Sample Size Calculator
5%
50%
50% gives the largest sample size. Use a different value only if you have a good estimate.
What is a Sample Size Calculator?
A sample size calculator helps researchers determine how many subjects or observations they need to include in a statistical sample to get results that reflect the target population as precisely as needed.
Using an appropriate sample size is crucial for conducting statistically significant research. Too small a sample may lead to inaccurate results, while too large a sample might waste resources.
How to Calculate Sample Size
The formula for calculating sample size is:
n = [z² × p(1-p)] ÷ e²
Adjusted for finite population: n = n₀ ÷ [1 + (n₀ - 1) ÷ N]
Where:
- n = required sample size
- z = z-score (based on confidence level)
- p = estimated proportion (usually 0.5 for maximum sample size)
- e = margin of error
- N = population size
Common Confidence Levels and Z-Scores
| Confidence Level | Z-Score |
|---|---|
| 90% | 1.645 |
| 95% | 1.96 |
| 99% | 2.576 |
Applications of Sample Size Calculation
- Market Research: Determining how many consumers to survey for product feedback.
- Medical Studies: Calculating the number of patients needed for clinical trials.
- Political Polling: Figuring out how many voters to poll for accurate election predictions.
- Quality Control: Determining how many products to test from a production batch.
Factors Affecting Sample Size
- Confidence Level: Higher confidence levels require larger sample sizes.
- Margin of Error: Smaller margins of error require larger sample sizes.
- Population Size: For small populations, the required sample size is relatively larger compared to the population.
- Population Variance: Greater heterogeneity in the population requires larger sample sizes.
Tips for Sample Size Determination
- Start with a clear research question and hypothesis.
- Consider the practical constraints of your study (time, budget, resources).
- Use previous similar studies as a reference point.
- When in doubt, opt for a larger sample size to increase precision.
- For pilot studies, smaller sample sizes (10-30) may be sufficient.