Power Analysis
Analyze → Power Analysis. Plans a study before you collect it: how likely a test is to detect an effect of a given size (its power), how many cases you need to reach a target power, or the smallest effect a given sample can detect. Power analysis takes no dataset (every input is a number you supply), so it works with an empty grid, and Select, Weight and Split have no effect on it.
Five designs sit under the menu, one dialog each:
| Design | Effect size | Sample size means |
|---|---|---|
| Means (t test): one sample, paired samples, or two independent samples | Cohen's d | per group for two samples; the number of observations (pairs) otherwise |
| One-Way ANOVA: k groups | Cohen's f | the total N |
| Correlation: Pearson's r against zero | the correlation r | N |
| Two Proportions: two independent groups | the two proportions (Cohen's h is computed from them) | per group |
| Multiple Regression (R²): u predictors tested together | Cohen's f² | the total N |
Filling the dialog
Pick what to solve for (Power (1 − β), Sample size or Effect size) and fill the other two, with the significance level (α) (default 0.05). The t test, correlation and two-proportion designs also take Two-tailed (default) or One-tailed; ANOVA and the regression R² test are F tests, one-sided by nature. The two-proportion design solves for power or sample size only: its effect is fixed by the two proportions you enter.
Conventional effect sizes (Cohen's) if you have nothing better: d = 0.2 / 0.5 / 0.8, f = 0.10 / 0.25 / 0.40, r = 0.1 / 0.3 / 0.5, f² = 0.02 / 0.15 / 0.35 for small / medium / large. An effect estimated from a pilot or the literature is always better.
Reading the output
One table, Power Analysis — design, lists the inputs and the answer. Solving for sample size rounds up to the next whole case and also prints the Achieved power at that size, which is at least the target. Solving for effect size prints the Detectable effect: the smallest effect the design reaches the target power for. The note under the table names the distribution the power came from.
Example. Two independent groups, d = 0.5, α = 0.05 two-tailed, target power 0.80: solving for sample size gives 64 per group (achieved power about 0.80).
How this is computed
This section names which method each procedure prints: the estimator, the statistic, its degrees of freedom, and the tie, missing-value and weight rules. Each line links the recorded convention that explains the choice. The full index is the convention inventory; every number here is validated against independent packages per the validation suite.
- Every design: power is the probability, under the alternative, of landing beyond the central critical value: a tail of the noncentral distribution at the alternative's noncentrality; two-tailed by default (power analysis). Sample size and detectable effect invert that function by a bracketing root-find; a sample size is rounded up.
- Means: noncentral t: df = n − 1 and δ = d√n for one sample or pairs; df = 2n − 2 and δ = d√(n/2) for two groups of n.
- One-way ANOVA: noncentral F on (k − 1, N − k) df with λ = f²N.
- Correlation: the Fisher z normal approximation: δ = atanh(|r|)·√(N − 3).
- Two proportions: Cohen's h = 2 asin√p₁ − 2 asin√p₂; two-tailed through the noncentral χ²(1) with λ = h²n/2, one-tailed through the equivalent normal tail.
- Multiple regression: noncentral F on (u, N − u − 1) df with λ = f²N.
Reproducibility
Each run journals a syntax command, for example:
power_means test=two_sample, solve=n, effect=0.5, power=0.8
and the five designs are the tools power_means, power_anova,
power_correlation, power_proportions and power_regression, available to
the AI assistant, MCP and batch scripts like every analysis. See the
command reference for every argument.