A single-case randomization test compares an observed statistic with the statistic under every permissible assignment, or a declared random sample of those assignments. The treatment or phase schedule must have been selected prospectively by the matching randomization scheme. Define the assignment set, statistic, direction, ties, and analysis before the draw. Report the p value with visual analysis, effect magnitude, design replications, and inference limits.

Confirm the randomized design prerequisite

Find the prospective protocol and assignment record. Verify that chance selected the actual treatment schedule or phase-change moment from a predetermined set. A retrospective label shuffle answers a different question.

Reconstruct the complete assignment set

List every arrangement that had a nonzero chance under the actual scheme. Preserve clinical constraints, blocked choices, unequal probabilities, and the reason each arrangement was allowed.

Lock the statistic and tail

Name the formula, improvement direction, one- or two-sided rule, and treatment of equal statistics before calculation. The statistic should match the expected effect pattern.

Build the randomization distribution

Apply the same statistic to the observed schedule and every permissible schedule. Keep assignment IDs and statistics so another analyst can reproduce the tail count.

Interpret within the design

State what the randomization supports about this experiment, what the p value omits, and which conclusions still depend on visual, clinical, and replication evidence.

Build Cali's randomization analysis packet

Start Cali's analysis packet with a versioned record for the prospectively randomized phase-start design. For the 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 Cali'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 Cali

Cali's plan permits an intervention phase to begin after observation 4, 5, 6, 7, or 8. One of those five schedules is selected at random before data collection. The predeclared statistic is mean intervention level minus mean baseline level. After the study, the observed schedule has the second-largest statistic: two of five permissible schedules are at least as large, so the one-sided exact p value is 2/5, or 0.40. 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 Cali's community vocational program.

Audit Cali's randomization evidence

Cali's packet preserves the five candidate schedules, equal 1/5 selection probabilities, the random draw, time-stamped protocol, raw sequence, calculation for each schedule, inclusive tail rule, and the two schedules counted in the numerator. The test is reproducible without inventing alternate schedules after outcomes are known. 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 Cali's review

A routine AB record with a clinician-selected phase change cannot gain a valid randomization test merely because software can shuffle its labels. Cali's release gate requires evidence that the actual schedule came from the same prospectively defined set used for the reference distribution. 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 Cali

The research team reports p=0.40 as the resolution of this design and dataset. It also reviews the graph, original-unit change, phase stability, client experience, feasibility, and later replications. The p value is neither a magnitude estimate nor a population-generalization claim. 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 Cali

Research design never outranks Cali'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 Cali

For Cali's single-case randomization test, 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 Cali's analysis before outcomes exist

Before the community vocational program begins, Cali's team runs the randomization analysis packet 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 single-case randomization test 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 prospectively randomized phase-start analysis; it never uses Cali's future outcomes or changes the predeclared analysis after data collection.

Close Cali's methods review

Review the randomization analysis packet with Cali, 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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