Statistical Power Calculator
Study inputs Updates automatically
Statistical test
Alternative
Effect size (Cohen’s d)0.2 small • 0.5 medium • 0.8 large
Significance level (α)Type I error
Target power (1 − β)Common: 0.80–0.90
Sample sizeTotal or per group
Allocation ratio n₂ / n₁1 = equal groups
Degrees of freedomχ² df
Number of groupsBalanced ANOVA
Independent groups, pooled variance, standardized mean difference d, and noncentral t power.
Result Noncentral t
80.0%
Power
Required sample size
64 + 64
128 total participants
Alpha
0.050
Beta
0.200
Effect
d = 0.50
Power curve by sample size
The highlighted point represents the current design.
Interpretation
A study with this design reaches approximately 80% power.
Effect size
Cohen’s d = 0.50, conventionally described as a medium standardized mean difference.
Planning note
Consider inflating the sample for expected attrition, exclusions, clustering, or incomplete data.
How this is calculated
For a two-sample t test, the noncentrality parameter is based on the standardized difference and group sizes.
δ = d / √(1/n₁ + 1/n₂)
δ = 0.50 / √(1/64 + 1/64) = 2.828
Power is the probability that a noncentral t random variable falls beyond the critical t boundary under the alternative hypothesis.
Method notes, assumptions, and references
Mean tests: noncentral t distribution with pooled-variance degrees of freedom for two independent groups, and df = n − 1 for one-sample/paired designs.
Proportions: Cohen’s h with a normal z approximation. For raw proportions, h = 2asin(√p₁) − 2asin(√p₂).
Correlation: Fisher’s z = atanh(r) approximation with standard error 1/√(n − 3).
Chi-square: noncentral chi-square with λ = Nw².
ANOVA: balanced one-way F test with Cohen’s f and λ = Nf².
Important: Power analysis is model-dependent. Use an effect size justified by prior evidence, pilot data, or the smallest effect of scientific interest. Clustered, repeated-measures, survival, noninferiority, equivalence, and complex survey designs require specialized methods.
