An ABA Krippendorff alpha calculator can summarize nominal agreement when observer participation varies across independent units. This bounded worksheet accepts missing cells, constructs the coincidence matrix, and calculates nominal alpha. It deliberately does not offer ordinal, interval, ratio, circular, unitizing, or custom-distance variants. Preserve the missingness pattern and every observed rating before reducing the data to one coefficient.

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

Choose nominal alpha for the stated design

Krippendorff's alpha resources at the University of Pennsylvania describe a family of reliability coefficients for two or more observers, multiple measurement levels, and incomplete data. This calculator implements only the nominal case. Every disagreement between different categories receives distance 1; matching categories receive distance 0.

Use the ABA Krippendorff alpha calculator when:

  • Every column represents the same defined type of independent unit.
  • Two or more observed values remain on each unit used in the coefficient.
  • Categories are mutually exclusive nominal labels.
  • Observers work independently under common coding instructions.
  • Missing means not observed, not a behavior category and not zero.
  • Variable observer participation is part of the documented design.

Do not choose nominal alpha merely because the dataset contains blank cells. First determine why values are missing, whether observer assignment creates systematic gaps, and whether the remaining units support the intended use.

Distinguish the observer matrix from a contingency table

Enter observers in rows and units in columns. A two-rater contingency table counts units once at each row-column combination. Krippendorff's coincidence matrix instead counts ordered pairs of values within each pairable unit. Units with more observed values contribute more coincidences, but normalization by mu - 1 makes their coincidence contribution sum to mu.

The primary computation note explains this construction for any number of observers and missing data. Do not paste a familiar confusion matrix into the formulas below.

For a fixed number of ratings per unit with nominal categories and a rater-pool design matching Fleiss's assumptions, compare the Fleiss kappa calculator. The coefficients use different chance models and should not be selected after comparing which number is larger.

Prespecify missingness and pairability

Copy this record before calculation.

FieldPrespecified entryObservable constructIndependent unit of analysisNominal category labelsOperational definition for each categoryEligible observer poolObserver independence procedureMissing-value symbol. or blankWhy ratings may be missingPairable-unit ruleAt least two observed valuesSampling period and exclusionsData and coding-rule versionIntended decision consequenceAnalyst and independent verifier

The BACB Ethics Codes and BCBA Test Content Outline support professional, measurement, and data-review context. They do not prescribe alpha or an acceptance threshold. The Standards for Educational and Psychological Testing call for evidence suited to the proposed interpretation and use, not a statistic chosen after inspecting results.

Enter the observer-by-unit matrix

Each observed cell contains one category. Use the declared missing symbol for no rating and retain the source identifier needed for authorized verification.

Observer / unitU1U2U3U4U5U6Observer 1Observer 2Observer 3Observer 4Observed count m_uPairable?

Exclude a unit from the coefficient when m_u < 2. Preserve it in the audit record with the reason it was not pairable. Do not convert the single value to a matching pair or let it alter category marginals.

Construct observed coincidences

For pairable unit u, let nuc be the number of observed values in category c, and let mu be the total number of observed values. The construction counts ordered value pairs, so an A-B pair and its B-A counterpart occupy separate symmetric cells. Add these quantities to the observed coincidence matrix:

  • Diagonal cell occ: nuc(nuc - 1) / (mu - 1).
  • Off-diagonal cell ock: nuc nuk / (mu - 1) for c != k.

Sum each contribution across pairable units. Fractional cells are expected when m_u > 2; do not round them before the final coefficient. The matrix is symmetric. Its grand total is:

n = sumu(mu) = sumc sumk(o_ck)

Category marginal nc is the row total sumk(ock). Confirm that row marginals sum to n and match the column marginals before continuing. For this nominal worksheet, define deltack^2 = 0 when c = k and 1 otherwise.

