Sampling Error Calculator
Enter population size, sample size, and observed successes to quantify sampling error and apply finite population correction (FPC) when necessary.
Sample proportion (p̂): 52.00%
Standard error (without FPC): 0.015799
Finite population correction factor: 1.000000
Adjusted standard error (with FPC): 0.015799
How to Use This Calculator
- Provide the population size N (use a large number or skip FPC if the population is effectively infinite).
- Enter the number of observations in your sample.
- Provide the count of successes (or positive responses) observed.
- Review the sample proportion, standard error, and adjusted standard error when FPC applies (n/N ≥ 5%).
Formula
Sample proportion p̂ = successes / n
Standard error SE = √[p̂(1 − p̂) / n]
Finite population correction (FPC) = √[(N − n) / (N − 1)] (when sampling without replacement)
Adjusted SE = SE × FPC
Full Description
Sampling error quantifies uncertainty in sample estimates due to random variation. For proportions, it depends on the observed proportion p̂ and sample size n. When sampling without replacement from a finite population, the finite population correction reduces the standard error to reflect the reduced variability.
Understanding sampling error is essential for designing surveys, interpreting poll results, and constructing confidence intervals.
Frequently Asked Questions
When should I apply finite population correction?
Apply FPC when sampling without replacement and the sample is at least 5% of the population (n/N ≥ 0.05).
Does this calculator handle confidence intervals?
No, but you can multiply the standard error by a z-score to obtain margins of error for confidence intervals.
What if I don’t know the population size?
Set N to a large number or ignore FPC if the population is effectively infinite.
How does sample size affect sampling error?
Sampling error decreases with larger sample sizes because estimates become more precise.