Finite Population Correction Calculator Formula
Understand the math behind the finite population correction calculator. Each variable explained with a worked example.
Formulas Used
Corrected Standard Error
corrected_se = se * fpcFPC Factor
fpc_factor = fpcSampling Fraction (n/N)
sampling_fraction = n / NSE Reduction (%)
reduction_pct = (1 - fpc) * 100Variables
| Variable | Description | Default |
|---|---|---|
se | Uncorrected Standard Error | 2.5 |
n | Sample Size | 100 |
N | Population Size | 500 |
fpc | Derived value= sqrt((N - n) / (N - 1)) | calculated |
How It Works
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).
Worked Example
Standard error = 2.5, sample of 100 from a population of 500.
- 01Sampling fraction = 100/500 = 0.20 (20% of population)
- 02FPC = sqrt((500-100)/(500-1)) = sqrt(400/499) = sqrt(0.8016) = 0.8954
- 03Corrected SE = 2.5 * 0.8954 = 2.2384
- 04The standard error is reduced by 10.5%
Frequently Asked Questions
When should I apply the finite population correction?
Apply FPC when the sampling fraction (n/N) exceeds 5% (rule of thumb). For n/N < 0.05, FPC is close to 1 and can be ignored. For large populations (millions), the correction is almost never needed.
Why does the correction reduce the standard error?
When you sample a large fraction of the population, there is less uncertainty because you have already observed much of the population. In the extreme (census, n = N), the standard error is zero because you know the exact population parameter.
Does FPC apply to sampling with replacement?
No. FPC only applies to sampling without replacement. With replacement, each draw is independent of previous draws, and the population effectively remains infinite.
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Open Finite Population Correction Calculator