How many do you need — and how do you assign them?

Describe the comparison you are planning and set the test, the effect size, alpha and power. Your browser computes the sample size, the power curve, the smallest effect you could detect and the enrolment after dropout and clustering — free, before you sign in — and generates the seeded randomisation schedule. Then the model either drafts the paragraph that justifies the sample size in your protocol, or lays out the design and randomisation section, from those numbers alone.

Each example ships with a saved model run, so you can see a whole justification and a whole layout — including the reconciliation — without signing in and without spending a credit.

For study planning and education. The text is an AI-drafted starting point, not a substitute for a statistician, a trial methodologist or ethics committee (IRB/REC) review — have the numbers and the wording checked before they go into a protocol, a grant or a registration.

The study — what is compared, on what unit, with what primary outcome; the nuisance factors you know about nothing written yet

Planned test

Solve for

Effect size Cohen's d

Where the effect size comes from

Its source, in a sentence — optional

Alpha

Sides

Target power

Allocation ratio group 2 : group 1

Adjustments — multiple tests, dropout, clustering

Tests sharing alpha Bonferroni

Expected dropout fraction, 0–0.95

ICC if observations are clustered

Cluster size observations per cluster

Your draft, to check — optional: the sample-size or design paragraph you already wrote nothing pasted yet

The numbers — free, in your browser, no model

Sensitivity to the effect size

× effect	effect	n per group	enrol

Power against n

Free — no account, no run. Closed-form power; two-sided counts both tails.

Describe the study to price the run.

lane

n per group

enrol

power

figures checked

disagreements

The statement for the protocol

The basis for the effect size

Adjustments

Adjustment	Status	Note

Reading the sensitivity table

Pitfalls, each judged

Pitfall	Applies	Note

The design

Unit and replication

Nuisance factors

Factor	Handling	How

The schedule, read

Design and randomisation section for the protocol

Controls and blinding

Reconciliation with the engine

Every number the model wrote was re-read against the figures the browser computed. A disagreement here means the prose, not the arithmetic, is wrong.

Notes on the input

Risks

Next steps

Summary

Raw model reply

The reply did not parse as the structured result, so it is shown as it arrived.

What this does, and what it does not

The numbers are computed, not looked up. Power for the t tests uses the noncentral t distribution (AS 243), the ANOVA and regression tests the noncentral F, the chi-square test the noncentral chi-square, the proportions the arcsine transformation, and the correlation the Fisher z with the small-sample term — the same conventions as statsmodels and R's pwr. The build compared every distribution function and every test against R 4.4 on 1,277 checks (worst disagreement 9 × 10^-10), and confirmed that three things that should differ do: the z shortcut against the exact t, the arcsine against the pooled-variance formula for two proportions, and one rejection tail against two. Sample sizes are the smallest integers that reach the target; two-sided power counts both tails.

The schedules are seeded, so the same inputs and seed reproduce the same allocation on any machine — archive the seed with the protocol. Permuted blocks draw their sizes at random from the multiples you allow so the last cell of a block cannot be guessed. Every figure the model then writes is re-read against this engine, and the page shows you where the two disagree. It does not choose your effect size for you, it does not run your analysis, and it will not compute post-hoc power. It is a planning and teaching aid: for a clinical trial or any regulated study, a qualified statistician and the ethics review must sign off the sample size and the randomisation, not this page. Derived from the agent skills @k-dense-ai/statistical-power and @k-dense-ai/experimental-design (k-dense-ai/scientific-agent-skills, MIT, licence text); not affiliated with K-Dense.

Nothing to hand? Load the — d = 0.5 as a minimal important difference, 20% dropout — or the , where 480 cells are not 480 replicates, or the with stratified permuted blocks. All three replay a saved run for free.