When a single-case randomization test produces tied statistics, use a rule chosen before analysis. For the usual exact inclusive tail, count every permissible assignment whose statistic is at least as extreme as the observed statistic, including equal values and the observed assignment. Report counts above, equal to, and below the observed value. A strict, mid-p, or randomized convention answers a modified question and requires explicit methods justification.

Define equality at calculation precision

Keep full computational precision and state any tolerance used for floating-point comparison. Display rounding happens after assignment classification.

Count above, equal, and below separately

A three-way ledger reveals which schedules drive the tail and prevents silent omission of tied assignments.

Include the observed assignment

The observed schedule belongs to the permissible set and its statistic belongs to the randomization distribution. Its inclusion should be visible.

Predeclare any alternative convention

A mid-p or randomized p value has different properties. Use it only with qualified methods justification and report the ordinary inclusive result when relevant.

Review the statistic's granularity

Many ties may indicate a binary, bounded, or coarse measure. Report that limitation and consider a better prospectively chosen statistic in future work.

Build Farah's tied-statistic ledger

Start with a versioned record for Farah's equal statistics in the randomization distribution. For the tied statistics single-case randomization test question, record the protocol date, design, randomization unit, complete permissible assignment set, assignment probabilities, actual draw, test statistic, direction, tail, tie rule, missing-data rule, analysis mode, software, and reviewer. Keep Farah's raw time series in chronological order and link every derived value to its source. The packet should let an independent analyst reproduce both the observed statistic and its reference distribution.

Work the example for Farah

Farah's assignment set contains 10 schedules. The observed statistic is 2.0. One other schedule is greater and three schedules, including the observed one, equal 2.0. The inclusive one-sided numerator is 1 greater plus 3 equal, so p=4/10, or 0.40. A strict greater-than calculation would be 1/10 and is not substituted after seeing the result. Preserve every intermediate assignment count, statistic, fraction, and rounding step. The example is fictional and teaches the stated method; it does not create a universal alpha, minimum design, treatment recommendation, or effect category for Farah's telehealth communication study.

Audit Farah's randomization evidence

Farah's ledger groups all 10 schedules into one above, three equal, and six below. It identifies the observed schedule within the tied group, retains full-precision statistics before grouping, and names the inclusive rule in the protocol and software call. The audit also checks protocol amendments, assignment deviations, duplicate or missing observations, phase-label changes, output precision, code and package versions, and whether the reported test matches the actual randomization. Unresolved discrepancies remain on hold with an owner and due date.

Prevent the main inference error in Farah's review

Rounding can manufacture ties or hide them. Another error changes from greater-than-or-equal to greater-than because the latter produces a smaller number. Farah's review uses full precision and preserves any alternative convention as a labeled sensitivity analysis. A randomization p value depends on the assignment mechanism and predeclared statistic. It does not turn nonrandom treatment changes into randomized experiments, quantify the effect's size, establish clinical importance, or estimate a population effect.

Integrate design evidence for Farah

The team describes why ties arose, such as discrete outcomes or a coarse statistic, and considers whether the statistic had enough resolution for the design. It does not treat a different tie convention as new data or a reason to ignore the visual pattern. The WWC Version 5.0 handbook is a research-review standard rather than a universal care protocol. The responsible team still evaluates the design's prediction, verification, replication, phase patterns, attrition, assignment fidelity, measurement quality, and fit to the question.

Protect participation and access for Farah

Research design never outranks Farah's welfare. Keep augmentative and alternative communication, interpreters, mobility, food, water, bathroom use, prescribed care, health support, rest, relationships, and emergency help available. Use accessible communication for consent and assent processes, withdrawal, discomfort, and feedback. If the selected schedule becomes unwanted, unsafe, medically inappropriate, or infeasible, qualified people act for safety and document the design consequence.

Use randomized single-case sources within scope for Farah

For Farah's randomization-test tie rule, the BACB ethics hub and CASP public summary provide professional context, and the BCBA Test Content Outline identifies examination content on measurement and single-case design. A randomized SCED methods paper explains prospective assignment sets, randomization tests, and attainable p-value limits. An effect-measure paper describes a priori statistic choice and the boundary between tentative causal inference and effect magnitude. Research on rapidly alternating designs, changing-criterion designs, and randomized case series shows that assignment schemes and test behavior are design-specific. ASHA supports continuous AAC access.

Rehearse Farah's analysis before outcomes exist

Before the telehealth communication study begins, Farah's team runs the tied-statistic ledger with a small fictional sequence. The dry run confirms that the assignment generator returns exactly the permitted schedules, the selected schedule can be traced to the random draw, and the randomization-test tie rule statistic matches a hand calculation. Reviewers deliberately include a tie, a missing observation, and an assignment at each boundary so default behavior becomes visible. They save the test inputs, expected outputs, code version, and correction log. This rehearsal checks the machinery for equal statistics in the randomization distribution; it never uses Farah's future outcomes or changes the predeclared analysis after data collection.

Tied Statistics Single-Case Randomization Test Review

Review the tied-statistic ledger with Farah, the responsible clinician, and a statistician or methodologist experienced in randomization inference. Preserve protocol, assignments, raw observations, graph, code, outputs, deviations, inference limits, client input, decisions, and future design changes. Keep the page draft and noindex until the named external reviews confirm that the research description, accessible participation, and clinical boundary are accurate.

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