= Finite Population Correction = A '''finite population correction''' ('''FPC''') is a multiplicative adjustment used in variance estimation. <> ---- == Description == Most formulations of standard errors assume the population is unknown and/or infinite. If the population is finite and the sampling rate is high (above 5%), the standard error is in fact too conservative. Intuitively, there is no uncertainty (i.e., zero variance) to the estimate derived from a census with perfect response. An adjustment factor is used to correct for this: {{attachment:fpc.svg}} Again, following from the intuitive case, the factor is 0 when ''n = N'' because there is no uncertainty given a census with perfect response. Contrarily, the factor approaches 1 as ''n'' approaches 0, demonstrating that no correction is required for low sampling rates. Note that this formula (that is, specifying ''N-1'' in the denominator) is appropriate with samples, which is mostly how FPCs are applied anyway. A denominator of ''N'' alone ''is'' appropriate for populations. And note that given a sampling fraction ''f'' defined as ''n/N'', such an FPC can equivalently be expressed as ''√(1-f)''. ---- CategoryRicottone