Sample Size Calculator: Two-Sided Proportion (One Sample)
Introduction & Importance
Sample size calculation is a critical step in ensuring the validity and reliability of statistical analyses. The two-sided proportion (one sample) test is used to determine if there’s a significant difference between the proportion of a characteristic in a sample and a known or hypothesized proportion in the population.
How to Use This Calculator
- Select the desired confidence level using the Z-score dropdown.
- Enter the proportion of the characteristic in the population.
- Enter the desired margin of error.
- Click the “Calculate” button.
Formula & Methodology
The formula used in this calculator is:
n = (Z^2 * p * (1 – p)) / d^2
Where:
- n is the sample size
- Z is the Z-score (confidence level)
- p is the proportion
- d is the margin of error
Real-World Examples
Data & Statistics
| Confidence Level | Z-score | Proportion (p) | Margin of Error (d) | Sample Size (n) |
|---|---|---|---|---|
| 95% | 1.96 | 0.5 | 0.05 | 384.16 |
| 90% | 1.645 | 0.5 | 0.05 | 306.40 |
| 80% | 1.28 | 0.5 | 0.05 | 196.00 |
Expert Tips
- Always round up the calculated sample size to the nearest whole number.
- Consider using a larger sample size than calculated to account for potential dropouts or non-response.
Interactive FAQ
What is a Z-score?
A Z-score is a statistical measure that indicates how many standard deviations an element is from the mean.
What is a margin of error?
The margin of error is the range within which the true population parameter is likely to fall.