6.2.1 Probability sampling: common organizational forms 概率抽样：常用组织形式在线视频

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Hello, everyone! Welcome to

轻松学统计的课堂
the Easy Learning Statistics Class

下面我要给大家介绍几种
Now I'd like to introduce some

常用的抽样组织形式
common sampling organization forms to you

比如说分层随机抽样
including Stratified sampling

整群抽样 等距抽样等等
cluster sampling, systematic sampling, etc.

那么我们先来说这个
Let's start with

分层随机抽样
stratified sampling

分层随机抽样是将抽样单位
Stratified sampling means that

按照某种特征或者某种规则
we divide sample units

划分为不同的层
into different stratums according to some characteristics or rules

然后从不同的层当中
and then take samples

独立随机的抽取样本
independently and randomly from different stratums

那么大家来看一下
Let's take a look

我们这个图片
at this picture

那么在这个图片上
There are many small animals

我们有很多的小动物
in this picture

有海豚 有恐龙 有青蛙
such as dolphins, dinosaurs and frogs

那么我们如果是采取
If we adopt

简单随机抽样的话
simple random sampling

我们应该怎么做呢
then what should we do

我们是首先要对它们
First of all, we need to

一一的进行编号
number all sample units one by one

然后采取抓阄 生成随机数等等方式
and then we need to draw lots, generate random numbers or take other ways

