Definition
Statistical power is the probability that a test detects an effect that really exists (1 − β). It depends on effect size, significance level, data variability and sample size. Power analysis is done before data collection: it tells you how many observations you need so the study is neither too small nor needlessly expensive.
Foundations & hypothesis testing
A study with low power (below 50 %) has a better-than-even chance of missing a real effect, and its non-significant result proves nothing. The standard is 80 % power, 90 % in regulated fields. The calculation needs an effect-size estimate — from pilot data, the literature or the smallest difference that would matter in practice.
Power can be raised with a larger sample, more precise measurement, a paired design or a one-sided test when justified. Post-hoc power computed from data already collected has no evidential value — plan ahead.
In Statistica
The Power Analysis module in Statistica computes the required sample size for t-tests, ANOVA, correlations, proportions and regression, and conversely the power for a given sample size; it plots power × sample-size curves that fit straight into a study protocol.
Related terms
- Significance level and Type I / Type II errorsThe significance level α is the maximum risk of a Type I error — rejecting a null hypothesis that is actually true (a false alarm).
- Effect sizeEffect size expresses how large a difference is or how strong an association is — independently of sample size.
- Population and sampleA population is the entire group of units you want to make a claim about — all patients, every product from a line.
- p-valueThe p-value is the probability of obtaining a result at least as extreme as the one observed if the null hypothesis…
Knowledgebase guides
FAQ
- How many observations do I need for a t-test?
- For a medium effect (d = 0.5), α = 0.05 and 80 % power roughly 64 per group; for a small effect (d = 0.2) over 390 per group. The Power Analysis module gives exact numbers.
- Is it worth computing power after the study?
- No — "observed power" merely restates the p-value. Use the confidence interval of the effect instead.
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Foundations & hypothesis testing
Updated: September 2026.