# Statistical Power Analysis Calculator

Calculate required sample size for your study. Enter effect size, significance level, and desired power for one-sample, two-sample, or paired t-tests.

## What this calculates

Determine the sample size needed to detect an effect of a given size with a specified level of confidence. Power analysis is essential for planning experiments and clinical trials.

## Inputs

- **Effect Size (Cohen's d)** — min 0.01, max 5 — Standardized effect size. Small=0.2, Medium=0.5, Large=0.8.
- **Significance Level (α)** — min 0.001, max 0.5 — Type I error rate (typically 0.05).
- **Desired Power (1 - β)** — min 0.5, max 0.999 — Probability of detecting a true effect (typically 0.80).
- **Test Type** — options: One-Sample t-test, Two-Sample t-test, Paired t-test — The type of statistical test you plan to run.

## Outputs

- **Sample Size (per group)** — Required number of participants per group.
- **Total Participants** — Total number of participants needed across all groups.
- **Actual Power** — Achieved power with the computed sample size.
- **Summary** — formatted as text — Interpretation of the power analysis.

## Details

Statistical power is the probability that a test correctly rejects a false null hypothesis (i.e., detects a real effect). Power analysis helps you determine how many participants you need before running your study.

Key parameters: Effect size (Cohen's d) measures the magnitude of the difference in standard deviation units. The significance level (alpha) is the acceptable false positive rate. Power (1 - beta) is the desired probability of detecting the effect. A standard setup is d = 0.5, alpha = 0.05, power = 0.80.

Cohen's d guidelines: Small = 0.2 (subtle effect, large sample needed), Medium = 0.5 (moderate effect, practical significance), Large = 0.8 (obvious effect, smaller sample sufficient). These are conventions; the appropriate effect size depends on your field and research question. An underpowered study wastes resources and may miss real effects, while an overpowered study may detect trivially small effects.

## Frequently Asked Questions

**Q: What is an appropriate power level?**

A: The conventional standard is 80% power, meaning an 80% chance of detecting a real effect. Some fields (e.g., clinical trials) use 90% for higher sensitivity. Lower power means more risk of Type II errors (missing real effects).

**Q: How do I choose the right effect size?**

A: Ideally, base it on pilot data, prior studies, or the smallest effect that would be practically meaningful. Cohen's conventions (0.2 = small, 0.5 = medium, 0.8 = large) are starting points. Using too large an effect size leads to underpowered studies.

**Q: What happens if my study is underpowered?**

A: An underpowered study has a low probability of detecting a real effect, leading to non-significant results even when the effect exists (Type II error). This wastes time and resources. Published underpowered studies with significant results also tend to overestimate effect sizes.

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Source: https://vastcalc.com/calculators/statistics/power-analysis
Category: Statistics
Last updated: 2026-04-21