Understanding Sample Size
Sample size is a statistical concept that involves determining the number of observations or replicates that should be included in a statistical sample. It is an essential aspect of any empirical study requiring that inferences be made about a population based on a sample.
Why Not Survey Everyone?
Surveying an entire population (a census) is often impossible, too expensive, or too time-consuming. Instead, researchers select a representative subset—a sample. Calculating the correct sample size ensures that the results are statistically significant and accurately reflect the population within a chosen margin of error and confidence level.
Key Terms
- Confidence LevelHow certain you are that the true value lies within the interval (e.g., 95%)
- Margin of ErrorThe maximum expected difference between the true and sampled results (e.g., ±5%)
- Population ProportionEstimated percentage of the population that holds a certain characteristic.
Calculating Sample Size
To carry out this calculation, set the margin of error, e, or the maximum distance desired for the sample estimate to deviate from the true value. The equation for determining sample size (assuming an unlimited population) is:
Where z is the z-score corresponding to your confidence level, p is the estimated population proportion (usually set to 0.5 to maximize the required sample size if unknown), and e is your margin of error as a decimal.
Finite Population Correction (FPC)
If the total population is known and relatively small (the sample will be more than 5% of the population), the required sample size decreases because a significant portion of the population is being sampled. The Finite Population Correction factor is applied:
Where N is the population size. Our calculator automatically applies this correction if you provide a population size.