Power and sample size
How many replicates you need — worked out before the experiment, not after.
The smallest difference worth acting on.
Per group
128 in total
Gives 80.1% power. One fewer drops it to 79.5%.
power = P(|T′| > t₍₁−α/2₎), T′ noncentral t with δ = d√(n/2)- Cumulative distribution function of the noncentral t — Applied Statistics, 1989
- Conventional small, medium and large effect sizes — Statistical Power Analysis for the Behavioral Sciences, 1988
Do this before the experiment. Power computed after a non-significant result, from the effect you happened to observe, is circular and tells you nothing.
When to use this
Use this before an experiment to work out how many replicates you need, or after one to understand what it could realistically have detected. It is most useful as a design tool — power computed after a null result mostly restates the p-value.
Worked example
Planning a two-group comparison expecting a medium effect.
- Design
- Two-sample
- Effect size (d)
- 0.5
- Power / alpha
- 80% / 0.05
Result
If that is more animals than you can run, the honest conclusion is that the experiment cannot answer the question as designed.
What people get wrong
- Computing power after the fact from the observed effect. Observed power is a deterministic function of the p-value and adds nothing.
- Picking an effect size because it gives a convenient n. It should be the smallest difference that would change what you do, decided before you look.
- Forgetting that n is per group. A two-sample calculation returning 64 means 128 animals in total.
Questions
+Where do I get an effect size?
From pilot data, from the literature, or from the smallest difference that would matter biologically. The last is usually the most defensible.
+Why does the tool use the noncentral t distribution?
Because the normal approximation understates the required sample size at small n, which is precisely where the answer matters.
+Is 80% power a rule?
It is a convention, not a law. It means accepting a one in five chance of missing a real effect of the size you specified.
Related tools
- t-test calculator — Compare two groups and get the effect size and interval, not just a p-value.
- One-way ANOVA — Compare three or more groups, with variance explained and every pair tested.
Science last reviewed .