An ABA runs test calculator turns one ordered numeric sequence into two symbols around a prespecified cutoff, then counts uninterrupted blocks of the same symbol. The result summarizes the arrangement of those symbols under a stated large-sample reference model. It cannot determine why a pattern occurred or replace the original graph.

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

Decide whether the observed symbol sequence deserves closer review

Treat the ABA runs test calculator as a descriptive sequence diagnostic, with the original ordered values available for review.

This page uses a median split selected before calculation. Values above the median receive H; values below it receive L. A value exactly equal to the cutoff stops this implementation because silently discarding or assigning ties changes the sequence. Another prospectively chosen method may handle ties differently, but its rule, rationale, and source must remain visible.

Prespecify the sequence, cutoff, tie rule, and use

The order is part of the question. Record the sequence key and the planned cutoff method before deriving symbols.

Scope fieldRequired entryStop signalMeasure and unitObservable response and stable unitDefinition or unit changedSequence keyDate, session, opportunity, or fixed indexOrder is unknown or reconstructed post hocSpacingPlanned adjacency and known gapsGaps or irregular spacing change the questionCutoff ruleMedian fixed before symbol reviewCutoff selected to alter run countTie ruleStop on any value equal to cutoffTies were silently assigned or removedInclusion rulesVersioned before result reviewRows excluded after viewing the sequenceIntended useDescriptive sequence diagnosticCausal, treatment-effect, or universal decision rule

Keep phase changes, setting changes, treatment modifications, staffing changes, missing observations, and data-system changes on the same review record. A runs result detached from that context is incomplete.

Build an auditable value-to-symbol ledger

Preserve every raw value in its original order. Derive symbols without sorting. A run is one uninterrupted block of identical symbols, so the first row begins run one and each symbol change begins the next run.

IndexAuthorized sequence keyRaw valueCutoffSymbolRun numberContext1123...

Post hoc sorting destroys the prespecified order and therefore changes the estimand. Keep any sorted illustration clearly labeled as a sensitivity demonstration, never as a replacement for the source sequence.

Use the visible runs formulas

Let n1 be the number of H symbols, n2 the number of L symbols, N = n1 + n2, and R the observed number of runs. The NIST formulas are:

E(R) = (2n1n2 / N) + 1

Var(R) = 2n1n2(2n1n2 - n1 - n2) / (N^2(N - 1))

SD(R) = sqrt(Var(R))

z = (R - E(R)) / SD(R)

This worksheet displays the uncorrected large-sample z only when both n1 > 10 and n2 > 10, matching the stated condition in the NIST runs-test documentation. It does not generate a p-value, critical-value lookup, or automatic hypothesis decision.

Copy the blank runs worksheet

Summary fieldValueAudit noteNIncluded nontied valuesMedian cutoffFixed before symbol reviewTies at cutoffMust be zero for this implementationn_1 high symbolsMust exceed 10 for displayed large-sample zn_2 low symbolsMust exceed 10 for displayed large-sample zObserved runs RRecount from symbol ledgerExpected runs E(R)Full precisionVariance and SDVariance must be positiveUncorrected zDescriptive large-sample reference only

Run numberStart indexEnd indexSymbolLengthPhase or context note12...

Preserve full precision, calculator version, analyst, reviewer, date, cutoff rationale, tie rule, and any independent software cross-check.

Work a fictional twenty-four-value example

Consider a fictional sequence with low values 4, high values 6, and a median cutoff of 5. The derived symbols, in source order, are:

H H H | L L | H H | L L L | H | L | H H | L L | H H | L L L L | H H

The vertical bars mark the 11 observed runs. There are 12 high symbols and 12 low symbols, so N = 24, n1 = 12, and n2 = 12. No value equals the cutoff.

QuantityCalculationResultExpected runs(21212/24)+113.0000000000Run-count variance21212(288-24)/(24^223)5.7391304348Run-count SDsqrt(5.7391304348)2.3956482285Uncorrected z(11-13)/2.3956482285-0.8348471099

The two side counts exceed 10, so the NIST large-sample condition is met. The value remains a diagnostic summary. It does not prove that the process is random, stable, clinically acceptable, or generated by a particular mechanism.

Recount before interpreting

Walk left to right. The first H starts run one, and repeated H values remain in that run. The first L starts run two. Continue until the final H H block, which is run 11. A second reviewer should reproduce the symbols and boundaries without seeing the calculated z.

Then calculate the two group counts, expected run count, variance, SD, and z. If a spreadsheet returns a different value, compare continuity-correction settings, cutoff rules, tie handling, and symbol ordering before comparing conclusions.

Keep implementation variants explicit

The current statsmodels one-sample runs-test documentation permits a mean, median, or numeric cutoff and documents an optional continuity correction for samples below 50. This page deliberately displays the uncorrected NIST formula and records the software setting rather than mixing variants.

Do not present a corrected and uncorrected result as interchangeable. If a qualified reviewer needs inference, the cutoff, tie convention, sample-size rule, continuity correction, tail, alpha, and software version must be specified prospectively. This drafting tool stops before that inference.

Test invariance and failure boundaries

CheckExpected behaviorInterpretation limitReverse the sequenceRun count and z stay the sameReverse time is clinically equivalentSwap H and L labelsRun count and z stay the sameLabel meaning can be omittedApply a + b*x, b > 0, and transform cutoffSymbols and result stay the sameUnits or measures are interchangeableSort all highs then lowsR = 2, z = -4.5916591047 in the exampleSorted result may replace source orderAll values on one sideOne side count is zero; stopA run statistic is definedAny value equals cutoffStop under this tie ruleThe row may be silently discarded

These checks assess implementation behavior. They do not certify measurement quality, sampling, clinical relevance, or the reference model.

Read runs beside the source graph

The NIST run-sequence plot guidance uses observation index on the horizontal axis and can reveal shifts, scale changes, and outliers. The symbol test compresses each value to one of two sides of a cutoff, discarding magnitude. A sequence with similar symbols can contain very different clinical changes.

Few runs can reflect clustering on one side; many runs can reflect rapid alternation. Either pattern can arise from phase changes, schedule effects, changing opportunity counts, autocorrelation, measurement artifacts, or ordinary variation. Review the original values, graph, and context before considering another model or clinical action.

Stop when ordering or dichotomization is not credible

Stop if order is uncertain, spacing changes the question, phases were pooled, or the cutoff was selected after viewing patterns. Also stop when ties lack a prespecified rule; rows were removed post hoc; either side is empty; variance is zero; missing values were silently bridged; or repeated and clustered sequences require another analysis.

Also stop if either side count is 10 or less and someone asks this page to supply a normal-approximation conclusion. Preserve the descriptive symbol ledger and seek qualified methods review or an appropriate exact procedure. Do not convert z into a universal ABA cutoff.

Protect clinical meaning, ethics, and data handling

The BACB Ethics Codes page provides the current professional source. The BCBA Test Content Outline addresses measurement, data display, interpretation, and experimental design, while the Standards for Educational and Psychological Testing provide broader testing guidance. They do not certify this worksheet or turn a runs result into evidence of treatment effect, experimental control, client benefit, or competence.

Use synthetic or appropriately de-identified values for training. For authorized identifiable data, minimize fields, restrict access, preserve versions, and follow approved retention and security controls. HHS publishes a Privacy Rule overview and a separate Security Rule overview. Those federal summaries neither certify this worksheet nor replace the organization's applicability analysis and safeguards.

Related resources

Sources