Power Analysis Calculator

What this tool does

Calculate power analysis using your data. Normal approximation, labelled as such: exact t-based power (noncentral t) differs slightly, especially at small n. Power is a pre-study design quantity — 'post-hoc power' computed from an observed effect adds no information beyond the p-value.

How to use the Power Analysis Calculator

1. Enter or select design.
2. Enter or select effect size — cohen's d (t-test).
3. Enter or select proportion 1 (%) (proportions).
4. Enter or select proportion 2 (%) (proportions).
5. Enter or select significance level (α).
6. Enter or select desired power.
7. Enter or select actual sample size per group (for achieved power).
8. Read the calculated result; change any measurement to compare alternatives.

Formula

normal approximation: t-test n per group = 2((z₁₋α/2 + z_power)/d)²; proportions use the pooled/unpooled two-proportion formula; achieved power inverts the same formulas

mode

Design

d

Effect size — Cohen's d (t-test)

p1

Proportion 1 (%) (proportions)

p2

Proportion 2 (%) (proportions)

alpha

Significance level (α)

power

Desired power

ngiven

Actual sample size per group (for achieved power)

Normal approximation, labelled as such: exact t-based power (noncentral t) differs slightly, especially at small n. Power is a pre-study design quantity — 'post-hoc power' computed from an observed effect adds no information beyond the p-value.

Worked example

For power analysis calculator, the following measurements illustrate the exact method: Design: t; Effect size — Cohen's d (t-test): 0.5; Proportion 1 (%) (proportions): 10; Proportion 2 (%) (proportions): 12; Significance level (α): 0.05; Desired power: 0.80; Actual sample size per group (for achieved power): 50.

Results explained

Required sample size per group

Required sample size per group from the formula above. Normal approximation, labelled as such: exact t-based power (noncentral t) differs slightly, especially at small n. Power is a pre-study design quantity — 'post-hoc power' computed from an observed effect adds no information beyond the p-value.

Total sample size (both groups)

Total sample size (both groups) from the formula above. Normal approximation, labelled as such: exact t-based power (noncentral t) differs slightly, especially at small n. Power is a pre-study design quantity — 'post-hoc power' computed from an observed effect adds no information beyond the p-value.

Achieved power at the entered n per group (%)

Achieved power at the entered n per group (%) from the formula above. Normal approximation, labelled as such: exact t-based power (noncentral t) differs slightly, especially at small n. Power is a pre-study design quantity — 'post-hoc power' computed from an observed effect adds no information beyond the p-value.

Frequently asked questions