How to decide your sample size
Few methodological decisions generate as much anxiety — or as many reviewer questions — as the number of participants. The most common mistake is to pick a round number ("I'll interview 100 people") and then hunt for a formula that justifies it. The correct path runs the other way: you define the parameters of the study and the mathematics returns the number.
First, identify the type of question
There are two completely different logics of sample size, and confusing them is the root of nearly every error:
- Estimating a parameter (survey). You want to know what proportion of a population thinks or does something. "What percentage of undergraduates exercise regularly?" Here what matters is precision: how narrow you want the confidence interval around your estimate.
- Testing a hypothesis (comparison). You want to know whether two groups differ, or whether two variables are associated. "Does the training improve performance?" Here what matters is power: the probability of detecting an effect that genuinely exists.
The four parameters you have to decide
Confidence level (1 − α). The academic convention is 95%, corresponding to α = .05. It means accepting a 5% risk of concluding an effect exists when it does not (Type I error). Raising it to 99% increases the required sample by roughly 75%.
Margin of error (e). Specific to surveys. If you find 60% approval with a 5% margin, the population value lies between 55% and 65%. Five per cent is the defensible standard; below that the sample grows quadratically — halving the error quadruples the sample.
Statistical power (1 − β). Specific to hypothesis testing. Cohen proposed 80% as the acceptable floor: if the effect exists, you have an 80% chance of finding it and a 20% risk of wrongly concluding there is no effect (Type II error). Studies with power below 80% are commonly criticised as underpowered — a null result in such a study does not license the conclusion that no effect exists.
Expected effect size. The hardest and most important parameter. It is not calculated, it is estimated, from (a) comparable prior studies, (b) a pilot study, or (c) failing both, Cohen's conventions — d = 0.2 small, 0.5 medium, 0.8 large. The smaller the effect you want to detect, the larger the sample required, and the relationship is unforgiving: detecting a small effect (d = 0.2) takes about 394 participants per group, against just 64 for a medium effect.
The finite population correction
This is the detail most tutorials skip. If your population is small and known — the 340 students on a course, the 80 employees at a company — you do not need the sample computed for an infinite population. The correction reduces the number substantially:
n = n₀ ÷ [1 + (n₀ − 1) ÷ N]
Where n₀ is the sample for an infinite population and N the actual population. For N = 1,000 at a 5% margin, the sample drops from 384 to 278 participants. For N = 100, it drops to just 80. Using the correction where it applies is a sign of rigour, not of cutting corners.
Don't forget the attrition rate
The number you compute is the count of valid cases at the end of analysis, not the number of invitations sent. Online questionnaires typically see response rates between 10% and 30%. Longitudinal studies lose participants to follow-up. The recommended practice is to inflate the planned sample:
n_recruit = n_calculated ÷ (1 − expected attrition rate)
With 20% expected attrition and a calculated n of 128, plan to recruit 160 participants.
Frequently asked questions
My sample came out smaller than calculated. Is my study ruined?
No, but it demands methodological honesty. Use this calculator's "observed power" mode, report the power you achieved, and address the limitation explicitly in your limitations section. A sentence such as "the observed power of 62% indicates that small-magnitude effects may have gone undetected" is received far better than omitting the problem.
Can I use a convenience sample?
Yes, and it is the most common approach in student research. But note: sample size calculation presupposes probability sampling. With a convenience sample, the computed number serves as a statistical power reference, and you must declare the sampling technique as non-probabilistic, acknowledging the limits on generalisability.
Does qualitative research need a sample size calculation?
No. In qualitative research the criterion is theoretical saturation — you collect until new interviews stop producing new categories. Typically between 12 and 30 participants, depending on how homogeneous the group is. Statistical sample size calculation does not apply, and using it inappropriately signals a paradigm confusion.
How do I cite the calculation method?
Cite the source of the formula, not the tool. For surveys: Cochran, W. G. (1977). Sampling Techniques (3rd ed.). Wiley. For hypothesis tests: Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Erlbaum. The justification generated above is already written in the expected style — adapt it and check with your advisor.
Next steps
Once the sample is defined and collection is complete, the next step is to check your assumptions and run the appropriate test. Use the normality test to decide between a parametric and a non-parametric approach, then the statistics calculator, which returns the result with the APA paragraph already drafted.