Introduction
This statistical power calculator is designed for researchers and statisticians to determine the sample size needed for hypothesis testing, ensuring your study has sufficient power to detect meaningful effects.
Results
Data Source and Methodology
All calculations are based on standard statistical methods and formulas. For more information, please refer to the authoritative sources in the field of statistics.
The Formula Explained
Sample Size Formula: \(N = \frac{{(Z_{\alpha/2} + Z_{\beta})^2 \cdot 2 \cdot \sigma^2}}{{\Delta^2}}\)
Glossary of Terms
- Effect Size (Cohen's d): The estimated size of the effect you are trying to detect.
- Significance Level (\u03B1): The probability of rejecting the null hypothesis when it is true.
- Power (1 - \u03B2): The probability of correctly rejecting the null hypothesis.
- Sample Size (N): The number of observations required to achieve the desired power.
Frequently Asked Questions (FAQ)
What is statistical power?
Statistical power is the probability that a test will detect an effect if there is an actual effect present.
How does effect size influence sample size?
Larger effect sizes require smaller sample sizes to achieve the same power, and vice versa.
What is considered a good power level?
A power level of 0.8 or 80% is commonly considered adequate for most research studies.
How can I determine the effect size?
The effect size can be estimated from previous studies or calculated based on expected differences and variability.
Why is statistical power important?
Ensuring adequate power helps avoid Type II errors, where a study may fail to detect an effect that actually exists.