Exact versus Monte Carlo single-case randomization differs in how the reference distribution is built. Exact analysis evaluates every permissible assignment. Monte Carlo analysis draws a declared random sample when enumeration is impractical. Label the method, complete-set size, number of draws, seed, replacement rule, finite-sample correction, tail, ties, uncertainty, software, and reproducibility check. A simulated p value should not be described as exact.

Determine whether enumeration is feasible

Calculate or obtain the size of the permissible assignment set. Confirm that software can evaluate the complete design without silently truncating it.

Specify the Monte Carlo algorithm

Record draw count, with- or without-replacement sampling, seed, tail, tie rule, and the precise p-value correction.

Report simulation uncertainty

Give a reproducibility interval or another declared precision check suitable for the estimator. More printed decimals do not create more information.

Keep exact and estimated labels separate

Use exact only for full enumeration under the stated assignment scheme. Call a sampled result Monte Carlo or estimated.

Archive a reproducible run

Preserve inputs, code, package and language versions, seed, session information, assignment count, output, and an independently checked small example.

Build Juno's enumeration and simulation log

Start with a versioned record for Juno's complete and sampled reference distributions. For the exact versus Monte Carlo single-case randomization 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 Juno'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 Juno

Juno's small example has 60 permissible schedules. Exact enumeration finds four statistics at least as extreme as observed, so p=4/60, or 0.0667. A separate demonstration samples 999 schedules and finds 65 as extreme; under the predeclared add-one calculation, (65+1)/(999+1)=0.066. The close values are illustrative and do not make the sampled result exact. 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 Juno's middle school participation study.

Audit Juno's randomization evidence

Juno's log records R=60 for enumeration, the full statistic table, Monte Carlo draws=999, seed, sampling-with-replacement rule, b=65, add-one formula, package version, machine environment, and rerun output. Exact and sampled results occupy separate fields. 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 Juno's review

A software default may sample assignments silently or change the result across runs when the seed is absent. Juno's release check confirms whether enumeration or simulation occurred and reproduces the simulation from the recorded seed. 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 Juno

When the Monte Carlo estimate is near a decision threshold, the analyst increases draws under a predeclared precision rule or performs exact enumeration if feasible. The report emphasizes the estimate's simulation error and avoids binary clinical decisions based on a fragile last decimal. 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 Juno

Research design never outranks Juno'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 Juno

For Juno's exact-versus-Monte-Carlo randomization result, 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 Juno's analysis before outcomes exist

Before the middle-school participation study begins, Juno's team runs the enumeration and simulation log 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 exact-versus-Monte-Carlo randomization result 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 complete and sampled reference distributions; it never uses Juno's future outcomes or changes the predeclared analysis after data collection.

Close Juno's methods review

Review the enumeration and simulation log with Juno, 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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