Calculate observed and expected disagreement

Observed disagreement is:

Do = [sumc sumk(ock x delta_ck^2)] / n

Expected disagreement is:

De = [sumc(nc x sumk(nk x deltack^2))] / [n(n - 1)]

Finally:

alpha = 1 - Do / De

Retain full precision. If there are no pairable units, stop. If D_e = 0, alpha is undefined because the usable values do not vary across categories. Negative alpha is possible when observed disagreement exceeds expected disagreement and must remain visible.

Hayes and Krippendorff's methods paper emphasizes independent observers, common instructions, an appropriate unit sample, and a coefficient matched to the level of measurement. The page does not adopt the paper's recommendation as a universal ABA rule.

Fictional matrix with variable participation

Assume four fictional observers, eleven units, and three nominal categories. A period means no rating.

UnitObserver 1Observer 2Observer 3Observer 4m_uPairable?1AAAA4Yes2AABA4Yes3BBB.3Yes4BCBB4Yes5CCCC4Yes6CC.C3Yes7A.AB3Yes8BBA.3Yes9CBCC4Yes10.AAA3Yes11..B.1No

Unit 11 remains documented but contributes neither coincidences nor a category marginal. The ten pairable units contain n = 35 observed values.

Reproduce the fictional coincidence matrix

Applying the unit weights gives:

Observed coincidenceABCRow total n_cA10.00000000003.00000000000.000000000013.0000000000B3.00000000006.00000000002.000000000011.0000000000C0.00000000002.00000000009.000000000011.0000000000Column total13.000000000011.000000000011.000000000035.0000000000

Off-diagonal coincidences total 10, so Do = 10 / 35 = 0.2857142857. The marginal-based nominal expected disagreement is De = 0.6840336134. Therefore:

alpha = 1 - 0.2857142857 / 0.6840336134 = 0.5823095823

The result is a fictional arithmetic demonstration. It does not establish accuracy, sufficient coverage, randomness of missingness, category validity, or a decision threshold.

Compare complete-case deletion without calling it repair

If an analyst deletes every unit with any missing value, only Units 1, 2, 4, 5, and 9 remain. That complete-case subset has n = 20, Do = 0.3000000000, De = 0.6894736842, and alpha = 0.5648854962.

AnalysisUnits retainedObserved values nD_oD_eNominal alphaVariable-participation calculation10350.28571428570.68403361340.5823095823Complete cases only5200.30000000000.68947368420.5648854962

The change reflects a different dataset, not a correction. Complete-case deletion can also change the observer mix and contexts represented, so compare the retained and excluded units before interpreting either value. Never choose the missing-data rule after seeing which result is more favorable.

Keep the worksheet nominal and bounded

This page gives all off-diagonal disagreements equal distance. It cannot evaluate whether one ordinal step is less serious than three steps. It does not calculate interval, ratio, circular, polar, custom-metric, unitizing, or multivariate alpha. Those variants require correctly defined distance functions and qualified methods review.

The tool also omits confidence intervals, bootstrap distributions, sample-size planning, clustered inference, repeated dependent units, rater-specific bias estimates, adjudicated consensus, and imputation. Do not treat a lone observed rating as agreement. Do not recode missing as a clinical category. Do not silently omit difficult units without preserving the exclusion.

Interpret missingness before the summary

Alpha describes reproducibility under the supplied design; it does not reveal which category is correct. Review the observer matrix, category marginals, pairable-unit counts, missingness by observer and context, coincidence cells, direct observation records, graphs, training history, drift, and ambiguous definitions.

Prespecify what action a result could support. Possibilities may include checking coding instructions, observing additional units, retraining, requesting statistical consultation, or leaving the clinical decision unchanged. A universal qualitative label can conceal sampling uncertainty, systematic missingness, limited category variation, repeated observations, or important disagreements.

Restrict the matrix to necessary data. The HHS Privacy Rule summary and HHS Security Rule summary provide general federal context, not permission to process a particular record set. Apply relevant consent, assent, access, confidentiality, retention, accessibility, payer, contractual, state, organizational, and legal requirements.

Related resources

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