Power analysis is the calculation that tells you how many participants a study needs to have a good chance of detecting an effect that is really there. G*Power is the most widely used free software for running it. Before collecting data, you specify the size of effect you care about, the significance level, and the statistical power you want, and the calculation returns the required sample size. Done in advance, it protects a study from being too small to find anything or wastefully larger than necessary.
The logic rests on four quantities that are mathematically linked: the effect size, the alpha level or significance threshold, statistical power, and the sample size. Fix any three and the fourth is determined. A study planned this way states its assumptions openly, which is exactly what funders, ethics committees, and reviewers now expect.
Why an a priori power analysis matters
Running the calculation a priori, before data collection, is the only version that genuinely informs design. An underpowered study, one with too few participants, is likely to miss a real effect and produce a false negative, while also making any significant result it does find less trustworthy. An oversized study wastes resources and, in clinical contexts, exposes more participants than necessary. A correct sample size sits between those failures.
The calculation is also a transparency device. By forcing you to state the smallest effect worth detecting, your significance level, and your target power, it makes the study's assumptions explicit and checkable. That is why an a priori power analysis has become a standard expectation in grant applications and ethics submissions, and why our biostatistics consulting service builds one into study design routinely.
The four ingredients
Effect size is the magnitude of the relationship or difference you want to be able to detect. It is the hardest input to choose and the one reviewers scrutinize most, because the required sample is extremely sensitive to it. Base it on a meaningful difference in your field, a pilot study, or prior literature, not on a number reverse-engineered to make the sample feel achievable.
Alpha, the significance level, is the tolerated rate of false positives, conventionally 0.05. Power is the probability of detecting the effect if it exists, conventionally set at 0.80, with 0.90 increasingly preferred. Sample size is usually the unknown you solve for. The test you plan to run, whether a comparison of means, a correlation, a regression, or an analysis of variance, determines which formula applies, so the analysis is specific to your design.