来找到样本单位
to find sample units

但是我们这样去抽取样本单位
However, if we draw sample units in this way

我们可能会有一个弊端
there may be a disadvantage

就是我们抽取到的这个样本单位
that is, the sample units we have drawn

有可能集中在某一种动物上
may be concentrated on a certain animal

比如说很可能青蛙比较多
For example, frogs likely are

然后恐龙很少
much more than dinosaurs

那么这样的话
In this case

我们这个样本的结构
The structure of our sample

跟总体的结构
does not match

我们说就没有匹配上
that of the population

那么这样的话
which

就会影响我们样本的代表性
may affect the representativeness of our sample

那么我们分层随机抽样怎么抽呢
So how to take sample units in stratified sampling

我们分层随机抽样
Stratified sampling

就是要把这些小动物
means that we should classify

我们说同类的归为一层
the same type of small animals into a stratum

然后我们就在每一个类里面
and then randomly select sample units

随机的去抽取样本单位
In each stratum

比如说我会在海豚里面抽几个
for example, I draw a few units from dolphins

在恐龙里面抽几个
dinosaurs

在青蛙里面抽几个
and frogs respectively

这样的话
In this way

我有多少种动物
all types of animals I have

我抽到的这个样本
will be included in the sample

就会包含哪几种动物
I have selected

这样的话我们样本的结构
In this case, the structure of our sample

就跟总体的结构非常的接近
is very close to that of the population

这样的话
which

有助于提高抽样的精度
helps to improve the accuracy of sampling

比如说我们另外一个例子
There is another example

我们在40名同学当中抽10名同学
If we want to select 10 students from 40 students

那么我们完全可以
we can absolutely

先对我们这个总体进行分层
stratify the population first

我们对我们40位同学
What characteristics

可以按哪些特征进行分层
can we stratify these 40 students by

当然我们可以按照性别
Of course, we can divide them

按照民族 按照年龄等等特征
according to their gender, ethnic group, age

进行分层
or any other characteristic

那么我们分好了层之后
After we have stratified them

我们再对每一个层展开随机抽样
we need to carry out random sampling for each stratum

就在每一个层里
That is to say, we need to

再去随机抽取样本单位
randomly take sample units in each stratum

这样的话
Then

我们就完成了
we will have completed

分层随机抽样的这个过程
the process of Stratified sampling

那么分层随机抽样的优点
Of course, stratified sampling

当然是非常明显的
has a very obvious advantage

就是我们能够保证
That is, it can ensure that

我们的样本的结构
the structure of the sample we take

跟总体的结构比较相近
is relatively similar to that of the population

提高估计精度
so as to improve the estimation accuracy

那么在说到这一点
Speaking of this

也希望大家在做
I also hope that you can

分层随机抽样的时候注意一点
pay attention to a point when doing Stratified sampling

就是我们分层随机抽样
That is, when doing stratified sampling

我们对各个层
we conduct a comprehensive investigation

是展开全面调查的
on each stratum

那么到了层内
but then we do random sampling

我们是展开随机抽样的
within the stratum

这样的话
In this case

我们分层随机抽样的抽样误差
the sampling error in Stratified sampling

它主要来源于层内的方差
mainly comes from the variance within the stratum

而跟层间的方差是没有关系的
but has nothing to do with the variance between stratums

那么这样的话
Therefore

就要求我们
we should

在分层随机抽样的过程当中
divide the individuals with the same properties

我们应该使性质相同的个体
into a stratum

划为一层
during stratified sampling

而层和层之间的差异
And the differences between stratums

应尽可能的大
should be as large as possible

这样的话我们分层随机抽样
In this way, stratified sampling

它就有助于提高
Will help to improve the accuracy of

我们抽样调查的精度
sampling investigation

另外我们分层随机抽样的优点
In addition, stratified sampling

是它的组织实施起来比较方便
has the advantage of convenient organization and implementation

因为我们可以针对各个层
Because we can

它具体的一些特点
carry out investigation

来展开我们的调查
according to some specific characteristics of each stratum

那么分层随机抽样
through Stratified sampling

我们说除了可以对总体参数
We can not only estimate

进行估计
the parameters of the population

我们也可以对各层的目标量
but also estimate

进行估计
the target quantity of each stratum

这都是分层随机抽样的优点
These are the advantages of Stratified samplingd

那么分层随机抽样的缺点
The disadvantage of stratified sampling

就是需要我们事先准备好
lies in that we need to prepare

层的抽样框
the sampling frame for each stratum in advance

因为我们要对
because we need to

各个层展开全面调查
carry out comprehensive investigation on each stratum

下面我们再来看一个例子
Let's take another example

那么一个单位
A enterprise

他的职工有500人
has 500 employees

那么不到35岁的有125个人
including 125 less than 35 years old

35岁到49岁有280个人
280 35 to 49 years old

50岁以上有95个人
and 95 over 50 years old

那么我们这个时候如果想了解
At this time, if we want to know about

这个职工身体状况方面的
a certain physical

某项指标
indicator of employees

那么这个时候
then

我们要在这500个人里面
we need to take a sample consisting of 100

抽取100个人的样本
of these 500 people

那么因为职工的年龄
Because the age of employees

跟身体状况的这个指标有关系
is related to this physical indicator

所以我们可以采取
we can take the sample

分层随机抽样的方法进行抽取
through Stratified sampling

那么这个时候我们的样本容量
Here the ratio of our sample size

与总体的单位数的比为1比5
to the total number of units of the population is 1:5

因为我们要在500个里面抽100个
Because we need to select 100 of 500 people

所以我们在各个年龄段抽取的
The number of people we will select from each age group

个数依次应该为125除以5
should be equal to 125÷5

280除以5和95除以5
280÷5 and 95÷5

也就是我们在各个年龄段
That is, we need to select 25, 56 and 19 people

要分别抽取25 56 19个人
from each age group respectively

那么大家想一下
Just think about it

如果在这个例子当中
If we adopt simple random sampling

我们采取简单随机抽样的话
in this example

很可能我们抽的这个年龄段
It's likely that the people we select

集中在某一个年龄段上
will be concentrated on the same age group

那么这样的话
thus

就影响了样本的这个代表性
affecting the representativeness of the sample

那么我们采取分层随机抽样
If we adopt Stratified sampling

我在每一个年龄段都抽取了
we take the corresponding number of sample units

相应的这个样本单位数
in each age group

这样的话
In this case

我们说我们样本的结构
the structure of our sample

就跟总体的结构非常的接近了
is very close to that of the population

那么有利于提高估计的精度
which is conducive to improving the accuracy of estimation

那么这就是分层随机抽样
This is stratified sampling

那么接下来我们给大家再介绍
Next, we will introduce

一种常见的抽样组织形式
a common sampling organization form

整群抽样
cluster sampling

整群抽样是将总体所有的单位
Cluster sampling means that

首先合并为组或者说是群
we combine all units of the population into groups or clusters first

然后在抽样的时候
then directly select clusters

我们直接去抽取群
during sampling

然后对抽中的群的所有单位
and finally conduct a comprehensive investigation

展开全面调查
on all units of each cluster selected

这就是整群抽样
This is cluster sampling

那么这个整群抽样
Then let's compare

我们说他跟这个分层随机抽样
cluster sampling

我们来做一个对比
with Stratified sampling

在刚刚讲过的分层随机抽样当中
In stratified sampling just mentioned

我们是要求大家把
you are required to

类型相同的个体划分为同一个层
divide individuals of the same type into the same stratum

也就是层内的这个方差
That is, the variance within the stratum

要尽可能的小
should be as small as possible

层间的方差要尽可能的大
while the variance between stratums should be as large as possible

那么刚才我给大家介绍整群抽样
When I just introduced cluster sampling to you

我们说我们也有一个分群的这个过程
there was also a process of clustering

那么我们这个分群的过程
so is the process of clustering

跟刚才分层随机抽样当中
same as the process of stratification

分层的过程是不是一样的呢
in Stratified sampling

我们说当然不一样
Of course not

整群抽样过程当中
During cluster sampling

我们分群的过程是要使
the process of clustering

群和群之间的这个差距尽可能的小
is aimed to make the difference between clusters as small as possible

