Use this Power Analysis Calculator to estimate statistical power or required sample size for a balanced comparison of two group means.

Calculation Method

This calculator uses a two-sample z-approximation with equal group sizes.

Power = 1 − β

The standard error of the difference is:

SE = σ × √(2/n)

Standardized effect size:

d = Δ ÷ σ

An approximate two-sided sample-size formula is:

n ≈ 2 × [(z_1−α/2 + z_power) × σ ÷ Δ]²

Example

Suppose you want:

80% power
α = 0.05
Standard deviation = 10
Minimum detectable difference = 4
Two-sided test

d = 4 ÷ 10 = 0.40

The approximate requirement is about 99 observations per group, or approximately 198 total observations.

Important Note

This calculator is specifically an approximate balanced two-group mean model. It is not a general power calculator for proportions, regression, ANOVA, clustered designs, unequal allocation, survival analysis, or other study designs.

Power results depend strongly on the assumed effect size and standard deviation, so planning values should come from prior research, pilot data, or a meaningful target effect when possible.

Source

• UCLA Statistical Methods — Power Analysis and Effect Size