V2EX finite population correction

Finite Population Correction

释义 Definition

有限总体修正(FPC):在不放回抽样(without replacement)且样本量相对总体不算很小(例如抽样比例较高)时,用来修正标准误/方差的系数,使估计的不确定性更符合“总体是有限的、被抽走一部分后剩余个体更少”的现实。常见形式为
\[ \sqrt{\frac{N-n}{N-1}} \] 其中 \(N\) 为总体容量,\(n\) 为样本量。(也常写成方差层面的 \(\frac{N-n}{N-1}\))

发音 Pronunciation (IPA)

/fanat ppjlen krkn/

例句 Examples

The finite population correction reduces the standard error when the sample is a large part of the population.
当样本占总体比例较大时,有限总体修正会降低标准误。

In a survey sampling 400 students from a school of 1,000, applying the finite population correction can noticeably narrow the confidence interval compared with assuming an infinite population.
在对一所1000名学生的学校抽取400人做调查时,使用有限总体修正,相比假设“无限总体”,会明显缩小置信区间。

词源 Etymology

该术语由三部分构成:finite(有限的)+ population(总体)+ correction(修正)。它来自抽样理论的需求:当总体是有限集合且采用不放回抽样时,样本之间会产生一定的“负相关”,从而使方差/标准误比“近似无限总体或放回抽样”的情形更小,因此需要一个“修正项”来反映这种差异。

相关词 Related Words

文献与著作 Literary / Notable Works

  • Sampling Techniques William G. Cochran(抽样技术经典教材,系统讨论FPC)
  • Sampling: Design and Analysis Sharon L. Lohr(抽样设计与分析中常规出现该概念)
  • Survey Sampling Leslie Kish(调查抽样领域名著,涉及有限总体下的方差修正)
  • Sampling Theory of Surveys with Applications P. V. Sukhatme 等(抽样理论与应用中讨论有限总体修正)
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