Calculate Test Power by Hand
Calculating the power of a test by hand is a crucial step in statistical analysis. It helps determine the likelihood of detecting an effect if there is one, given the sample size and margin of error.
- Enter the sample size, margin of error, and desired confidence level.
- Click ‘Calculate’.
- View the results and chart below.
The formula for calculating power is:
Power = 1 – β
Where β is the probability of not detecting an effect when there is one (Type II error).
β is calculated using the following formula:
β = 1 – Φ[(Z_α/2 + Z_β) / √(2 * N)]
Where:
- Φ is the standard normal cumulative distribution function.
- Z_α/2 is the critical value of the normal distribution at the α/2 level.
- Z_β is the critical value of the normal distribution at the β level.
- N is the sample size.
| Sample Size | 90% Confidence | 95% Confidence | 99% Confidence |
|---|---|---|---|
| 50 | 30.82 | 23.85 | 14.89 |
| 100 | 50.70 | 42.65 | 28.14 |
| 200 | 74.22 | 65.52 | 47.53 |
- Increase sample size to improve power.
- Consider the trade-off between power and Type I error rate (α).
- Use a power analysis to determine the appropriate sample size before collecting data.
What is power in statistics?
Power in statistics is the probability of detecting an effect when there is one. It’s a measure of the sensitivity of a statistical test.
How do I interpret power?
Power tells you the likelihood of detecting an effect, given that there is one. A power of 0.8 (or 80%) means there’s an 80% chance of detecting an effect if it exists.
For more information, see the power analysis guide from Statistics How To.
Learn more about statistical power from the U.S. Census Bureau.