FinitePopulationKorrektur

FinitePopulationKorrektur, also known as finite population correction (FPC), is a statistical adjustment applied when sampling without replacement from a finite population. It modifies the variance and standard error of estimated statistics to reflect the reduced variability that occurs because the sample is a larger proportion of the entire population. The correction factor is typically expressed as the square root of (N – n) divided by (N – 1), where N is the population size and n is the sample size. For small sample fractions (n/N < 0.05), the correction is negligible, but as the sample becomes a substantial portion of the population, the FPC increasingly reduces the estimated standard error.

The FPC is incorporated into formulas for the variance of sample means, proportions, and other estimators. For example, the variance of a sample mean with simple random sampling without replacement is Var(ȳ) = σ²(1 – n/N) / n, where σ² is the population variance. In practical survey contexts, statistical software often applies the FPC automatically when the sample fraction exceeds a preset threshold, ensuring accurate confidence intervals and hypothesis tests.

FinitePopulationKorrektur has applications in demographic studies, market research, quality control, and any field where data are drawn from limited populations. Despite its simplicity, the correction is essential for valid inference when the sampling fraction is nontrivial, preventing overestimation of variability and overly conservative decision-making. The concept is grounded in classical survey sampling theory and remains an important tool in modern statistical analysis.