Finite Population Multiplier and Sampling Fraction

The finite population multiplier is a correction factor that is applied to the standard error of a sample mean or proportion when the sample is drawn from a finite population. It accounts for the fact that sampling without replacement reduces the variability of the sample mean or proportion compared to sampling with replacement from an infinite population.

The sampling fraction is the proportion of the population that is included in the sample. It is calculated as the sample size divided by the population size.

When is the Finite Population Multiplier Ignored?

The finite population multiplier is ignored when the sampling fraction is less than 0.05. This means that the sample is considered to be small relative to the population, and the correction factor is not necessary to obtain accurate estimates of the population mean or proportion.

If the sampling fraction is greater than 0.05, the finite population multiplier should be applied to the standard error to obtain accurate estimates of the population parameters. However, if the sampling fraction is too large (greater than 0.5), the sample may become too similar to the population, and the standard error may become unstable, making it difficult to obtain accurate estimates.

In summary, the finite population multiplier is only necessary when the sample is drawn from a finite population and the sampling fraction is greater than 0.05. If the sampling fraction is less than 0.05, the correction factor can be ignored.