1. What is Statistical Power?

Statistical power is the probability that a test will correctly reject a false null hypothesis (avoid a Type II error). Power = 1 - β, where β is the probability of a Type II error.

2. How Does Power Calculation Work?

The power calculation depends on several factors:

Where:

• \( \alpha \) — Significance level (Type I error rate)
• \( \beta \) — Type II error rate
• Effect size — Standardized magnitude of the effect
• Sample size — Number of observations in each group
• Test type — One-tailed or two-tailed test

Explanation: Power increases with larger effect sizes, larger sample sizes, higher α levels, and when using one-tailed tests.

3. Importance of Power Analysis

Details: Power analysis helps researchers determine the sample size needed to detect an effect of a given size with a certain degree of confidence. It's crucial for study design to avoid underpowered studies.

4. Using the Calculator

Tips: Enter the significance level (typically 0.05), effect size (small=0.2, medium=0.5, large=0.8), sample size per group, and select test type. All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What is considered good statistical power?
A: Typically 80% power is considered acceptable, though some studies aim for 90% or higher depending on the context.

Q2: How does effect size affect power?
A: Larger effect sizes are easier to detect, requiring smaller sample sizes to achieve the same power.

Q3: Why does sample size increase power?
A: Larger samples reduce sampling error, making it easier to detect true effects.

Q4: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests have more power to detect effects in a specified direction, while two-tailed tests are more conservative.

Q5: When should I do a power analysis?
A: Before conducting a study to determine sample size requirements, or after a study to interpret negative results.