Which inputs do I need for a power analysis?

You typically need the effect size you care about, the sample size (or sample size per group), the significance level (alpha, often 0.05), and the expected variability (standard deviation) or proportions.

What is a good power value?

A power of 0.8 (80%) is a common benchmark in research, meaning there is an 80% chance to detect the effect if it is truly present.

Statistical Power Calculator & Power Analysis

2A. Inputs for means

Example: control mean = 10, treatment mean = 12 → effect size = 2. SD is the common standard deviation.

Mean (group A)

Mean (group B)

Standard deviation (common)

Sample size per group

3. Test settings

Alpha (significance)

Tails

4. Results

Estimated power

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Effect size (absolute)

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Indicative n per group for 80% power

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What is statistical power?

Statistical power is the probability that your test will detect an effect if the effect is really there. Low power → high chance of false negatives.

Key determinants of power

Effect size: bigger differences are easier to detect.
Sample size: more data → narrower standard error → higher power.
Alpha: a higher alpha (e.g. 0.1) makes it easier to reject H0, increasing power.
Variability: lower standard deviation → higher power.

Formula idea (z-approximation)

For a two-sample test on means (equal n), the test statistic roughly follows

z = (μ₂ − μ₁) / (σ √(2/n))

We compare this to the critical value for the chosen α and tails, then compute the corresponding power as the probability the test statistic falls in the rejection region.

Statistical Power Calculator

1. Choose test type