Sample Size and Population Size FIU（样本大小和人口规模、事业）.pdfVIP

Sample Size and Population Size ß A large random sample almost always gives an estimate that is close to the parameter. ß 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. ß According to Moore/McCabe, this is true, strictly speaking, as long as the population is at least 100 times larger than the sample. ß 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. This is true if the sample is only a small part of the population, which is the usual case” (p. 367). ß 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 : ß 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 (Stats http://www.childrens- /stats/size/population.asp). ß So, even when the sample is a large portion of the population, use fpc only when descriptive precision, rather than inference, is the priority. ß See Freedman et al., pp. 367-370: fpc = square root of (N – n/N – 1) N=population size n=sample size ß Here’s what the UCLA-Stata Resources web site has to say (/STAT/stata/seminars/svy_stata_intro/ default.htm): 1 FPC: This is the finite population correction. This is used when the sampling fraction (the number of elements