ABA Log Response Ratio Calculator for Clinicians

An ABA log response ratio calculator can summarize proportionate phase-mean change when the measurement scale and assumptions fit. This worksheet deliberately performs one narrow calculation: the uncorrected natural log of the ratio between two positive phase means for the same positive ratio-scale count or rate. Eligibility, raw sign, direction of desired change, and one disputed-observation sensitivity remain visible throughout.

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

The narrow calculation on this page

For an eligible adjacent Phase A and Phase B contrast, this tool calculates:

the arithmetic mean of valid Phase A observations;
the arithmetic mean of valid Phase B observations;
the response ratio, mean B / mean A;
the uncorrected log response ratio, ln(mean B / mean A);
the arithmetic phase-mean change, 100 x [exp(LRR) - 1];
the same outputs after one prespecified, documented sensitivity change.

The raw LRR sign follows the arithmetic ratio. A positive value means the Phase B mean is larger than the Phase A mean. A negative value means it is smaller. Whether that movement is preferred depends on the outcome and the person's goals. Keep raw increase/decrease separate from preferred/nonpreferred direction.

This implementation supplies no truncation, continuity correction, bias correction, standard error, p-value, confidence interval, or universal magnitude label. It does not claim parity with the default bias-corrected estimators available in current statistical software. Its purpose is a transparent, reproducible assumption check and descriptive sensitivity record.

Check eligibility before entering values

The outcome must meet every condition below for this worksheet:

one count or rate measured on a ratio scale with a meaningful true zero;
the same operational definition, unit, opportunity or exposure base, and recording procedure in both phases;
comparable observation lengths, or rates already calculated from valid comparable exposure data;
positive numeric values in the active calculation and positive phase means;
two ordered adjacent phases with a defensible boundary;
within-phase level stability reviewed on the full chronological graph;
missing, invalid, late, corrected, and disputed observations identified rather than recoded silently;
the desired direction and analysis plan declared before inspecting a preferred result.

Examples that may fit after qualified review include occurrences per fixed observation or responses per fixed opportunity when the count or rate has a meaningful ratio interpretation. Percentages and proportions do not fit this worksheet. Neither do ordinal ratings, interval scales without a meaningful zero, or mixed units.

An observed zero also stops this narrow calculator. Zero can be meaningful on a ratio scale, yet the appropriate statistical handling requires a declared method. This page does not manufacture a small constant, replace zero with one, or choose a truncation rule. A qualified methods reviewer should select and document another estimator when zeros occur.

Arithmetic eligibility does not establish the assumed phase model. The primary LRR methods source describes stable phase mean levels and independent repeated measurements. Real clinical series may have trend, serial dependence, changing variability, or recording effects. Preserve those concerns as limitations and assess them with the graph and design.

Assumption and input record

FieldLocked entryEligible for this narrow tool?Reviewer noteOutcome and operational definitionyes / no / unresolvedCount or rateMeaningful true zeroUnit and exposure baseObservation duration comparabilityRecording procedure unchangedEvery active value positiveWithin-phase level stability reviewedDesired direction prespecifiedMissing and disputed states resolved

If any required field is no or unresolved, return not calculated and retain the reason. Do not use a computed number to overrule an eligibility concern.

Copyable ordered input

PhaseOrderDate or sequenceRaw valueCount/rate unit and exposureStatusRecording or context noteA1valid / missing / invalid / disputedA2A3A4B1B2B3B4

Desired direction: higher values preferred / lower values preferred

Reason that direction matters to the client: ____________________________

Graph and raw-data version: ____________________________

Formulas and sign display

Let m be the valid Phase A count and n the valid Phase B count.

mean A = sum of valid A values / m

mean B = sum of valid B values / n

response ratio = mean B / mean A

uncorrected raw LRR = ln(response ratio)

arithmetic phase-mean change = 100 x [exp(LRR) - 1]

Since exp(LRR) returns the response ratio, the final expression is also 100 x (response ratio - 1). It describes the arithmetic difference between phase means relative to Phase A. It is not automatically a percentage improvement.

Raw resultArithmetic descriptionTherapeutic-direction labelLRR > 0Phase B mean is higherpreferred only if higher was prespecifiedLRR = 0Phase means are equalno phase-mean directionLRR < 0Phase B mean is lowerpreferred only if lower was prespecified

For outcomes where lower values are preferred, a negative raw LRR can align with the desired direction. Preserve the negative sign. A separate label may state that the direction was preferred, with the client-centered rationale and reviewer.

Blank result and sensitivity ledger

OutputPrimary stateSensitivity stateReconciliation noteValid Phase A count, mMatches active raw rowsPhase A sumPhase A meanValid Phase B count, nMatches active raw rowsPhase B sumPhase B meanResponse ratiomean B / mean AUncorrected raw LRRNatural logarithmArithmetic phase-mean changeNot a clinical labelRaw directionhigher / equal / lowerPrespecified desired directionSensitivity change and rationaleOne disclosed changeDisplay precisionFull precision retained

Append a new version when source data, phase membership, status, unit, formula, or rounding changes. Keep the earlier result and reason for revision.

