How to Calculate and Justify Your Sample Size (With Worked Examples)

"How did you arrive at this sample size?" is one of the most reliable questions at any proposal defence in Uganda, and "I used a formula" is not an answer. Reviewers want to see the formula, the assumptions you fed into it, where those assumptions came from, and what you did about non-response. This guide covers the three most common situations and shows you how to write the justification paragraph that survives scrutiny.

Surveys and prevalence studies: the Cochran approach

If your study estimates a proportion in a population, for example the proportion of women using a modern contraceptive method in a district, the standard starting point is Cochran's formula. It needs three inputs: your desired confidence level (usually 95%), your margin of error (usually 5%), and an expected proportion. The expected proportion is where students get caught. Do not default to 50% without thinking; 50% gives the maximum sample size and is the right choice only when no prior estimate exists. If a previous study, a DHS report, or routine programme data gives you an estimate, use it and cite it. That citation is the difference between a defensible assumption and a guess.

After the base calculation, adjust honestly. If your population is small and finite, apply the finite population correction. If you are using cluster sampling rather than simple random sampling, multiply by a design effect, commonly around 1.5 to 2 for community-based cluster surveys, and justify the value you choose. Finally, inflate for expected non-response, typically 10%, and say so explicitly.

Comparing two groups: power calculations

If your study compares an outcome between two groups, for example intervention versus control, you need a power calculation rather than a prevalence formula. The inputs are your significance level (usually 5%), your desired power (usually 80% or 90%), and the effect size you want to be able to detect. The effect size is the assumption that matters most and the one reviewers probe hardest. It should come from previous studies of similar interventions or from the smallest difference that would be clinically or programmatically meaningful, and you should state which logic you used. A study powered to detect an implausibly large effect is underpowered for the effect you will actually observe, and reviewers know it.

Qualitative studies: saturation, not formulas

Qualitative sample sizes are not calculated; they are justified. The standard concept is saturation, the point at which additional interviews stop producing new themes. In practice, proposals state a planned range, commonly 12 to 20 in-depth interviews per participant group or 4 to 8 focus group discussions, justified by reference to the study design, the homogeneity of the group, and methodological literature on saturation. The honest formulation is a planned number with a commitment to continue until saturation is reached, and a brief note on how you will recognise it, for example through ongoing analysis alongside data collection. What reviewers penalise is a bare number with no reasoning attached.

Writing the justification paragraph

A complete sample size paragraph in a proposal does five things in order: names the formula or approach, states each assumption with its source, shows the calculation, states the adjustments (design effect, finite population correction, non-response), and gives the final number. Two or three sentences of prose around the working is enough. If a reviewer can reproduce your number from your paragraph alone, you have written it correctly.

Our free Sample Size Calculator does exactly this: it handles Cochran's formula, two-group power calculations, and qualitative saturation planning, and it shows every step of the working so you can adapt it straight into your proposal.

Frequently asked questions

What if my calculated sample size is bigger than my budget allows? Do not quietly collect fewer participants and report the original calculation. Either revise the design honestly (wider margin of error, different outcome, different design) and recalculate, or scope the study to match the resources. Reviewers respect a transparent constraint far more than a mismatch they discover later.

Is 384 always the right answer? 384 is what Cochran's formula gives with 95% confidence, 5% margin of error, and a 50% proportion in a large population. It is correct only when those exact assumptions are correct for your study. Treat it as a special case, not a default.

Do I need a statistician? For standard designs, a carefully justified calculation of your own is fine. For cluster randomised trials, repeated measures, equivalence designs, or anything with multiple primary outcomes, involving a statistician early is money and time well spent.

If you would like someone to check your calculation and the assumptions behind it before your defence or submission, our methods support service does exactly that.