|
Size: 1936
Comment: FPC
|
← Revision 3 as of 2025-05-26 21:15:22 ⇥
Size: 0
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 1: | Line 1: |
| = Standard Error = A '''standard error''' of some statistic is the standard deviation of that statistic's sampling distribution. This concept is particularly common for describing the variance of a sample mean; '''standard error of the mean''' is sometimes abbreviated '''SEM'''. <<TableOfContents>> ---- == Evaluation == For an independent sample, the standard error of a mean measurement is the standard deviation of the measurements divided by the root of the sample size: ''σ,,X‾,, = σ,,X,,/(√n)''. Given a random sample of ''n'' observations (''x,,i,,'') from a larger unknown population (''X''), the standard error can be estimated using the sample standard deviation (''s,,X,,''). {{attachment:sem.svg}} === Bernoulli === For a [[Statistics/BernoulliDistribution|Bernoulli-distributed]] mean (i.e., ''p''), the true standard error is ''p(1-p)''. When the mean is unknown or abstracted out, it can be appropriate to assume ''p=0.5''. This maximizes the standard error at 0.25, and is generally considered 'close enough' for a mean between 0.2 and 0.8. As an example, when evaluating sampling plans, standard errors can be 'calculated' for subpopulations without considering any specific measurement by assuming the maximum possible error. ---- == Finite Population Correction == The above evaluation assumes that the population (''X'') is unknown and/or infinitely large. If the population is in fact finite and the sampling rate is high (generally above 5%), that evaluation of standard error is inflated. The '''finite population correction''' ('''FPC''') is a correction factor, calculated as: {{attachment:fpc.svg}} Intuitively, the FPC is 0 when ''n = N'' because there is no room for sampling error in a census. FPC approaches 1 when ''n'' approaches 0, demonstrating that the factor is meaningless for low sampling rates. ---- CategoryRicottone |
