Achieved power for a stepped-wedge trial (means)

When to use it

Assess a rollout in which every cluster starts on control and crosses to the intervention at a randomised time.

Not for

A cohort followed through every period needs a model of repeated measurements on each participant.

Notation

$C$: Clusters, a multiple of the number of steps.
$S$: Steps; there are S + 1 periods.
$m$: Measurements per cluster in each period.
$\rho$: Intracluster correlation.
$\sigma^2$: Total variance of one measurement.
$\Delta$: Difference in means between intervention and control.

Formulas

GLS variance of the treatment effect

\operatorname{Var}(\hat\theta)=\left[(X^\top V^{-1}X)^{-1}\right]_{\theta\theta}, \qquad V=\rho\sigma^2 J+\frac{(1-\rho)\sigma^2}{m}I

Each period has its own term, so the secular trend is adjusted for rather than assumed away [1, 2].

Normal power

\text{Power}=\Phi\!\left(\frac{|\Delta|}{\sqrt{\operatorname{Var}(\hat\theta)}}-z_{1-\alpha/\text{tails}}\right)

With few clusters this can overstate power; the planned small-sample analysis should inform the design.

Parameters

Number of clusters $C$

Values: A multiple of the steps

Clusters split equally across the steps, one group switching at each.

Steps $S$

Values: Integer, at least 1

Times at which a group of clusters crosses to the intervention.

Measurements per cluster per period $m$

Values: Positive

A fresh sample in each period (cross-sectional design).

Intracluster correlation $\rho$

Values: Between 0 and 1

From earlier cluster data on the same outcome.

Mean difference $\Delta$

Values: Any non-zero value

Expected difference between intervention and control.

Standard deviation $\sigma$

Values: Positive

Total SD of one measurement.

Significance level $\alpha$

Values: Between 0 and 1

The type I error rate for the specified test.

Test direction $s$

Values: 1 or 2

One-sided tests use the upper rejection tail. Two-sided tests split α equally between both tails.

Assumptions

A fresh sample in every period, equal cluster-period sizes, and a constant intracluster correlation over time.
One-sided tests use the upper rejection tail. Two-sided tests split α equally between both tails.

Worked examples

A worked input set

With 12 clusters over 4 steps (5 periods), 20 measurements per cluster-period, ρ = 0.05, a difference of 0.25, and σ = 1 at α = 0.05.

Sample size: 12

Open this example in the calculator

Validation

At the size the stepped-wedge calculator returns, this power reaches that calculator’s target, and one fewer falls short; it is checked against an independent calculation in R.

How to cite

StatWisely. Achieved power for a stepped-wedge trial (means). Method document, engine version 1.0.0, reviewed 2026-10-03. https://statwisely.com/methods/power-stepped-wedge-means/

Cite the original references for the formulas your design uses as well.

References

1.Hussey MA, Hughes JP. Design and analysis of stepped wedge cluster randomized trials. Contemporary Clinical Trials. 2007;28(2):182–191.
2.Hemming K, Haines TP, Chilton PJ, Girling AJ, Lilford RJ. The stepped wedge cluster randomised trial: rationale, design, analysis, and reporting. BMJ. 2015;350:h391.