Sample Size Calculation you can justify

Sample size sits at the heart of a credible study. Recruit too few participants and a real effect can be missed — an under-powered study that wastes the effort of everyone involved. Recruit too many and you expose more people than necessary to the burden of research, which is itself an ethical concern. The right number is neither a guess nor a round figure; it flows logically from your study design, the effect you expect to detect, and the error you are willing to accept — and it must be stated with a justification a reviewer can check.

We calculate a sample size tailored to your exact design and, just as importantly, write the paragraph that explains it: the formula, the inputs, the assumptions, and the references. That justification is what turns a number into something an ethics committee and a journal will accept.

The ingredients of a sample-size calculation

Whatever the design, a sample-size calculation rests on a small set of decisions, and getting each one right is where our input matters:

• The primary outcome — the single result the study is powered to detect, and whether it is a proportion, a mean, a correlation, or a time-to-event
• The expected effect size — the difference, ratio, or correlation you anticipate, justified from pilot data or the published literature
• Significance level (α) — conventionally 0.05, setting the false-positive rate
• Power (1−β) — conventionally 80% or 90%, the chance of detecting the effect if it exists
• Variability — the standard deviation or event rate, again drawn from the literature or a pilot
• Adjustments — a finite-population correction for small defined populations, an allocation ratio for unequal groups, a design effect for cluster sampling, and an uplift for expected non-response or drop-out

Designs we calculate for

• Prevalence / single-proportion studies using Cochran’s formula, with finite-population correction
• Comparison of two means or two proportions for cross-sectional and experimental designs
• Case-control studies, from an expected odds ratio and control-exposure rate, with a controls-per-case ratio
• Cohort and relative-risk designs
• Correlation studies using Fisher’s z transformation
• Diagnostic accuracy / ROC studies powered on sensitivity or specificity
• Survival / time-to-event designs powered on the number of events
• Randomised trials, including adjustments for clustering and non-adherence

Why a bare number is not enough

A figure with no explanation is the fastest way to a reviewer query. Ethics committees want to see that the number was derived, not chosen — which formula was used, where the expected effect and variability came from, and how adjustments were applied. We provide a complete, referenced justification paragraph so your protocol reads as the work of someone who understands the design, and so you can answer any follow-up question with confidence.

Powering the study you can actually run

A calculation is only useful if the resulting sample is achievable. Where the ideal number is out of reach, we help you think through the trade-offs honestly — a larger minimum detectable effect, a longer recruitment window, a multi-centre design, or a clearly stated limitation — rather than quietly powering the study on an implausibly large effect. This realism is what keeps your conclusions defensible when the data are in.

What you receive

A calculated sample size for your primary outcome, with finite-population and non-response adjustments where relevant; a written, referenced justification ready for your synopsis or ethics submission; and a short explanation of the assumptions so you can defend the figure in review or in your viva. If your design changes, we update the calculation accordingly.