What Is the Finite Population Correction Factor?

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The finite population correction (FPC) factor is used to adjust the standard error of a sample mean when sampling is done without replacement and the sample size is at least 5 percent of the population. The FPC factor always has a value of less than one.

Simple random sampling, or sampling without replacement, is a sampling technique wherein all the elements of a sample are randomly selected from a given population. Each element of the sample has an equal probability of being chosen. A simple random sample is an impartial representation of a group. Errors may occur if the sample does not reflect the population from which it was taken from. The standard error of the mean, also known as the standard deviation, refers to the measure of the margin of error of a sampling distribution.

In a relatively small, finite population size, of which the value is known, the finite population correction factor can be used to estimate the standard error of the mean. This accounts for the increase in accuracy if a larger percentage of a population is randomly sampled. Given a sample containing an n number of objects, which were randomly selected from a population of size N, the FPC factor is calculated by taking the square root of (N-n) / (N-1).