Power Analysis Calculator

Statistical power (1-β) is the probability that a study will correctly detect a true effect when one exists. Low power means your study may miss a real difference — a false negative (Type II error). A power of 0.80 (80%) is the widely accepted minimum in most research fields, meaning there is an 80% chance of detecting a true effect of the specified size.

Effect size (Cohen's d) quantifies the magnitude of the difference between groups relative to variability. By convention, d = 0.2 is small, d = 0.5 is medium, and d = 0.8 is large. The best approach is to base effect size on pilot study data or published literature from similar studies. When no prior data exist, a medium effect size (0.5) is a common default.

The significance level α is the probability of a Type I error — concluding an effect exists when it does not. The conventional threshold is α = 0.05 (5%), meaning you accept a 5% risk of a false positive. For high-stakes clinical research or multiple testing scenarios, α = 0.01 is sometimes used. Lowering α requires a larger sample size to maintain power.

The allocation ratio (n₂/n₁) defines how many participants are in Group 2 relative to Group 1. A ratio of 1 means equal group sizes, which is most statistically efficient. Unequal ratios (e.g., 2:1) are used when one group is harder or more expensive to recruit, or when ethical constraints limit exposure to an experimental treatment.

A two-tailed test is appropriate when you want to detect a difference in either direction — whether Group 1 is higher or lower than Group 2. A one-tailed test is used only when theory or prior evidence firmly establishes the direction of the expected effect before data collection. Two-tailed tests are the standard default and are more conservative.

Participant attrition is common in longitudinal and clinical studies. If you enroll exactly the calculated minimum and some participants drop out, your effective sample falls below the required size — reducing power and potentially invalidating your conclusions. Inflating the enrollment target by your expected dropout rate (e.g., 10–20%) protects the integrity of your study.

Sample size and power are directly related: larger samples yield greater power for the same effect size and significance level. Conversely, a small sample may be underpowered, producing unreliable results. This calculator uses the standard normal approximation formula to find the exact minimum n that achieves your desired power.

Yes, this calculator applies the widely accepted two-sample independent means formula based on the normal distribution, which is standard in medical, clinical, and behavioral research. For specialized designs — such as crossover trials, survival analysis, or cluster-randomized trials — consult a biostatistician, as additional adjustments beyond this tool may be required.