Glossary
Finite Population Correction
The finite population correction (FPC) is an adjustment to the standard error applied when the sample represents more than about 5% of the population. The correction factor is √((N − n) / (N − 1)), where N is the population size and n is the sample size.
Definition
The finite population correction (FPC) is an adjustment to the standard error applied when the sample represents more than about 5% of the population. The correction factor is √((N − n) / (N − 1)), where N is the population size and n is the sample size.
Why It Matters
Without the FPC, standard error formulas assume an infinitely large population. When a substantial fraction of the population is sampled, the variability of the estimate is reduced because there are fewer unsampled units that could differ from the observed data. Ignoring the FPC in such cases leads to unnecessarily wide confidence intervals and overly conservative hypothesis tests. The correction becomes increasingly important as the sampling fraction grows, and it shrinks toward zero as the sample approaches the full population — reflecting the intuitive result that sampling everyone produces no sampling error at all.
Example
A quality inspector tests 200 items from a production lot of 1,000. The sampling fraction is 20%, well above the 5% threshold. The standard error without FPC is 2.5, but applying √((1000 − 200) / (1000 − 1)) ≈ 0.894 reduces it to approximately 2.24. The resulting confidence interval narrows noticeably, giving a more precise estimate without collecting additional data.
Related Terms
Software Notes
- SPSS: Not applied by default; compute manually via Transform > Compute Variable using the FPC formula
- R: Apply manually:
se_fpc <- se * sqrt((N - n) / (N - 1)); thesurveypackage applies FPC automatically when population sizes are specified - Stata:
svysetwithfpc(varname)applies the correction automatically in survey commands
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