Margin of error - Effect of population size


The margin of error is a statistic expressing the amount of random sampling error in a survey’s results. The larger the margin of error, the less confidence one should have that the poll’s reported results are close to the “true” figures; that is, the figures for the whole population. Margin of error is positive whenever a population is incompletely sampled and the outcome measure has positive variance (that is, it varies).

ccording to sampling theory, this assumption is reasonable when the sampling fraction is small. The margin of error for a particular sampling method is essentially the same regardless of whether the population of interest is the size of a school, city, state, or country, as long as the sampling fraction is less than 5%.

In cases where the sampling fraction exceeds 5%, analysts can adjust the margin of error using a “finite population correction” (FPC), to account for the added precision gained by sampling close to a larger percentage of the population. FPC can be calculated using the shown formula

Related formulas


FPCfinite population correction (dimensionless)
Npopulation size (dimensionless)
nsample size (dimensionless)