Overview
Ethics committees, funders and journals increasingly expect a formal sample-size justification rather than a rule of thumb such as '30 per group' or '10 cases per variable'. A good justification names the analysis, the expected effect size and where it came from, the alpha level, the target power and any adjustments for clustering, attrition or multiple comparisons.
Choosing the effect size is the hard part. Values copied from Cohen's 'small, medium, large' benchmarks, or from a single small pilot study, often produce unrealistic targets. We help you base the effect size on meta-analyses, comparable studies or a smallest effect size of interest (SESOI), and show how the required sample changes if the assumption is wrong.
Sampling strategy is the other half. We help you choose between probability methods (simple random, stratified, cluster, systematic) and non-probability methods (purposive, quota, convenience, snowball), and to be honest about what each allows you to generalize to.
Who it’s for and the problems it solves
This is for you if you are…
- Students completing the sample-size section of a proposal or ethics application
- Researchers planning experiments, surveys, trials or multilevel studies
- Grant applicants who need a power calculation in the methods and budget
- Authors whose manuscript was criticized as 'underpowered'
- Qualitative researchers asked to justify the number of interviews
Common problems we help with
- You do not know which G*Power test family and options match your analysis
- Your calculation gives 1,200 participants and you can realistically recruit 150
- Your design has clustering, repeated measures or a mediation model that G*Power cannot handle well
- An ethics committee rejected 'convenience sample of 100' as a justification
- You need to explain why 15 interviews may be enough
What’s included — and what isn’t
Included
- A priori power analysis for t tests, ANOVA and ANCOVA, correlation, chi-square, logistic and multiple regression
- Effect size selection from prior literature or a smallest effect size of interest, with conversions between d, f, f², r, odds ratios and η²
- Sensitivity analysis: the smallest effect detectable with the sample you can realistically obtain
- Adjustments for attrition, non-response, clustering (design effect using ICC) and multiple comparisons
- Simulation-based power for mixed models, multilevel designs, mediation and SEM using R (for example simr, pwr and lavaan-based simulations) or Mplus Monte Carlo
- Precision-based sample sizes for surveys and prevalence estimates using margin of error and confidence level, with finite population correction
- Sampling strategy design: sampling frame, probability or non-probability method, stratification, quotas and recruitment channels
- Qualitative sample-size reasoning using saturation and information power concepts
- A written justification paragraph with a reproducible record (G*Power protocol output or R script)
Not included
- Post hoc ('observed') power calculated from your results to explain non-significance; we explain why it is not informative and suggest sensitivity analysis instead
- Choosing an effect size simply to reach a convenient number
- Recruiting participants or buying panel samples on your behalf
- Writing your proposal or methodology chapter for submission as your own work
What you receive
- Power analysis report
- The calculation for each primary hypothesis, with test, effect size and its source, alpha, power and resulting sample, plus the adjustments applied.
- Sensitivity table or curve
- How required sample size changes across plausible effect sizes, or the minimum detectable effect for your feasible sample.
- Reproducible record
- G*Power protocol output, an annotated R script or simulation code so a reviewer can verify the numbers.
- Sampling plan
- Sampling frame, method, strata or quotas, recruitment channels and expected response or attrition rates.
- Justification text notes
- Plain-language notes explaining each element so you can write the sample-size section of your proposal or ethics form yourself.
How it works
Design and analysis check
We confirm the design and primary analysis, because power is always calculated for a specific test.
Effect size evidence
We review prior studies or meta-analyses with you and agree a defensible effect size or SESOI.
Calculation or simulation
We run the calculation in G*Power or R, or build a simulation for complex models, and test sensitivity.
Sampling plan
We translate the target into a realistic recruitment plan, adjusting for response and attrition.
Tools and approaches
- G*Power
- Free software from Heinrich Heine University Düsseldorf for common tests. The current Windows release is 3.1.9.7 and the Mac release 3.1.9.6; a new version for Apple silicon has been announced, so we note your version in the record.
- R packages
- pwr for standard tests, simr for mixed models, WebPower for several designs and custom simulation code where no closed-form solution exists.
- Monte Carlo simulation
- Generating many datasets under assumed parameters to estimate power for SEM, mediation, multilevel and non-standard designs; Mplus Monte Carlo is an alternative.
- Precision-based planning
- For descriptive surveys, sample size from desired margin of error and confidence level, corrected for finite populations and design effects.
