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). It depends on effect size, sample size, alpha level, and whether the test is one- or two-tailed.

2. How Does the Calculator Work?

The calculator estimates power using the formula:

Where:

• \( t \) — Test statistic
• \( t_{\text{crit}} \) — Critical t-value for given α and df
• effect — Effect size and sample size combined in non-centrality parameter

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

3. Importance of Power Analysis

Details: Conducting power analysis before a study helps determine the required sample size to detect an effect. Post-hoc power analysis can help interpret negative results.

4. Using the Calculator

Tips: Enter the expected effect size (Cohen's d), planned sample size, alpha level (typically 0.05), and specify whether the test is one- or two-tailed.

5. Frequently Asked Questions (FAQ)

Q1: What is a good power level?
A: Typically 80% or higher is considered adequate, though 90% is preferred for important studies.

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

Q3: What's the relationship between α and power?
A: Higher α (e.g., 0.10 vs 0.05) increases power but also increases Type I error rate.

Q4: Why does one-tailed testing increase power?
A: One-tailed tests concentrate all α in one tail, making the critical value less extreme.

Q5: Can I calculate required sample size from desired power?
A: Yes, this is called a priori power analysis and is the most common use of power calculations.