Unconditional event probability ABC data uses the number of valid observation units containing the event divided by all valid observation units, regardless of the target response. It estimates background occurrence under the selected unit and sample. Define interval length, event coding, overlap, and missing states. Pair the result with raw counts and coverage whenever it is compared with a conditional probability.

Define the background question

Unconditional event probability ABC data asks how often the event appears across all valid units in the sampled background, without requiring the target response. Use P(event) = valid observation units containing the event / all valid observation units. Name the event, unit, observation period, settings, coding method, and use of the result before calculating.

The denominator could be intervals, momentary checkpoints, trials, transitions, or another defined opportunity. An interval probability cannot be read as event rate or duration. If several help offers occur inside one interval, interval presence still contributes one positive unit. Retain a separate event count or duration measure when recurrence or time occupied matters.

Build the coverage denominator

List planned, observed, valid, missed, excluded, and unresolved units. A missed interval is not an event-absent interval. If the observer missed the busiest routine, the valid sample may understate or overstate background occurrence. Report valid units divided by planned units and describe concentrated missingness.

Check that interval length and sampling method stay constant. Shorter intervals can change the probability of recording any occurrence. A 25% probability across ten-second intervals is not directly interchangeable with 25% across five-minute intervals. Preserve exact clock times, source records, observer, setting, and protocol version.

Code presence without losing detail

Create one row per valid background unit with event present, event absent, missing, inapplicable, or disputed. If event definitions overlap, maintain separate marginal columns or predeclared exclusive combinations. Do not force a help offer into one category when it can also contain attention or another coded event.

Retain event onset, count, and duration outside the binary presence calculation when available. The probability table can show background availability while a timeline or count graph shows how often the event repeated. This prevents a single help offer and five help offers inside an interval from looking identical in every report.

Verify Quinn’s results

Quinn has 72 valid background intervals. A help offer occurs in 18, so P(help offer) = 18 / 72 = 0.25, or 25%. Fifty-four valid intervals contain no coded help offer under the declared presence rule. Planned or missed intervals remain in the coverage statement and do not enter the 72 until resolved.

In a separate conditional table, a help offer follows 8 of 12 response events with complete windows: 8 / 12 = 0.6667, or 66.7%. The raw contrast is 66.7% − 25% = 41.7 percentage points. Its descriptive meaning depends on compatible event definitions and observation opportunities because one denominator uses response windows and the other uses background intervals.

The background table shows help offers outside response sequences too. At least some of the 18 positive intervals are not represented by the eight response-following sequences, although exact overlap requires linked timestamps. Avoid subtracting raw counts across different unit systems unless each event-to-interval mapping is known.

Address zero cells and missingness

If the help offer occurs in none of 72 valid intervals, unconditional probability is 0 / 72 = 0%. If there are no valid background intervals, the result is undefined. Report the zero denominator and investigate observation coverage instead of substituting 0%.

Missing intervals should remain visible by time, setting, observer, and routine. A complete-looking 72-row table may still be unrepresentative if observations exclude home transitions, health appointments, preferred activities, or difficult periods. Recalculate after resolving disputed or late records and retain the earlier version.

Graph and report the base rate

A simple display can show 18 positive and 54 negative valid intervals, accompanied by planned and valid coverage. Use session-level panels when the 18 positive intervals may cluster on one day. Add the conditional 8-of-12 value only in a separate mark with its response-conditioned denominator.

Suggested wording: “Help offer occurred in 18 of 72 valid background intervals (25%). It followed 8 of 12 response events with complete follow-up windows (66.7%). These estimates use different denominators. Valid background coverage, interval length, response-window rules, and session distribution are reported with the table.”

Bound the clinical interpretation

Background probability provides context for a sequence probability. It does not tell whether help was contingent, whether it influenced later responding, whether help quality was consistent, or whether either event was meaningful to Quinn. A frequent event can appear after many responses because it is common throughout observation.

Antecedent-versus-consequent research and contingency space analysis show the value of background comparison. Descriptive-method research reports limited correspondence with experimental outcomes, and functional-assessment ambiguity research separates association from experimental demonstration.

Include accessible client review

Ask Quinn how help was offered, whether it was understandable, timely, wanted, or available through a usable communication method. Keep AAC continuously accessible under ASHA guidance. Record assent, dissent, communication attempts, comfort, and priorities.

Observation must preserve food, water, bathroom use, mobility, prescribed health care, rest, relationships, and emergency help. The BACB ethics hub and CASP public summary provide professional context. Medical, safety, privacy, payer, and legal matters stay with qualified reviewers.

Clinician checklist and practical limits

Before using the background value, confirm:

  • event definition, interval length, sampling method, settings, and dates are stable;
  • planned, observed, valid, missed, excluded, and unresolved units reconcile;
  • 18 positive plus 54 negative intervals equals the 72-unit denominator;
  • zero-event and zero-valid-unit cases have different labels;
  • event counts, duration, overlaps, and session clustering remain visible where relevant;
  • conditional comparisons retain their separate response-window denominators; and
  • accessible client input, causal limits, next assessment step, owner, and review date are documented.

Quinn’s 25% is a sampled interval-presence estimate. It changes with interval width, schedule, setting mix, missingness, and event definition. It cannot be generalized to unobserved routines or converted into rate without source timing. Reopen the worksheet when observation units, coverage, data, access, health context, observer, or software changes, and preserve all released versions.

Related resources

Sources