群内的差异尽可能的大
and the difference within clusters as large as possible

这是为什么
Why

因为整群抽样
Because in cluster sampling

我们对抽中的群
we conduct a comprehensive investigation of

是展开全面调查的
each selected cluster

其实我们抽中的群展开全面调查
In fact, after we conduct a comprehensive investigation of each selected cluster

我们对它的了解
we have a very thorough

其实就已经非常的透彻了
understanding of it

那么这个时候就要求群和群之间
At this time, it is required that different clusters

是尽可能相似的
should be as similar as possible

那么我们只要抽中部分的群
So we only need to select some clusters

那么就可以对总体的情况
to have a full understanding of

有一个比较充分的了解了
the population

所以这是整群抽样 分群
This is the difference between

和我们分层随机抽样 分层
clustering in cluster sampling

它的区别
and stratification in Stratified sampling

也就是说
That is to say

分层我们要层和层之间的差距
we should make the difference between stratums

尽可能的大
as large as possible during stratification

而分群我们要群和群之间的差异
while we should make the difference between clusters

尽可能的小
as small as possible during clustering

那么这主要就是因为整群抽样的
This is mainly because the sampling error

这个我们的抽样误差
in cluster sampling

主要来源于群内的方差
mainly comes from the variance within the stratum

而跟群间的方差无关
but has nothing to do with the variance between clusters

大家想一想
Let's think about

为什么跟群间的方差无关呢
why does it have nothing to do with the variance between clusters

因为我们对所有
Because we have carried out

我们对抽中的群
a comprehensive investigation on

展开的是全面调查
each selected cluster

就是这个原因
That is the reason

那么整群抽样
So how should we

我们刚刚讲过它怎么做了
do cluster sampling as we just introduced

那么在这里
Here

大家再想想
Let's think about

我们刚才举的那个小动物的那个例子
that example of small animals we just mentioned

那你整群抽样怎么抽呢
How should we take the sample during cluster sampling

其实我们就是说
In fact

你每个群里都应该有海豚
every cluster should include dolphins

都应该有青蛙
frogs

都应该有恐龙
and dinosaurs

那么我们每个群都很接近
All of our clusters are very similar

都是这样的
and all of them

都包含这三种小动物
include these three small animals

那么这个时候
At this time

我们了解这个总体
if we want to understand the population

完全就可以在所有的群里面
we can randomly select several clusters from the population

随机抽取几个群展开全面调查
and then carry out a comprehensive investigation of each of them

对不对
right

所以这个就是整群抽样的这个做法
So this is cluster sampling

那么另外再比如说
Take another example again

我们要在
If we want to

我要在江西财经大学
sample 200 students

所有的学生里面
from all students

我要抽两百个同学
in Jiangxi University of Finance and Economics

那么当然我可以采取
Of course, I can adopt

简单随机抽样的方式
simple random sampling

但是这个简单随机抽样的方式
but the process of simple random sampling

太麻烦了
is too troublesome

我们要对江西财经大学
First of all, we need to number

所有的学生进行一个编号
all students of Jiangxi University of Finance and Economics one by one

