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1 英语原意

置信区间：Confidence Intervals

2 英文解释

2.1 单词解释

1) confidence noun (CERTAINTY)

the quality of being certain of your abilities or of having trust in people, plans, or the future

自信；信心，把握；信赖，信任

2) interval noun [C] (TIME/DISTANCE)

a period between two events or times

间隔;间距

2.2 What is Confidence Interval? 什么是置信区间？

A Confidence Interval is a range of values we are fairly sure our true value lies in.

置信区间是我们相当确定其真实值所在的范围。

Example: Average Height 

例子：平均身高

We measure the heights of 40 randomly chosen men, and get a mean height of 175cm,

我们测量了 40 名随机选择的男性的身高，得到的平均身高为 175 厘米，

We also know the standard deviation of men's heights is 20cm. 我们也知道男性身高的标准差是20厘米。

The 95% Confidence Interval (we show how to calculate it later) is: 95% 置信区间（稍后我们将介绍如何计算）为：

The "±" means "plus or minus", so 175cm ± 6.2cm means

±”表示“正负”，因此 175cm ± 6.2cm 可以表示为：

• 175cm − 6.2cm = 168.8cm to 
• 175cm + 6.2cm = 181.2cm

And our result says the true mean of ALL men (if we could measure all their heights) is likely to be between 168.8cm and 181.2cm

我们的结果是，所有男性的真实平均值（如果我们能测量他们所有的身高）可能在168.8厘米到181.2厘米之间

But it might not be!

但事实可能并非如此！

The "95%" says that 95% of experiments like we just did will include the true mean, but 5% won't.

“95%”表示，像我们刚才所做的那样，95%的值为真实平均值，但有5%不是。

So there is a 1-in-20 chance (5%) that our Confidence Interval does NOT include the true mean.

因此，我们的置信区间有 1/20 的几率（5%）不包括真实平均值。

2.3 Calculating the Confidence Interval 置信区间的计算

Step 1: start with

• the number of observations n
• the mean X
• and the standard deviation s

Note: we should use the standard deviation of the entire population, but in many cases we won't know it.

We can use the standard deviation for the sample if we have enough observations (at least n=30, hopefully more).

Using our example:

• number of observations n = 40
• mean X = 175
• standard deviation s = 20

Step 2: decide what Confidence Interval we want: 95% or 99% are common choices. Then find the "Z" value for that Confidence Interval here:

or 95% the Z value is 1.960

Step 3: use that Z value in this formula for the Confidence Interval

Where:

• X is the mean
• Z is the chosen Z-value from the table above
• s is the standard deviation
• n is the number of observations

And we have:

Which is:

In other words: from 168.8cm to 181.2cm

The value after the ± is called the margin of error

The margin of error in our example is 6.20cm

3 中文解释

置信区间是指由样本统计量所构造的总体参数的估计区间。在统计学中，一个概率样本的置信区间（Confidence interval）是对这个样本的某个总体参数的区间估计。置信区间展现的是这个参数的真实值有一定概率落在测量结果的周围的程度，其给出的是被测量参数的测量值的可信程度，即前面所要求的“一个概率”。

置信区间是一种常用的区间估计方法，所谓置信区间就是分别以统计量的置信上限和置信下限为上下界构成的区间 [2]。对于一组给定的样本数据，其平均值为μ，标准偏差为σ，则其整体数据的平均值的100(1-α)%置信区间为(μ-Ζα/2σ , μ+Ζα/2σ) ，其中α为非置信水平在正态分布内的覆盖面积 ，Ζα/2即为对应的标准分数。

4 感想体会

置信区间 Confidence Intervals，Confidence 是信心的意思，Intervals是间隔多长的意思，Confidence Intervals就是样本实测值有多大信心落在一个制定的区间范围内。中文翻译成置信区间，让人一头雾水。

参考文献：https://www.mathsisfun.com/data/confidence-interval.html