Plan studies with standard deviation power analysis. Compare one-sample and two-sample designs under flexible assumptions. See sample needs, power curves, and practical decision guidance.
These examples show how variability, sample size, and expected difference affect power planning.
| Scenario | Design | Expected difference | SD 1 | SD 2 | n1 | n2 | Alpha | Approx. interpretation |
|---|---|---|---|---|---|---|---|---|
| A/B product metric | Two-sample | 5.0 | 12.0 | 12.0 | 50 | 50 | 0.05 | Moderate effect with balanced variance and practical sample size. |
| Process improvement audit | One-sample | 3.5 | 8.0 | Not used | 40 | Not used | 0.05 | Smaller spread improves detection strength with fewer records. |
| Marketing lift test | Two-sample | 2.0 | 10.0 | 14.0 | 120 | 180 | 0.01 | Stricter alpha and unequal variance demand larger samples. |
One-sample: SE = σ / √n
Two-sample: SE = √(σ₁² / n₁ + σ₂² / n₂)
λ = |Δ| / SE, where Δ is the expected mean difference.
For two-sided tests, the calculator uses z(1 − α/2). For one-sided tests, it uses z(1 − α).
One-sided: Power = 1 − Φ(zcrit − λ)
Two-sided: Power = 1 − Φ(zcrit − λ) + Φ(−zcrit − λ)
The initial estimate uses (zcrit + zβ)² × variance term / Δ², then the calculator searches upward until the target power is reached.
This tool uses a normal approximation for mean-based power planning. It is practical for fast design work, sensitivity checks, and early experiment scoping.
It estimates statistical power, required sample size, or the minimum detectable mean difference using standard deviation inputs. It is useful for experiment planning, A/B testing, quality checks, and mean-comparison studies.
Standard deviation controls noise. Larger spread makes true differences harder to detect, increases standard error, lowers power, and usually forces a larger sample to keep the same confidence and sensitivity.
Use one-sample mode when you compare a sample mean against a fixed benchmark or historical target. Use two-sample mode when you compare two independent groups, such as control versus treatment.
A target of 80% is common for routine work. High-stakes studies often use 90% or more. Higher target power increases sample needs because the design must detect effects more reliably.
The allocation ratio is n2 / n1. A ratio of 1 means equal groups. Unequal allocation is sometimes practical, but it can reduce efficiency when the total sample budget stays fixed.
Yes. It works well for early planning when you have rough estimates for spread and effect size. For final protocols, pair it with domain review, historical data, and any required regulatory standards.
It shows the smallest mean shift your design is likely to detect at the chosen power and alpha. That helps decide whether the planned study is sensitive enough to justify running.
No. It is a fast planning calculator. It gives clear, practical estimates, but specialized workflows may still need advanced modeling, exact distributions, simulation, or expert statistical review.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.