Rowan's fictional worked example

Rowan is fictional. Every number below is synthetic and represents no real client, caregiver, clinician, or practice. The outcome is independent responses per fixed observation, recorded consistently as a positive ratio-scale count. The analysis plan identifies larger counts as preferred.

Phase A is 20, 20, 26, 25, 22, 23. Its sum is 136 across six observations.

mean A = 136 / 6 = 22.6666666667

Phase B is 28, 25, 24, 27, 30, 30, 29. Its sum is 193 across seven observations.

mean B = 193 / 7 = 27.5714285714

The response ratio is:

27.5714285714 / 22.6666666667 = 1.2163865546

The uncorrected raw log response ratio is:

ln(1.2163865546) = 0.1958846233

The arithmetic phase-mean change is:

100 x [exp(0.1958846233) - 1] = 21.6386554622%

The primary record says that the Phase B mean is 21.6387% higher than the Phase A mean under this uncorrected arithmetic. Because higher values were prespecified as preferred, the raw direction aligns with the desired direction. The tool does not call the difference clinically important or caused by the intervention.

One disclosed sensitivity

The Phase B value 24 has a documented disputed status. The team reruns the worksheet after excluding that value only. This is a traceable data-quality question, not a search for a more favorable result.

The sensitivity Phase B sum is 169 across six observations.

mean B_sensitivity = 169 / 6 = 28.1666666667

response ratio_sensitivity = 28.1666666667 / 22.6666666667 = 1.2426470588

uncorrected raw LRR_sensitivity = ln(1.2426470588) = 0.2172438292

arithmetic phase-mean change_sensitivity = 24.2647058824%

Analysis statemMean AnMean BRatioRaw LRRArithmetic changeLocked primary622.6666666667727.57142857141.21638655460.195884623321.6386554622%Exclude disputed B=24622.6666666667628.16666666671.24264705880.217243829224.2647058824%

The spread shows how the declared input decision affects the summary. The primary and sensitivity states remain together, with the dispute reason and reviewer. A larger sensitivity value does not earn priority.

What the arithmetic cannot settle

The primary response-ratio methods paper develops LRR for proportionate change in ratio-scale behavioral outcomes under a simple phase model. The calculation is attractive because a ratio has a direct proportional interpretation and the logarithm treats reciprocal ratios symmetrically. Those properties do not verify measurement quality or the model in a specific series.

Recording procedures matter. A simulation study of procedural sensitivity found that LRR can still be affected by features such as partial-interval recording. Observation length, opportunity, exposure, operational definition, observer training, and data-collection changes belong in the record. Comparing means across changed systems can create an arithmetic difference that reflects measurement rather than behavior.

Current SingleCaseES LRR documentation and its mathematical definitions describe increasing and decreasing variants, truncated means, bias corrections, standard errors, and optional percentage conversion. This ABA log response ratio calculator deliberately implements none of those additional choices. If the analysis needs them, use a qualified quantitative reviewer, name the estimator exactly, preserve its assumptions and software version, and keep it separate from the uncorrected row shown here.

Methods guidance on a priori justification of single-case effect measures supports choosing a measure for its question and assumptions before results are known. A 25-year review of single-case effect-size reporting documents continued variation in measure use and emphasizes the need for clear reporting. Do not shop across estimators, transformations, directions, or data states for the most favorable coefficient.

Visual analysis, design, and replication remain visible

Phase means remove chronology. The same means can arise from an abrupt level change, steady trend, delayed response, cyclic pattern, or unstable data. Examine the full graph for level, trend, variability, immediacy, overlap, consistency, and unexpected changes. Review measurement quality, treatment integrity, phase-change logic, repeated demonstrations, and alternative explanations.

The What Works Clearinghouse Version 5.0 handbook requires design-quality review and systematic inspection of the plotted series in single-case evidence review. A favorable LRR from one adjacent contrast does not demonstrate experimental control or causation.

Report harms, burdens, adverse effects, implementation changes, and uncertainty alongside the numeric direction. Leave decisions open when stability, measurement, design, replication, or product assumptions are unresolved.

Client meaning and accountable review

The client's experience and priorities determine whether the outcome and direction matter. Review benefits, burdens, feasibility, dignity, access, and tradeoffs through accessible communication. Preserve ordinary communication, mobility, sensory, and decision supports. Record assent, dissent, preferences, and requested changes where applicable.

The current BACB Ethics Codes page provides the professional source for certificants. It does not endorse this worksheet or turn a response ratio into ethical compliance. Qualified reviewers remain accountable for case-specific interpretation and action under competence, licensure, supervision, consent, payer, regulator, legal, and organizational requirements.

Privacy, security, and traceability

Use synthetic or de-identified data for training. For an authorized workflow involving identifiable information, use the least identifying data needed, approved systems, access controls, and version history. The federal Privacy Rule overview and Security Rule overview describe distinct HIPAA obligations for regulated entities. They neither certify this calculator nor replace an organization's applicability and risk analysis.

Retain raw-data and graph references, eligibility answers, the uncorrected formula name, full-precision results, sensitivity reason, recording procedure, reviewers, client input, disagreements, decision owner, and next review date.

ABA Uncorrected Log Response Ratio Assumption and Sensitivity Calculator for Clinicians