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 is influenced by effect size, sample size, significance level, and population variability.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( t_{\text{noncentral}} \) — Noncentral t-distribution parameter
• \( t_{\text{crit}} \) — Critical t-value for given significance level
• \( \Phi \) — Standard normal cumulative distribution function

Explanation: The formula calculates the probability under the alternative hypothesis that the test statistic will exceed the critical value.

3. Importance of Power Calculation

Details: Power analysis helps determine sample size needed to detect an effect and assess the reliability of study conclusions. Studies with low power may fail to detect true effects.

4. Using the Calculator

Tips: Enter the noncentral t parameter (which incorporates effect size and sample size) and the critical t-value for your desired significance level and degrees of freedom.

5. Frequently Asked Questions (FAQ)

Q1: What is considered good statistical power?
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 increase power, as they're easier to detect against background variability.

Q3: What's the relationship between power and sample size?
A: Power increases with sample size, as larger samples provide more precise estimates.

Q4: How does significance level affect power?
A: More stringent significance levels (e.g., 0.01 vs 0.05) decrease power by making the critical value more extreme.

Q5: When should power analysis be performed?
A: Ideally before data collection (a priori) to determine sample size, and sometimes after (post hoc) to interpret results.