How many participants does my dissertation need?
Committees rarely accept a round number. Set your design, the effect you actually care about, your confidence and your power — and get a figure you can defend, along with the reasoning to put in your methods chapter.
Don’t have d? Enter a raw difference and SD instead:
Free guide: choosing between qualitative, quantitative and mixed methods
Sampling logic differs completely across the three traditions — and picking the wrong one is a much more expensive mistake than getting a number slightly wrong. We’ll email you the guide.
Writing a sample size justification your committee will accept
The number itself is the easy part. What gets questioned at a proposal defence is the reasoning behind it — and a candidate who cannot say where their effect size came from is in trouble regardless of how large the sample is.
Four quantities are locked together: the effect you want to detect, your confidence level, your statistical power, and the sample size. Fix any three and the fourth follows. Fixing the first three before you look at your data is what makes the justification defensible; working backwards from the sample you happened to recruit is what makes it indefensible.
- Where the effect size comes from matters most. Cite a prior study, a pilot, or a minimum difference that would be clinically or practically meaningful in your field. “Cohen said 0.5 is medium” is the weakest of the defensible answers.
- Name your primary outcome. Power the study for one outcome — the one your main research question rests on. Secondary outcomes ride along underpowered, and you should say so.
- Inflate for attrition separately. This returns the analysable sample. Longitudinal doctoral studies routinely lose 20–30%.
- Show the arithmetic in an appendix. Stating the inputs, the assumed effect and the resulting n turns a contested number into a documented decision.
This covers the common two-sided designs and is a planning aid. Clustered, repeated-measures, survival and non-inferiority designs need a formal power analysis — take those to your statistician or your university's methods support, and budget time for it in your timeline.
Frequently asked questions
What exactly do I write in my proposal?
A sentence naming all four inputs and their source. For example: “Assuming a between-group difference of d = 0.5, consistent with Smith et al. (2021), a two-sided alpha of 0.05 and 80% power, 63 participants per group are required; allowing for 20% attrition, we will recruit 79 per group.” Reviewers are checking that every number has a stated origin. Note that published figures for this example sometimes read 64 rather than 63, because packages differ slightly in how they round the normal quantiles; either is fine so long as you state the software or formula you used.
My supervisor suggested 30 per group. Is that enough?
It depends entirely on the effect you need to detect. Thirty per group at 80% power and alpha 0.05 can only detect a standardised difference of roughly d = 0.72 — a large effect. If the effect in your field is nearer d = 0.4, that study is very likely to return a non-significant result you cannot interpret. Run the number and take the output back to the conversation.
The required number is far more than I can recruit. What are my options?
Four honest ones. Use a within-subject or paired design, which needs substantially fewer participants for the same power. Reduce measurement error so the same effect is easier to see. Reframe the study as explicitly exploratory or as a feasibility study with estimation rather than hypothesis-testing aims. Or widen recruitment. What you should not do is quietly assume a larger effect until the number becomes convenient.
Does this apply to qualitative studies?
No. Qualitative sample size is argued through saturation, information power, and the depth your analytic approach requires — not through power calculations. If your study is qualitative, justify your numbers against your chosen methodology instead, and plan your coding approach before you start recruiting.
Should the number I report include expected dropout?
Report both. This calculator returns the analysable sample you need at the end. Your recruitment target is that figure divided by the proportion you expect to retain — so for 20% attrition, divide by 0.8. Stating both numbers shows the committee you have thought about retention.
Is anything I enter stored or uploaded?
No. The whole calculation runs in your browser using JavaScript on this page. Nothing you type is transmitted, logged, or saved anywhere.