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Why Sample Size Matters
Sample size directly affects the reliability of your results. Too small a sample leads to unreliable conclusions with wide confidence intervals. Too large wastes resources. Calculating the right sample size before collecting data ensures your study has enough statistical power to detect meaningful differences.
How Sample Size Is Calculated
The formula uses four inputs: confidence level (z-score), margin of error, population proportion, and population size. For large populations, n = (z² × p × (1-p)) / e², where z is the z-score, p is the proportion, and e is the margin of error. A finite population correction is applied for smaller populations.
Choosing Your Parameters
A 95% confidence level and 5% margin of error are standard for most surveys. If you do not know the expected proportion, use 50% — this maximizes the required sample size, ensuring your estimate is conservative. Lower margins of error require larger samples.
Sample Size for Common Scenarios
For a national survey with 95% confidence and ±3% margin, you need about 1,067 respondents. For a small town of 5,000 with the same parameters, about 880. As population grows beyond ~20,000, the required sample size barely changes — you approach the infinite population formula.
Frequently Asked Questions
Using 50% gives the most conservative (largest) sample size estimate. When p = 0.5, the product p(1-p) is maximized at 0.25. If the actual proportion is different, you will have more than enough responses.
For populations above ~20,000, the required sample size barely changes. The finite population correction only makes a significant difference for small populations (under a few thousand).
Accept a wider margin of error, use a lower confidence level, or use a more specific population proportion estimate (if justified by prior research). Each of these reduces the required n.
As a general rule, at least 30 observations are needed for the Central Limit Theorem to apply. For surveys, most methodologists recommend a minimum of 100 respondents, with 384 being a common target for 95% confidence and ±5% margin.