Statistics 简明教程

Statistics - Standard Error ( SE )

抽样分布的标准偏差称为标准误差。在抽样中，三个最重要的特征是：准确性、偏差和精确性。可以这么说：

The standard deviation of a sampling distribution is called as standard error. In sampling, the three most important characteristics are: accuracy, bias and precision. It can be said that:

  1. The estimate derived from any one sample is accurate to the extent that it differs from the population parameter. Since the population parameters can only be determined by a sample survey, hence they are generally unknown and the actual difference between the sample estimate and population parameter cannot be measured.

  2. The estimator is unbiased if the mean of the estimates derived from all the possible samples equals the population parameter.

  3. Even if the estimator is unbiased an individual sample is most likely going to yield inaccurate estimate and as stated earlier, inaccuracy cannot be measured. However it is possible to measure the precision i.e. the range between which the true value of the population parameter is expected to lie, using the concept of standard error.

Formula

其中——

Where −

  1. ${s}$ = Standard Deviation

  2. and ${n}$ = No.of observations

Example

Problem Statement:

Problem Statement:

计算以下单独数据的标准误差：

Calculate Standard Error for the following individual data:

Items

14

36

45

70

105

Solution:

Solution:

首先计算算术平均值 $\bar{x}$

Let’s first compute the Arithmetic Mean $\bar{x}$

现在计算标准偏差 ${s}$

Let’s now compute the Standard Deviation ${s}$

因此，标准误差 $SE_\bar{x}$

Thus the Standard Error $SE_\bar{x}$

给定数字的标准误差为 15.63。

The Standard Error of the given numbers is 15.63.

抽样总体所占比例越小，这个倍数的影响就越小，因为这时有限倍数将接近 1，并且对标准误差的影响可以忽略不计。因此，如果样本量小于总体规模的 5%，则忽略有限倍数。

The smaller the proportion of the population that is sampled the less is the effect of this multiplier because then the finite multiplier will be close to one and will affect the standard error negligibly. Hence if the sample size is less than 5% of population, the finite multiplier is ignored.