How many participants do I need is the right question asked too late
Sample size is a design decision, and by the time data collection is finished it has already been made for you. Asked early it is answerable in an afternoon. Asked late it becomes a question about what your data can still support, which is a different and harder conversation.
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Power is the chance of finding an effect that is really there
If your study has 40% power and the effect you are looking for genuinely exists, you have a 60% chance of missing it. The convention is 80%, which already means accepting a one in five chance of a false negative. That is a considered trade-off rather than a law, and stating why you chose your threshold is part of a good methodology chapter.
Four things are connected: sample size, effect size, alpha, and power. Fix any three and the fourth follows. That is the whole of a power analysis, and it is why the hard part is not the arithmetic but deciding what effect size is worth detecting in your field.
The honest answer to where the effect size comes from is prior literature, a pilot study, or a judgment about the smallest effect that would matter practically. Using a conventional medium effect because it produces a convenient number is common and is exactly what a sharp examiner will ask about.
- A power analysis you can justify, not a number from a web calculator
- Effect size grounded in your literature or your pilot
- The analysis documented for your ethics application
- Honest options when recruitment does not reach target
What we work through
Before collection where possible, after it where necessary
- A priori power analysis in G*Power or R, with the parameters recorded
- Choosing an effect size you can defend in a viva
- Adjusting for expected attrition and unusable responses
- Sensitivity analysis when the sample is already fixed
- Writing the justification paragraph your committee expects
What can honestly be done, in order
There are real options here. Quietly proceeding as though nothing happened is not one of them.
Run a sensitivity analysis
Given the sample you actually have, what is the smallest effect you could have detected at 80% power? This is a legitimate and well-accepted move, and it reframes the question from what you failed to reach to what your study was able to see.
Report the shortfall plainly
In the limitations, with the numbers. Committees are far more forgiving of an acknowledged limitation than of one they discover themselves, and discovering it themselves is what happens when it is omitted.
Reconsider the analysis, not the data
Sometimes a simpler model, fewer predictors or a different test is a better fit for the sample you have. Changing the analysis to suit the data is fine. Changing the data is not.
Interpret with effect sizes and intervals
A wide confidence interval says something true and useful about what your study can conclude. Leaning on it is more defensible than leaning on a p value from an underpowered test.
Frame it as a pilot, if that is honest
Where the sample genuinely cannot support the original claims, repositioning the work as exploratory can be the right call. It has to be a real reframe of the aims, not a label added at the end.
We help you justify a sample, never disguise one
- We do not tell you a sample is adequate when it is not.
- We do not fabricate participants or supply data.
- We do not compute a post hoc power figure from your observed effect and present it as meaningful.
- We do not write your methodology or limitations section.
- We teach the analysis, run it with you, and help you write a justification that is true.
On post hoc power: calculating power from your own observed effect size after the fact is circular and adds nothing, though it is still widely requested. If a supervisor asks for it we will explain the problem and help you give them something more useful, usually a sensitivity analysis. Read the full policy.
Frequently Asked Questions
It depends on the effect size you want to detect, your alpha, your target power and the test you plan to run. For a between-groups comparison looking for a medium effect at 80% power, the number is often around 60 to 70 per group, but quoting that as a general answer would be misleading. The calculation takes minutes once the inputs are decided, and deciding the inputs is the actual work.
Ideally one taken from comparable studies in your own literature, or from a pilot. Where neither exists, the better question is what is the smallest effect that would be practically meaningful in your field, because detecting a trivial effect at great expense is not a good study design.
It depends entirely on the design and the effect. Thirty can be plenty for a within-subjects design detecting a large effect and badly insufficient for a between-groups comparison looking for a small one. The number alone carries no information, which is why the justification matters more than the figure.
Free software for power analysis, widely accepted and commonly named in methodology chapters. Record the test family, the effect size and its source, alpha, power and the resulting N, because that list is what your committee will want to see.
Usually a short paragraph stating the planned test, the effect size and where it came from, alpha, target power, the resulting minimum N, and your recruitment target including expected attrition. Boards are looking for evidence that the number was reasoned rather than chosen.
For a simple design, often yes. The risk is that most calculators assume a specific test and do not say which, so it is easy to get a number that does not correspond to the analysis you will actually run. Check the assumptions or use G*Power, where they are explicit.
Tell us the design and where recruitment stands
If you have not collected yet we will help you set a defensible target. If you have, we will tell you honestly what the data can support.
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