1. What is Statistical Power?

Statistical power (1-β) is the probability that a test correctly rejects the null hypothesis when the alternative hypothesis is true. It represents the test's ability to detect an effect when one exists.

2. How the Power Calculation Works

The calculator uses the standard normal distribution to compute power:

Where:

• \( \mu_1 - \mu_2 \) — True difference in means (effect size)
• \( \sigma \) — Standard deviation
• \( n \) — Sample size
• \( \alpha \) — Significance level (Type I error rate)
• \( z_{1-\alpha/2} \) — Critical value from standard normal distribution
• \( \Phi \) — Standard normal CDF

Explanation: The formula calculates the probability that the test statistic falls in the rejection region when the alternative hypothesis is true.

3. Importance of Power Analysis

Details: Power analysis helps researchers determine adequate sample sizes before conducting studies and interpret negative results. Studies with low power may fail to detect true effects.

4. Using the Calculator

Tips: Enter the expected effect size, population standard deviation, planned sample size, and desired alpha level. Typical power targets are 0.8 or higher.

5. Frequently Asked Questions (FAQ)

Q1: What is a good power value?
A: Generally, 0.8 or higher is considered adequate, meaning an 80% chance to detect an effect if it exists.

Q2: How does sample size affect power?
A: Power increases with larger sample sizes, as the standard error decreases.

Q3: What's the relationship between α and power?
A: For a fixed sample size, decreasing α (making the test more stringent) reduces power.

Q4: Can I calculate required sample size from power?
A: Yes, this calculator can be used iteratively to find the sample size needed to achieve desired power.

Q5: What if my data isn't normally distributed?
A: For non-normal data, consider non-parametric tests or simulation methods for power calculation.