然后我们再
Moreover

比如说查随机数字表
it is almost impossible to

然后确定样本单位
check the random number table

这个几乎是不可能完成的
and then determine sample units

那如果我要在所有的学生当中
Then if I want to select 200 students

抽200个学生
from all students

按照分层随机抽样的方式怎么抽呢
by stratified sampling, how should I do

那么大家也能想的到
you can imagine that

比如说我们就按年级
for example, we

进行一个分层
divide all students

我们比如说仅只限于这个本科生
(only including undergraduates) into different stratums by grade

那么一年级一个层
one stratum for grade one

二年级一个层
one stratum for grade two

三年级一个层
one stratum for grade three

四年级一个层
one stratum for grade four

那么我们可以按年级
and then we can take sample units

分别去抽取样本单位
by grade

这样的话
In this way

我的样本就都包含了
our sample includes

所有年级的这样一个总体单位数了
units of the population in all grades

那么如果我按整群抽样来做的话
If I do cluster sampling

我觉得应该是更加简便
I think it should be easier

我们怎么做呢
what should we do

我们是首先统计一下
First of all, let's count

我们江西财经大学的这个本科生
how many undergraduate classes

有多少个班级
There are in Jiangxi University of Finance and Economics

比如说我们假设有600个班级
For example, let's assume that there are 600 classes

那个这个班和班之间
the difference between classes

其实差异是很小的
is very small

其实也就是我们整群抽样当中
and these classes are actually

所说的群
the clusters involved in cluster sampling

那么我要抽两百个学生出来
If I want to select 200 students

我就可以在这600个班级当中
I can randomly select 4 classes

比如说我随机抽取4个班
from these 600 classes

假设一个班50人
Suppose there are 50 students in a class

4个班就200人
200 students are distributed in four classes

那么这样的话
then

我就对抽中的班
I can carry out a comprehensive investigation on

展开全面调查了
each selected class

这样的话
In this way

大家可以看出整群抽样
you can see that the advantage of cluster sampling

它的优点
lies in

就是它的调查的这个点
that the investigation involved in it

是当对比较集中的
is relatively concentrated

你要按简单随机抽样
If we adopt simple random sampling

即使抽到了200个学生
even if 200 students are selected

我一个一个去找这些学生
It is also a heavy workload for us

这个工作量也是很大的
to take these students out one by one

但是采取整群抽样
But if we adopt cluster sampling

我就抽到 比如说就抽到4个班
we only need to select four classes

我找这4个班相对是比较容易的
It is relatively easy for us to take these four classes out

那么这样的话
So

在具体的这个调查过程当中
in the specific investigation process

就有助于我们节省调查费用
it will be conducive to saving investigation costs

方便调查的这个实施
and promoting the implementation of investigation

另外我们在抽样的时候
In addition, we only need

只需要群的抽样框就可以了
the sampling frame of each cluster when sampling

那么这样的话
In this case

我们对抽中的群
we can only find out

我就找到他
each selected cluster

展开全面调查就可以了
and carry out a comprehensive investigation on it

没有抽中的群那就可以不管它
and we can ignore those unselected clusters

所以整体来讲是可以简化工作量的
On the whole, cluster sampling can reduce the workload

但是正如我们刚才举的例子当中
However, as reflected in

反映出来的
the example we just mentioned

那么我抽两百个学生
I select 200 students

然后对其实就是从600个班级当中
That is, I select these four classes

抽这四个班出来
from the 600 classes

那我对这四个班级的学生
and then carry out a comprehensive investigation of

展开全面调查
the students in these four classes

这个样本的代表性如何呢
How about the representativeness of this sample

那么大家也觉得
You also think that

其实代表性肯定是不如
the representativeness of this sample

我们之前讲的简单随机抽样
is certainly not as good as that of the sample taken

和分层随机抽样的
through simple random sampling or Stratified sampling we mentioned before

因为比如说我们就抽到了
Because if we have selected

会计的班
accounting class

抽到了金融的班
finance class

或者是抽到了这个国际商务的班
and/or international business class

那么你抽中这个班
and then we use

用这几个班来代表
one or more classes we have selected to

我们所有的这个总体单位
represent all units of the population

那么这个代表性肯定是
the representativeness is definitely

有所欠缺的
insufficient

那么这个就是我们要讲的
This is cluster sampling

整群抽样
We want to introduce

再下面我们就是系统抽样
next is systematic sampling

系统抽样是将总体当中所有的单位
Systematic sampling means that we arrange all units of the population

