An ABA Brennan-Prediger agreement calculator exposes a consequential assumption: expected agreement is 1/K, where K is the number of possible nominal categories fixed before the data are reviewed. The coefficient is easy to calculate. Defending the category universe, paired-unit design, and intended interpretation is the harder work.

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

Confirm the fixed-category question

Brennan and Prediger's original 1981 paper discusses uses, misuses, and alternatives for kappa-like agreement statistics. It examines how fixed-versus-free marginal assumptions affect chance correction and presents the 1/K alternative used here. This page implements that descriptive two-rater calculation; it does not make the model universally preferable or clinically sufficient.

Use this ABA Brennan Prediger agreement calculator when exactly two observers independently classify the same complete units into one of K mutually exclusive nominal categories and the possible category set has a defensible a priori meaning. The unit may be an opportunity, interval, or another observable event approved for the intended review. Ordered levels, multiple simultaneous codes, missing pairs, or shifting definitions require a different method.

Professional obligations come from the work and its consequences, not from the calculator. The BACB Ethics Codes and BCBA Test Content Outline provide current professional context but do not endorse this coefficient or prescribe an interpretation band. The Standards for Educational and Psychological Testing emphasize evidence supporting a proposed interpretation and use.

Register the design and category universe

Complete the fields before calculating any agreement statistic.

Design fieldPrespecified entryObservable constructIndependent unit definitionInclusion periodCategory universeJustification for every categoryKObserver A and Observer B rolesIndependence or blinding procedureMissing-pair ruleStop; complete pairs are requiredExclusions fixed in advanceData versionPrimary coefficientBrennan-PredigerPlanned sensitivity statisticsScott pi, Cohen kappa, or noneIntended decisionRequired reviewers

K must count categories that were genuinely possible under the protocol, including a possible category with zero observed use. It must equal the registered category universe represented on both table axes and must not include an invented category added after seeing the result. Save the original registration if the protocol later changes.

Preserve the complete paired table

Enter one count per paired unit in a square contingency table. Rows represent Observer A; columns represent Observer B.

Observer A \ Observer BCategory 1Category 2...Row totalCategory 1Category 2...Column totalN

Verify a square K x K table, nonnegative integer cells, matching category order, identical row and column grand totals, and one complete pair for each of the N units. Do not discard discordant rows or merge categories to improve agreement.

Calculate observed agreement

Add the diagonal counts and divide by N:

Po = (sumc n_cc) / N

Review the off-diagonal cells before reducing the table to one number. They show which category boundaries observers apply differently and may reveal a procedural or definitional problem that the coefficient cannot diagnose.

Apply the Brennan-Prediger chance term

For a prespecified category count K >= 2:

P_e,BP = 1 / K

Brennan-Prediger coefficient = (P_o - 1/K) / (1 - 1/K)

Use full precision and round only the final display. If K=1, the denominator is zero and the coefficient is undefined; a single-category design contains no classification contrast. If software returns a value outside the algebraic range implied by valid P_o and K, stop and inspect the implementation.

Work the fictional three-category example

The table below is invented solely to test the arithmetic. It contains 40 complete pairs and no real clinical or operational data.

Observer A \ Observer BIndependentPromptedNot observedRow totalIndependent122115Prompted39012Not observed121013Column total16131140

The diagonal is 12 + 9 + 10 = 31, so Po = 31/40 = 0.7750000000. The registered universe contains three categories, giving Pe,BP = 1/3 = 0.3333333333.

Brennan-Prediger = (0.7750000000 - 0.3333333333) / (1 - 0.3333333333) = 0.6625000000

Record the result with the table and the rationale for K=3. A reviewer should be able to reconstruct the number without guessing which categories were considered possible.

Test category-universe sensitivity without changing data

As an invalid sensitivity illustration, suppose someone adds an unused fourth category after inspecting the result. The observed table, diagonal, and P_o remain unchanged, but the chance term becomes 1/4 = 0.2500000000:

Brennan-Prediger with K=4 = (0.7750000000 - 0.2500000000) / 0.7500000000 = 0.7000000000

ViewJustified KP_oP_e,BPCoefficientReporting dispositionRegistered primary analysis30.77500000000.33333333330.6625000000ReportUnjustified unused category40.77500000000.25000000000.7000000000Do not substitute

The larger value is created by a changed assumption, not by better observer agreement. The related Randolph free-marginal conference paper demonstrates the same category-count sensitivity in a multi-rater formulation. It is supporting context, not authority to add a category or to treat the two procedures as interchangeable.

Compare other chance models only if planned

For the same fictional table, Observer A's proportions are 0.3750000000, 0.3000000000, and 0.3250000000; Observer B's are 0.4000000000, 0.3250000000, and 0.2750000000.

Cohen's kappa paper supplies the observer-specific marginal model. Its expected term here is 0.3368750000, producing kappa 0.6606974552. Scott's pooled-marginal article leads to pooled proportions 0.3875000000, 0.3125000000, and 0.3000000000; its expected term is 0.3378125000, producing pi 0.6602170835.

The three values happen to be close in this example, but that proximity is not evidence that the chance models are interchangeable or robust. Another table can separate them sharply. State the primary chance model before reviewing results and report every planned sensitivity analysis, including uncomfortable differences. Do not select the most favorable coefficient.

Keep the conclusion narrower than the number

The Brennan-Prediger coefficient summarizes exact nominal agreement relative to 1/K. It does not show which observer is accurate, validate the categories, establish treatment integrity, prove independence, demonstrate progress, or determine whether disagreement matters clinically.

Interpretation should include the full table, N, K and its rationale, raw category counts, P_o, the chance term, the coefficient, missingness, exclusions, version history, planned comparisons, and the consequence of error. Universal verbal bands can hide those facts. Qualified clinical and methods reviewers should decide whether the evidence is adequate for the stated purpose.

Escalate designs this page cannot analyze

Stop for more than two observers, missing or unequal paired data, ordered or weighted categories, multiple labels per unit, repeated observations nested within clients or staff, changing category universes, confidence intervals, hypothesis tests, sample-size planning, or accuracy against a reference standard. A statistician or psychometrician can select and implement a method that matches those features.

The fixed 1/K model is not a substitute for Cohen kappa, Scott pi, Fleiss kappa, Randolph free-marginal kappa, Gwet AC1, weighted kappa, Krippendorff alpha, or standard ABA IOA calculations. Each retains its own estimand and assumptions.

Retain clinical context and protect data

Review disagreements against direct observations, graphs, operational definitions, observer notes, environmental changes, treatment goals, and client and caregiver perspectives. Maintain competence and supervision, obtain consent or assent where applicable, and separate descriptive agreement from clinical effectiveness or causation.

Use minimum-necessary information and an approved system for any unit-level record. The HHS Privacy Rule summary and HHS Security Rule summary outline federal requirements for regulated entities. Apply organizational and state controls as well. This worksheet is not legal advice.

Copyable result record

Result fieldValueData versionN complete paired unitsRegistered category universeRationale for KFull contingency table retainedP_o1/KBrennan-Prediger coefficientPlanned Scott pi or Cohen kappa sensitivityOff-diagonal pattern reviewedMissing or excluded unitsInterpretation and limitationsReviewer and date

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