response-no consequence;
  • nonresponse denominator = no response-consequence + no response-no consequence.

The denominators should sum to the valid observation cohort when the states are mutually exclusive and exhaustive. Do not hide an unmatched cell after deriving the percentages. A reviewer should be able to return from the difference to both fractions and every underlying row.

Work Zane's calculation step by step

Zane's valid cohort contains 60 units. The response occurs in 12 units. Nine of those units contain the consequence within the fixed window and three do not. The remaining 48 units meet the no-response definition. Six contain the consequence and 42 do not.

First calculate each conditional proportion:

P(consequence | response) = 9 / 12 = 0.75.

P(consequence | no response) = 6 / 48 = 0.125.

Then subtract in the declared direction:

ABC contingency difference = 0.75 - 0.125 = 0.625.

The result is 0.625, or a 62.5 percentage-point difference. Calling it a 62.5% increase would answer a different relative-change question. Keep 9/12 and 6/48 next to the result so readers can see that the two component probabilities have different denominators.

Check exposure and missingness before interpretation

The 60 valid units are the calculation cohort, not necessarily the planned cohort. Report planned, observed, valid, missed, invalid, and truncated counts. If 80 units were scheduled but 20 were unavailable, overall valid coverage is 60/80, or 75%. The contingency difference still uses the valid response and nonresponse cells. Coverage loss concentrated in difficult routines or particular staff conditions can bias the pattern even when the arithmetic is correct.

Use the same consequence window and event rule across both states. Overlapping response windows, repeated events, variable interval lengths, or inconsistent opportunity rules can make the cells incomparable. If one unit contains more than one response or consequence, specify whether the procedure scores any occurrence, the first onset, an episode, or a count. Changing this rule creates a new measure and should start a new series.

Treat zero and sparse cells honestly

A conditional probability is zero when its numerator is zero and its denominator is positive. It is undefined when the denominator is zero. Therefore, a session with no valid response units cannot yield P(consequence | response) or a contingency difference. Do not replace an undefined component with zero. Likewise, missed and ambiguous units remain outside the cells until resolved.

Extreme differences can arise from very small denominators. If one of one response is followed by the consequence and zero of twenty nonresponse units contains it, the difference is 1.0, but the response estimate rests on a single exposure. Show counts, observation sessions, and context distribution. Replication across representative conditions matters more than a visually dramatic isolated value.

Interpret the sign as a descriptive result

Zane's positive 0.625 difference means the defined consequence appeared more often in the sampled response state than in the sampled nonresponse state. It does not establish that the consequence reinforced the response. Common antecedents, staff schedules, response duration, consequence availability, observation placement, and coding decisions can create or amplify an association. Descriptive findings may guide further assessment by a qualified clinician, but they cannot substitute for the full functional-assessment process.

The size of a difference has no universal treatment cutoff. Consider stability across sessions, raw exposure, client experience, relevant health information, safety, context, and other assessment evidence. A negative or near-zero result can also be useful when it is adequately sampled and reported without overclaiming.

Graph and describe all three values

Use paired points or bars for the two conditional probabilities and label each with its fraction. A separate marker can show the signed difference on a scale from -1 to 1. Facet by phase or setting only when every facet uses the same definitions and windows. Show gaps for invalid sessions instead of connecting them as observed zeros.

Clear report language is: "Across 60 valid units, the consequence occurred after 9 of 12 response units (0.75) and in 6 of 48 nonresponse units (0.125). The response-minus-nonresponse contingency difference was 0.625, or 62.5 percentage points. This descriptive association does not establish function." Add planned coverage, exclusion reasons, observation dates, and any contextual imbalance.

Conduct an accessible review with Zane

Review the events, sample rows, graph, uncertainty, and possible next steps with Zane through an accessible communication format. Maintain access to AAC, interpreters, mobility, food, water, bathroom use, health care, rest, relationships, and emergency support. ASHA's AAC resource supports ongoing access to communication systems. Document Zane's assent, dissent, corrections, concerns, and priorities as data with a source label.

Limit identifiable record access to people who need it for the authorized review. Separate direct observation, partner report, imported system events, and clinician inference. Urgent medical, safety, or reporting action always takes priority over completing a sequence window.

Use the research within its limits

Professional context comes from the BACB ethics hub, CASP guideline summary, and BCBA Test Content Outline. Research comparing antecedent and consequent predictors and describing contingency-space analysis supports explicit conditional cells. Response-stimulus sequence analysis informs timing questions. The precursor procedure highlights conditional direction, while comparative descriptive-assessment research cautions against assuming experimental correspondence. These sources do not validate a universal 0.625 decision rule.

Clinician calculation checklist

For an ABC contingency difference calculation, confirm the response, consequence, no-response state, opportunity, unit, window, overlap rule, planned and valid cohorts, four cell counts, denominator reconciliation, missing and truncated states, both conditional fractions, subtraction direction, signed result, percentage-point wording, graph, access review, safety actions, qualified interpretation owner, next step, and review date. Independently reproduce the result from raw rows before release.

Practical limits

The difference summarizes a selected sample under a selected coding protocol. It cannot show causality, treatment integrity, consequence quality or duration, unobserved sequences, future events, or clinical importance by itself. Sparse or uneven exposure, time-varying contexts, dependent observations, inaccurate clocks, and protocol changes can alter it. Preserve the four cells and coverage, and start a separately labeled series when definitions or windows change.

Related resources

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