How to Write a Power Analysis for a Grant

3 min read

A grant's power analysis is one paragraph whose job is to let a reviewer rebuild your sample size from scratch: the analysis it's based on, the effect size and where that number came from, the error rates, the resulting N, and how you padded it for dropout. Most weak ones aren't wrong on the math. They just leave out the part a reviewer needs to believe it.

What the paragraph has to contain

The test the power is calculated for. Name it, and make sure it matches the analysis in your plan. Powering a simple two-group t-test and then proposing a mixed model with repeated measures and clustered sites is a mismatch reviewers catch.
The effect size, with a source. The number and a sentence on where it came from. This is the single line reviewers read most closely (more on it below).
Alpha and power. Usually a two-sided alpha of .05 and 80% or 90% power. If you're correcting for several primary outcomes, the alpha should reflect that.
The resulting sample size. Per group, not just in total, so the reader can check it.
The attrition adjustment. Say what dropout you expect, why, and what you'll recruit to end up with the analyzable N you need.
The software or formula. "Calculated in G*Power 3.1" or "using the simr package in R" is enough. It tells the reviewer the number is reproducible.

Where the effect size should come from

This is where most justifications fall apart. The strongest source is the smallest effect that would actually matter: the difference a clinician, school district, or funder would care about. If the intervention moves the outcome by less than that, you don't need to detect it. The next best source is prior research, ideally a meta-analysis or several comparable studies, discounted somewhat because published effects tend to run high.

Two sources to avoid leaning on. First, a pilot study's effect estimate: with 20 people per arm, it's so noisy it can easily be twice or half the real effect. Use the pilot for variability and feasibility, not for the effect you plan around. Second, "a medium effect (d = 0.5) per Cohen" with no further reasoning. Cohen offered those labels as a last resort, and reviewers know it.

The choice matters more than it looks. For an illustrative two-group comparison at 80% power, detecting d = 0.5 takes about 64 people per group. Detecting d = 0.3 takes about 176. Pick the bigger effect without a reason and you've quietly proposed a study a third the size it needs to be.

Mistakes that draw reviewer comments

Working backward from the budget. Deciding you can afford 80 people and then finding the effect size that makes 80 look adequate. Reviewers can often tell, because the effect size has no independent justification.
Ignoring the design. Clustered, multi-site, or repeated-measures designs need power calculations that account for that structure. A calculation that treats everyone as independent overstates what the study can detect.
Powering one outcome, claiming five. If several outcomes are primary, each needs to be adequately powered, with the multiplicity handled.
No attrition plan. Needing 128 completers and recruiting 128 means you'll finish short. At 20% expected dropout you'd recruit 160.

When your sample size is fixed

Sometimes N is set by something outside your control: a single cohort, a registry, every clinic in a county. Then don't pretend you chose it. Say so plainly and report a sensitivity analysis instead: the smallest effect your fixed sample can detect with 80% power. Reviewers respect "we have 240 records; that gives 80% power to detect d = 0.36, which is smaller than the effects reported in comparable programs" far more than a calculation reverse-engineered to land on 240.

If you're drafting the sample-size section of a proposal and aren't sure your effect size will survive review, that's the kind of grant methods work we do with researchers every week.