Statistics Dictionary

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Finite Population Correction

Some formulas used to compute standard errors are based on the idea that (1) samples are selected from an infinite population or (2) samples are selected with replacement. In most actual surveys, neither of these ideas are correct.

This does not present much of a problem when the sample size (n) is small relative to the population size (N); that is, when the sample is less than 5% of the population. However, when the sample is larger, it is best to apply a correction to the formulas used to compute standard error (SE). This correction is called the finite population correction or fpc.

Here is the formula for the finite population correction, when the random variable is a mean score or proportion.

fpc = sqrt [ (N - n) / (N - 1) ]

Here is how the finite population correction is used to compute the standard error of a mean score.

SE = [ (standard deviation)/sqrt(n) ] * fpc

And here is how the it is used to compute the standard error of a proportion (p).

SE = [ sqrt[ p(1 - p) / n ] * fpc

Note that when n is very small relative to N, the finite population correction is almost equal to one; and it has only a small effect on the standard error. However, when n is large relative to N, the finite population correction can have a big effect on the standard error.