- Design effect
- For cluster samples, inflation of 1 + (m − 1) × ICC, where m is the average cluster size, to account for similarity within clusters.
- Qualitative sample reasoning
- Data saturation concepts and Malterud and colleagues' information power (aim, specificity, theory, dialogue quality, analysis strategy) to justify interview or focus group numbers.
Four numbers behind every power analysis
A standard calculation links four quantities: effect size, significance level (alpha, usually 0.05), power (commonly 0.80 or 0.90) and sample size. Fix any three and the fourth follows. Most disagreements with reviewers are about the effect size, so we document where it came from and why it is realistic for your population and measures.
- Effect size: from meta-analyses, similar studies or a smallest effect size of interest
- Alpha: adjusted if you test several primary hypotheses
- Power: the probability of detecting the effect if it exists
- Sample size: then inflated for expected attrition or non-response
When G*Power is not enough
G*Power handles many common tests well, but it does not model complex structures such as random slopes, nested data, indirect effects or latent variables. For these we use simulation: we specify plausible parameter values, generate thousands of datasets, fit your planned model to each and record how often the effect is detected. It takes longer but gives a justification that matches your actual analysis.
If you cannot reach the target
Sometimes the honest calculation produces a number you cannot recruit. Options include a within-subjects or repeated-measures design, a more reliable outcome measure, a covariate that explains outcome variance, a narrower focus on one primary hypothesis, collaboration across sites, or reframing the study as a pilot or feasibility study. A sensitivity analysis showing the smallest effect you can detect is often more convincing than an inflated effect size.
What the work can look like
Illustrative example — fictional data
Illustrative example: mindfulness app and nurse burnout, cluster design
A fictional research team planned to compare a mindfulness app with usual support across hospital wards, randomizing wards rather than individual nurses. Figures are invented.
Individual-level calculation
Based on a meta-analytic effect of d = 0.35 on burnout scores, a two-group comparison with alpha 0.05 and power 0.80 required 130 nurses per arm in G*Power.
Adjusting for clustering and attrition
With an average of 15 nurses per ward and an assumed ICC of 0.05, the design effect was 1.70, raising the target to 221 per arm. Allowing for 20% attrition gave 277 per arm, about 19 wards per arm, which led the team to add a second hospital.
Illustrative calculation with invented assumptions; real studies need effect sizes and ICCs justified from relevant evidence.
What you’ll need to provide
- Your design, hypotheses and planned analysis
- Relevant prior studies, meta-analyses or pilot data
- Realistic limits on recruitment: population size, access, time and budget
- Ethics or funder form requirements for the sample-size section
- For clustered designs, the number of available clusters (schools, clinics, firms)
You don’t need everything ready to ask for a quote — tell us what you have and we’ll say what’s missing.
What affects price and turnaround
Price depends on
- Number of primary hypotheses requiring calculations
- Formula-based calculation versus simulation for complex models
- Clustering, repeated measures or multiple comparisons
- Whether a full sampling and recruitment plan is included
- Effort needed to find and extract effect sizes from prior literature
Turnaround depends on
- Whether your design and primary analysis are settled
- Availability of prior effect sizes or pilot data
- Simulation run time for complex models
Every project is quoted individually. How we price our work.
Questions people ask before starting
Can you just tell me a number?
We can give you a number quickly for simple designs, but it is only as good as its assumptions. We always state the test, effect size, alpha and power so you can defend it in front of a committee.
What if there are no previous studies to base the effect size on?
We can use a smallest effect size of interest (the smallest effect that would matter in practice), effects from related outcomes or populations, or run a sensitivity analysis. Pilot studies are useful for feasibility but usually give unreliable effect size estimates.
My results were not significant. Should I report post hoc power?
Observed power calculated from your own results adds no information beyond the p-value. It is better to report confidence intervals and a sensitivity analysis showing what effect sizes the study could detect.
How many interviews do I need for qualitative research?
There is no power calculation for qualitative work. Sample size is justified by the study's aim, the specificity of participants, the depth of data and the analytic approach. We help you write a reasoned justification and plan to monitor saturation or information power during data collection.
Do I need G*Power installed?
No. We provide the protocol output or script. If your supervisor expects to see a G*Power screenshot, we can show you how to reproduce the calculation yourself.
Can this go straight into my ethics application?
The report gives you everything you need, and you write the justification in your own words on the form. We can review your wording for accuracy.