Sample Size and Population Size

A large random sample almost always gives an estimate that is close to the parameter. What fundamentally matters for the variability of a statistic from a random sample is the sample size, not the population size: The variability of a statistic from a random sample does not notably depend on the size of the population. According to Moore/McCabe, this is true, strictly speaking, as long as the population is at least 100 times larger than the sample. According to the other “state of the art” introductory statistics book, Freedman et al.’s Statistics: “When estimating percentages, it is the absolute size of the sample which determines accuracy, not the size relative to the population. There is a marginal difference, which the finite population correction factor (fpc) can compensate for, if the sample is a large portion of the population: There is a marginal difference, which the finite population correction factor (fpc) can compensate for, if the sample is a large portion of the population: Perhaps use fpc when the sample is a large portion (say, 30-40+%) of the population - but using it can cause uncertainty for inferring the sample’s results to a wider population. So, even when the sample is a large portion of the population, use fpc only when descriptive precision, rather than inference, is the priority. See Freedman et al., pp. 367-370: fpc = square root of (N – n/N – 1) N=population size n=sample size