To calculate an exact single-case randomization p value, compute the predeclared test statistic for the observed assignment and every assignment allowed by the actual randomization scheme. Count assignments whose statistics are at least as extreme as the observed value under the declared tail, including the observed assignment and ties under the standard inclusive rule. Divide that count by the total permissible assignments and report the discrete denominator.

Verify exact enumeration is possible

Confirm that the full permissible set is known and computationally manageable. Exact means every arrangement under the actual design is evaluated.

Calculate one statistic per assignment

Use identical data, formula, direction, missing-data rule, and precision for the observed and reassigned schedules. Preserve the complete table.

Apply the declared tail comparison

For a one-sided improvement test, count statistics at least as large as observed. A two-sided definition requires its own predeclared extremeness rule.

Keep the fraction and resolution

Report numerator, denominator, decimal, and smallest attainable positive p value. These details show how much information the assignment set can supply.

Separate p value from effect size

The tail proportion addresses compatibility with the randomized assignment under the null. It does not state the size, value, persistence, or generalizability of change.

Build Elin's exact tail-count worksheet

Start Elin's worksheet with a versioned record of the complete randomization distribution. For the calculate exact single-case randomization p value 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 Elin'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 Elin

Elin's design has 12 permissible schedules. The observed statistic is 4.5 in the improvement direction. Three schedules, including the observed one, produce statistics of 4.5 or greater. The exact one-sided p value is 3/12, or 0.25. The next smaller attainable positive value would be 2/12, or about 0.167. 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 Elin's inclusive classroom study.

Audit Elin's randomization evidence

Elin's worksheet lists assignment IDs 1 through 12, the same statistic formula for each, all 12 results, the observed assignment, declared greater-than-or-equal tail, three highlighted tail schedules, numerator 3, denominator 12, and unrounded fraction. A reviewer can reproduce 0.25 directly. 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 Elin's review

Excluding the observed schedule from the denominator or counting only statistics strictly greater than 4.5 can make the p value artificially small. Elin's formula uses the complete randomized set and the predeclared inclusive comparison. 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 Elin

The report gives the exact fraction beside the decimal and explains that the assignment count limits resolution. Elin's raw graph and original-unit outcome remain visible, along with the design's replications, any deviations, and the difference between evidence against the sharp null and effect magnitude. 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 Elin

Research design never outranks Elin'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 Elin

For Elin's exact randomization p value, 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 Elin's analysis before outcomes exist

Before the inclusive classroom study begins, Elin's team runs the exact tail-count worksheet 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 randomization p value 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 a complete randomization distribution; it never uses Elin's future outcomes or changes the predeclared analysis after data collection.

Calculate Exact Single-Case Randomization p Value Review

Review the exact tail-count worksheet with Elin, 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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