1. What is Statistical Power?

Statistical power is the probability that a test will correctly reject a false null hypothesis. It represents the test's ability to detect an effect when one truly exists, calculated as 1 - β, where β is the Type II error rate.

2. How Does the Power Calculator Work?

The calculator uses the standard power calculation formula:

Where:

• \( \alpha \) — Significance level (Type I error rate)
• \( \beta \) — Type II error rate
• Effect Size — Standardized measure of the effect magnitude
• Sample Size — Number of observations in the study

Explanation: Power increases with larger effect sizes, larger sample sizes, and higher significance levels. The calculation accounts for the test type (one-tailed vs two-tailed).

3. Importance of Power Analysis

Details: Adequate statistical power is crucial for study design. Underpowered studies may fail to detect true effects, leading to false negative results and wasted resources.

4. Using the Calculator

Tips: Enter alpha level (typically 0.05), effect size (Cohen's d or similar), sample size, and select test type. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is considered adequate statistical power?
A: Typically 80% or higher is considered adequate, though 90% is preferred for critical studies.

Q2: How does effect size impact power?
A: Larger effect sizes require smaller sample sizes to achieve the same power level.

Q3: What is the relationship between alpha and power?
A: Increasing alpha (e.g., from 0.05 to 0.10) increases power but also increases Type I error risk.

Q4: When should power analysis be conducted?
A: Before study initiation (a priori) to determine required sample size, or after (post hoc) to interpret results.

Q5: What are common reasons for low power?
A: Small sample sizes, small effect sizes, high variability in data, and overly conservative alpha levels.