An ABA Cook's distance calculator combines one case's residual magnitude and leverage within a documented ordinary least-squares regression. It helps reviewers see which included cases may materially influence the fitted coefficients. The result does not decide that a case is wrong, disposable, clinically unimportant, or responsible for an observed pattern.

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

Influence is not the same as leverage or residual size

Cook's distance is a case-level diagnostic for one fitted model. Leverage describes how unusual a row's predictor values are within the design matrix. The ordinary residual describes the observed-minus-fitted difference on the response scale. Cook's distance combines both ingredients and scales them by the model's residual mean square and parameter count.

Use the ABA Cook's distance calculator after the source regression has been fixed and audited. A large value means that deleting the row could change the fitted coefficient vector materially under this diagnostic. A high result does not prove that the observation is erroneous, that the model is valid without it, or that deletion improves a clinical decision.

Freeze the model record before calculating

Document the analysis scope before reviewing case influence. Changing rows, predictors, coding, weights, transformations, or the response after seeing preferred diagnostics creates a different analysis.

Scope fieldRequired recordStop signalResponseObservable response, denominator, unit, and directionDefinition or unit changedSource modelFormula, coding, intercept, weights, population, phase, and versionResiduals or leverage cannot be reproducedRow identityOne authorized key for every fitted rowRows are missing, duplicated, or shiftedResidual conventionei = yi - yhati or another named conventionResidual signs are uncertainDesign sizeIncluded rows n and parameter count p, including interceptRank or parameter count is unclearError scaleFull-model SSE, residual degrees of freedom, and MSEMSE is zero, negative, or undefinedLeverageHat diagonal h_ii from the same designh_ii is outside [0, 1]Intended useDescriptive influence reviewAutomatic deletion or clinical verdict

Keep phase, setting, staffing, schedule, measurement, denominator, and intervention changes beside the model record. A mathematically influential point can still be clinically valid and essential.

Calculate each Cook's distance transparently

For an ordinary least-squares model with n included rows and p estimated parameters, including the intercept:

df_resid = n - p

MSE = SSE / df_resid

Di = (ei^2 / (p MSE)) (hii / (1 - hii)^2)

The NIST regression-diagnostics reference presents this construction and explains that a high-leverage case need not be influential. The statsmodels Cook's-distance documentation identifies its implementation as using the original fit without an observation loop. Record the software and formula convention rather than assuming two outputs are interchangeable.

Do not calculate when p >= n, MSE <= 0, or h_ii is effectively one. Near-one leverage makes the denominator unstable. Preserve full precision and round only the displayed result.

Copy the blank influence worksheet

RowAuthorized keyy_iyhatie_ih_ii1 - h_iiD_iPhase or context123...

Model summaryValueAudit noteIncluded rows nMatch the fitted modelParameters pCount intercept and coded columnsResidual degrees of freedomn - pFull-model SSEPreserve source precisionFull-model MSESSE / (n - p)Largest displayed D_iDescriptive ordering onlySoftware and versionPreserve settings and cross-check

Store the row-level table with the model formula, coefficient vector, design-matrix version, analyst, reviewer, calculation date, code or spreadsheet version, and any independently reproduced result.

A fictional eight-row regression exposes the arithmetic

Consider fictional predictor values x = [1, 2, 3, 4, 5, 6, 7, 8] and outcomes y = [2, 3, 5, 4, 6, 7, 8, 14]. Fit an intercept and one slope, so p = 2. The fitted line is y_hat = -0.1428571429 + 1.3928571429*x.

The full-model SSE = 17.3928571429, residual degrees of freedom are 6, and MSE = 2.8988095238.

Rowxyyhatie_ih_iiCook's D_i1121.25000000000.75000000000.41666666670.11880316812232.64285714290.35714285710.27380952380.01142304043354.03571428570.96428571430.17857142860.04244574444445.4285714286-1.42857142860.13095238100.06103521745566.8214285714-0.82142857140.13095238100.02017976886678.2142857143-1.21428571430.17857142860.06730765507789.6071428571-1.60714285710.27380952380.2313165689881411.00000000003.00000000000.41666666671.9008506894

For row 8, the calculation is (3^2 / (2 2.8988095238)) (0.4166666667 / (1 - 0.4166666667)^2) = 1.9008506894. This value ranks row 8 as the most influential case in this fictional fit. That ranking does not authorize deletion.

Change only the last fictional outcome from 14 to 10 and refit the full model. Row 8's Cook's distance becomes 0.5988771054. The change demonstrates model dependence, not a reason to edit a real observation.

Run invariance and boundary checks

CheckExpected arithmetic behaviorWhat the check cannot proveAdd one constant to every outcome and refitResiduals, leverage, MSE, and Cook's distances stay the sameOutcome meaning is unchangedMultiply all outcomes by a nonzero constant and refitResiduals and MSE rescale; Cook's distances stay the sameUnits are clinically interchangeablePermute every row together and refitValues follow their row keysObservation order never matters elsewhereReverse residual signs while preserving leverage and MSECook's distances stay the sameResidual direction is irrelevant clinicallyHigh leverage with tiny residualCook's distance may remain smallThe case is harmless in every modelLarge residual with low leverageInfluence depends on both termsResidual extremeness equals influenceh_ii approaches oneDenominator becomes unstable; stopSoftware can resolve an unsupported design

These checks evaluate calculation behavior. They do not validate the response, design matrix, sampling plan, independence assumption, measurement system, or clinical use.

Interpret influence beside deletion fits and direct graphs

The R core regression deletion diagnostics place Cook's distance beside hat values, DFFITS, DFBETAs, covariance ratios, and studentized residuals. That collection reinforces a key boundary: one diagnostic does not describe every way a case can affect a model.

Plot residuals against fitted values and leverage. Display direct clinical data by time, phase, and meaningful context. For a reviewed case, compare the full fit with a clearly labeled leave-one-out sensitivity fit. Report how coefficients, fitted values, residual patterns, and clinically relevant predictions change. Never replace the primary analysis silently.

An unusual result can reflect a valid context shift, a rare predictor combination, a changed denominator, measurement drift, miscoding, omitted nonlinear structure, dependence, or an actual data error. Cook's distance does not identify which explanation is correct.

Stop when the fitted design cannot support the diagnostic

Stop when model provenance, row identity, response units, coding, intercept handling, weights, exclusions, or the hat diagonal cannot be reproduced. Stop for rank deficiency, nonpositive residual degrees of freedom, zero or undefined MSE, leverage at or near one, pooled phases, or rows selected for review only after a preferred result appeared.

Seek qualified methods review for repeated or clustered observations, generalized or mixed models, weighted fits, nonlinear models, small samples, multiple-case inference, robust regression, or any proposal to remove a case. A rule of thumb from a software display or textbook is not a universal ABA cutoff.

Clinical and data-governance review remains separate

The BACB Ethics Codes and BCBA Test Content Outline are current professional sources for ethics, measurement, graphing, interpretation, and experimental design. The Standards for Educational and Psychological Testing provide broader evidence and interpretation principles. None endorses this worksheet or defines an ABA influence threshold.

Use synthetic or appropriately de-identified data for training. When identifiable information is necessary in an authorized workflow, minimize fields and use approved storage, access, retention, and version controls. HHS provides separate Privacy Rule and Security Rule summaries. Those summaries do not determine applicability or certify an implementation.

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