Finite Population Correction Calculator — Formula
## How to Apply the Finite Population Correction
### Formula
**FPC = sqrt((N - n) / (N - 1))**
**Corrected SE = SE * FPC**
When sampling without replacement from a finite population, the standard error is smaller than the infinite-population formula suggests. The FPC factor accounts for this. It is close to 1 when n is small relative to N, and approaches 0 as n approaches N (census).
### Formula
**FPC = sqrt((N - n) / (N - 1))**
**Corrected SE = SE * FPC**
When sampling without replacement from a finite population, the standard error is smaller than the infinite-population formula suggests. The FPC factor accounts for this. It is close to 1 when n is small relative to N, and approaches 0 as n approaches N (census).
Esempio Risolto
Standard error = 2.5, sample of 100 from a population of 500.
- Sampling fraction = 100/500 = 0.20 (20% of population)
- FPC = sqrt((500-100)/(500-1)) = sqrt(400/499) = sqrt(0.8016) = 0.8954
- Corrected SE = 2.5 * 0.8954 = 2.2384
- The standard error is reduced by 10.5%