Sample Size Calculator
Calculate the required sample size for your statistical study with confidence level and margin of error.
Calculate Sample Size
Table of Contents
What is Sample Size?
Sample size is the number of observations or individuals included in a statistical sample. It is crucial for:
- Ensuring statistical validity of results
- Minimizing sampling error
- Achieving desired confidence level
- Maintaining acceptable margin of error
Factors Affecting Sample Size
Population Size
Larger populations generally require larger sample sizes for accurate representation.
Confidence Level
Higher confidence levels require larger sample sizes to maintain accuracy.
Margin of Error
Smaller margins of error require larger sample sizes for precise results.
Response Distribution
Expected distribution of responses affects the required sample size.
Sample Size Formula
The sample size is calculated using the following formula:
Where:
- n is the sample size
- Z is the Z-score for the confidence level
- p is the response distribution
- e is the margin of error
Examples
Example 1 Small Population
Population: 100
Confidence Level: 95%
Margin of Error: 5%
Response Distribution: 50%
Sample Size ≈ 80
Required for a small population study
Example 2 Large Population
Population: 10,000
Confidence Level: 99%
Margin of Error: 2%
Response Distribution: 50%
Sample Size ≈ 4,147
Required for a high-confidence study
Example 3 Market Research
Population: 1,000,000
Confidence Level: 90%
Margin of Error: 3%
Response Distribution: 30%
Sample Size ≈ 896
Required for market research study