Services / Power analysis & sample size
Power analysis and sample size, with the justification written for you
Ethics committees and funders do not want a number. They want the reasoning behind it — the effect size you are powering for, where it came from, and what happens if recruitment falls short. That is what you get.
- A priori power calculation
- Written justification paragraph
- Effect size sourced and referenced
- Sensitivity and shortfall scenarios
A power analysis calculates the sample size a study needs to detect an effect of a given size, at a chosen significance level and statistical power. An a priori power analysis is run before data collection and produces the written justification ethics committees and funders require.
What is included
What you get with power analysis & sample size
A priori power analysis
Calculated for your actual design and test, not a generic rule of thumb about thirty per group.
The justification paragraph
Written to drop straight into your protocol or application, in the form committees expect to read.
Effect size, properly sourced
Taken from comparable published work or a pilot, and referenced — rather than assumed to be medium.
Sensitivity analysis
What your study can detect at the sample size you can realistically recruit, which is the question that matters.
Attrition and shortfall
Recruitment targets adjusted for expected dropout, with the consequences of under-recruiting stated.
Committee questions answered
If reviewers query the calculation, we help you respond as part of the price.
Who it is for
Two kinds of client, one standard of work
- An ethics application needing sample size justification
- A proposal or upgrade requiring power analysis
- Recruitment falling short of the original plan
- A reviewer who has challenged your numbers
- Trial and pilot study design
- Survey sample sizes with margin-of-error targets
- Grant applications requiring statistical justification
- Deciding whether a planned study is worth running
The method
What a power analysis actually calculates
Statistical power is the probability that your study will detect an effect, if an effect of that size genuinely exists. A study powered at 80% has a one-in-five chance of missing a real effect — which is the conventional standard, not a comfortable one.
Four quantities are locked together: the effect size you want to be able to detect, the significance level (usually .05), the power you want (usually .80 or .90), and the sample size. Fix any three and the fourth follows. A power analysis is simply solving for whichever one you do not yet know.
Recruiting past the flattening point costs money and participant burden for almost no gain in detection. Recruiting well short of it means running a study that probably cannot answer its own question. The calculation tells you where you are on that curve.
Effect size
The part committees actually query
Almost every rejected power calculation fails on the same point: where the effect size came from. Reviewers rarely dispute the arithmetic; they dispute an assumed effect size that appears to have been chosen because it produced a convenient sample size.
What gets queried
- “A medium effect size (d = 0.5) was assumed” with no source
- An effect size taken from a study with a different population or outcome
- A pilot estimate used as if it were precise
- No justification for the power level chosen
What passes
- An effect size referenced to comparable published work
- The smallest effect that would be clinically or practically meaningful
- A pilot estimate used cautiously, with its imprecision acknowledged
- A stated rationale for 80% versus 90% power
Where no comparable literature exists, the defensible route is to power for the smallest effect worth detecting — the point below which a difference would not change practice. That is a judgement about your field, which we work out with you rather than assume.
Matching the method
Different designs need different calculations
The calculation depends on the analysis you plan to run. A power analysis for a t-test does not transfer to a mixed model.
| Planned analysis | What drives the calculation |
|---|---|
| Independent samples t-test | Standardised difference between two means, allocation ratio |
| Paired t-test / within-subjects | Correlation between the paired measurements — often overlooked, and it reduces the required n substantially |
| ANOVA | Number of groups, the contrast of interest rather than the omnibus test |
| Multiple regression | Number of predictors and the increment in R² you need to detect |
| Logistic regression | Event rate, and events per predictor rather than participants per predictor |
| Multilevel / clustered designs | Intracluster correlation and cluster size — clustering can multiply the required sample several times over |
| Survival analysis | Number of events, not number of participants, and expected follow-up |
Clustered designs. Powering a school-based or ward-based study as if participants were independent can understate the required sample by a factor of two or more, and it is usually discovered after recruitment has finished.
The deliverable
What you receive, and what to do if it is not feasible
When the required sample is bigger than you can recruit
This happens often, and finding out now is the entire point. There are usually options: measure the outcome more precisely to reduce variance, use a within-subjects design where the research question allows, reduce the number of predictors, extend follow-up in a survival design, or reframe the study as a feasibility study with explicitly descriptive aims.
What is not an option is running an underpowered study and hoping. A null result from an underpowered design tells you nothing — the effect might be absent, or it might simply have been undetectable. We will say so plainly if that is where the numbers land.
Practicalities
Turnaround, cost and committee questions
Most applications that come back with statistical queries are asking one of three things: where the effect size came from, why that power level was chosen, or how attrition was accounted for. All three are answered in the deliverable before the application goes in.
How it works
Three steps, entirely in writing
Send what you have
Attach the data, or just describe the project. No account, no mandatory call, and a five-field form rather than a fifteen-field one.
Approve a fixed quote
Usually within one working day, naming the statistician assigned, the deliverables and the deadline.
Receive the work
Output, syntax and a plain-English explanation — with follow-up questions answered at no extra cost.
Client feedback
What clients say about this work
“The sample size calculation was clearly explained and fully justified for my research proposal.”
“Great support with power analysis. My ethics application was approved without any questions about methodology.”
Proof
This work, on real projects
Clients are not named and no identifying detail is published, so what is described is the statistical problem — which is the part that shows whether a consultancy knows what it is doing.
Cox Proportional Hazards Modelling to Identify Patients Most at Risk of Readmission
Modelling time-to-event rather than event-or-not, so a large public sector organisation could target risk assessment where it mattered.
Life sciences · Linear mixed effects modelsLinear Mixed Effects Models for an Intervention Measured Over Six Occasions
Recovering a defensible effect estimate from repeated measures with missing follow-up, where repeated measures ANOVA could not be used.
Research · Meta-analysisRandom Effects Meta-analysis of Forty-Five Published Studies
Combining heterogeneous evidence into a defensible overall estimate, with publication bias investigated rather than assumed away.
Your statistician
Who does this work
Member of the Royal Statistical Society · International Society for Clinical Biostatistics
Clinical trials, epidemiology and evidence synthesis, with a focus on longitudinal and multicentre studies.
This page was reviewed for statistical accuracy by Sidra Khan on 14 August 2026.
Common questions
Answers before you ask
What do you need from me?
Your design, the outcome measure, the comparison you plan to test, and any pilot or published data you are basing expectations on. If you are unsure, send the protocol and we will work it out.
What if the required sample is bigger than I can recruit?
Then you need to know now rather than after data collection. We will show what is detectable at a feasible sample size, and where the design could be changed to improve power.
Which software do you use?
G*Power, R and Stata depending on the design. The output is included so your committee can see the calculation, not just the conclusion.
Can you help after data collection?
We can calculate achieved power, though post-hoc power is of limited value and often criticised by reviewers. We will tell you honestly whether it will help your case.
How quickly can you turn this round?
Usually two to three working days. Tell us the deadline and we will confirm before you commit.
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