Statistical Power

= · ( + )²

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Calculate

Example: a trial will compare a treatment with a control and expects a medium difference (Cohen's d = 0.5). How many participants per group are needed to detect it with 80% power at 5% significance? Use g = 2 for two independent groups and g = 1 for one sample or paired data. Change the values to work out your own case.

Effect size d Significance α (%) Power (%) Groups g

Step by step

What each term means

Sample Size (n): How many observations each group needs for the test to detect the effect with the requested power. With two groups, the total is twice that.
Number of Groups (g): 2 to compare two independent groups, such as treatment and control: each mean carries its own uncertainty, and the variance of the difference doubles. 1 for one sample against a fixed value or for paired data, where the mean of the differences is tested.
Critical Value (z_α/2): The threshold for rejecting H₀ in a two-sided test at level α. For α = 5%, z_α/2 ≈ 1.96. A smaller α pushes the threshold out and calls for more data.
Power Quantile (z_β): The standard normal value with β = 1 − power below it. For 80% power, β = 20% and z_β ≈ 0.84; for 90%, ≈ 1.28. It is the slack that makes the real effect clear the threshold in most samples.
Squared Effect Size (d²): Cohen's d is the difference in means divided by the standard deviation: 0.2 is small, 0.5 medium and 0.8 large. With paired data, use the d of the differences. Because it is squared, halving the effect quadruples the sample.