Power Analysis Calculator
Estimate statistical power for a one-sample test.
Statistical power is the chance of detecting a real effect of a given size.
How the Math Works
The Power Analysis Calculator uses the formula power = normal CDF of (d*sqrt(n) - z_alpha/2), where d is the effect size, n is the sample size, and z_alpha/2 is the critical value from the standard normal distribution for a given significance level. The term d*sqrt(n) represents the non-centrality parameter, which adjusts the test statistic under the alternative hypothesis. Subtracting z_alpha/2 accounts for the critical threshold, and the cumulative distribution function (CDF) converts this value into the probability of correctly rejecting the null hypothesis when the alternative is true, known as statistical power.
Practical Applications
To use this calculator, input the expected effect size (d), your planned sample size (n), and the significance level (alpha). The tool computes the statistical power, helping you determine if your study is adequately designed to detect a meaningful effect. For instance, if your calculated power is low (e.g., below 0.8), you may need to increase your sample size or adjust your effect size assumptions to ensure reliable results.
Day-to-Day Use
This calculation is vital in research planning, such as designing clinical trials or social science experiments. By estimating power beforehand, you avoid underpowered studies that might fail to detect real effects, saving time and resources. For example, a researcher testing a new medication can use this tool to confirm their sample size is sufficient to observe a clinically relevant improvement, ensuring their findings are both ethical and impactful.
Worked example
d 0.5, n 30, alpha 0.05 gives about 75% power.
FAQ
What if power is too low?
Increase the sample size or expect a larger effect.