按一定的顺序排列
in certain order

然后在规定的范围里面
then randomly select one unit

先随机的抽取一个单位
as the initial unit

作为初始单位
within the specified range

然后再按照规定好的这个规则
and finally determine other sample units

确定其他的样本单位
according to the specified rules

那么系统抽样当中
The most common form of

我们说最常见的就是
systematic sampling

等距抽样
is systematic sampling

等距抽样是怎么做的呢
How should we do systematic sampling

比如说我们所有的这个总体单位
That is, each unit of the population

它都有一个顺序
has a sequence number

那么我们先在前面的1到K个
First of all, we randomly select a number

这个单位之间随机选一个数字
between unit 1 and unit K

比如说R作为我们的初始单位
For example, suppose R is our initial unit

然后我们以K为
and K is

这个相等的这个间距
the equal interval

然后依次抽取
We take units in sequence

接下来就是抽R+K
So next we should take units R+K

R+2K R+3K等单位
R+2K, R+3K and so on

那么大家看
Please

我们这张图
look at this picture

这张图就展示了这个系统抽样
This picture shows

也就是我们这里举的例子
the implementation process of systematic sampling

等距抽样
in systematic sampling

它的这个抽样的这个实施的过程
that is, the example we give here

也就是说它先确定一个初始单位
In other words, we determine an initial unit first

然后按照相等的这个间距去抽
and then take sample units at equal intervals

那么下面我们再来看一个例子
Let's take another example

比如说我们要用系统抽样的方法
For example, if we want to

从160名学生当中
take a sample consisting of 20 students

抽取容量为20的一个样本
from 160 students through systematic sampling

那么先我们先当然对这160名学生
we should number these 160 students

要有一个编号
one by one first

然后这个编号我们就排序了
and then sort the numbers

排序之后
After sorting the numbers

我们按平均分
we divide them into 20 groups

就可以分成20组
on average

那么这20组分别是1到8号
so the 20 groups are 1 to 8

9到16号
9 to 16 …

依此类推
and so on

最后一组比如说153到160号
And the last group is 153 to 160

那么我们随机的在1到8号里面
Then we randomly determine an initial number X

先确定一个初始的编号X
in numbers 1 to 8

接下来我们就按照
Next

我们刚才所讲的
as we just mentioned

比如说我们按照
we will follow

X+K X+2K等等等等
the law of X+K, X+2K …

依次类推
and so on

这样的规律来确定样本单位
to determine sample units

那么这个就是我们系统抽样
This is the process of sampling

它的这个抽样的这个做法
in systematic sampling

那么这个系统抽样
Systematic sampling

我们说总体而言
Generally speaking

它的操作是比较简便的
is relatively easy to operate

那么可以提高估计的精度
and can improve the accuracy of estimation

那么具体在操作的时候
In the concrete operation

比如说等距抽样
in case of systematic sampling

我们可以按有关标志进行排队
we can sequence according to relevant signs

也可以按无关标志进行排队
or irrelevant signs

按有关标志排队的意思
sequencing according to relevant signs means

就是我们所这个依据排序的这个标志
that the signs based on which we sequence

跟我们所研究的这个内容
are related to

是联系在一起的
the contents we study

你比如说我要想这个
For example, if I want to

调查学生的这个学习成绩的情况
investigate students' academic performance

那我就按这个
First of all

首先把学生按成绩进行排序
I need to rank students according to their performance

那么确定初始单位之后
and determine an initial unit first

我按照相等的间距去抽
and then take sample units at equal intervals

那么这样的话
In this way

大家看看
Let’s take a look at

按照这个等距抽样
the sample units taken

抽取出来的这个样本单位
through systematic sampling

它对总体也有很好的代表性
They are also very representative of the population

因为所有的这个成绩的
Because they represent

这个分数段的这个学生
all students

我都有代表
at all levels of performance

那如果是按无关标志进行排队
Then if sequence is based on irrelevant signs

进行等距抽样
in systematic sampling

是怎么做的呢
how should we do

比如说我们还是想考察学生的成绩
For example, if we still want to investigate students' academic performance

但是我对学生排序的时候
but we rank these students

我们是按这个学生的姓氏笔划
according to their

来进行排序
surname strokes

然后再按一定的规则去抽
and then take sample units according to certain rules

按无关标志排序这种等距抽样
Systematic sampling, for which sequence is based on irrelevant signs

我们说比较类似于
is similar to

简单随机抽样
simple random sampling

而按有关标志进行排序
The main disadvantage of

进行的这个系统抽样
systematic sampling, for which sequence is based on relevant signs

我们说它的缺点主要在于
lies in

它的这个估计量的方差
that the estimator of variance

比较难以计算
is difficult to calculate

那么再接下来
Next

我们再给大家介绍
we will introduce to you

在现实当中
a commonly used sampling organization form

使用的比较多的一种抽样组织形式
in reality

就是多阶段抽样
-- multi-stage sampling

因为在具体的工作当中
Because the problems

我们说我们面临的问题
we face in specific work

相对是比较复杂的
are relatively complex

所以我们往往就是一阶段抽样
we often can't get

其实抽不到我们所要抽的
the sample units we want

这个样本单位
through one-stage sampling

这个时候需要
At this time

多阶段的这个工作才能完成
multi-stage sampling is required

那么多阶段抽样一般是这样的
Generally, multi-stage sampling goes like this

就是我先抽群
We should select clusters first

那么先抽群
When we are selecting clusters

如果是整群抽样
if we do cluster sampling

就是我抽到了群
after selecting clusters

我要对这个群里所有的单位
we need to conduct a comprehensive investigation of

要进行全面调查
all units in each cluster

但是多阶段抽样不是这样
but this is not the case with multi-stage sampling

就是我先抽到了群
That is, after I select clusters first

再接下来我对抽中的群
I need to take sample units

再去抽样
from each selected cluster

也就是说我对于抽中的群
That is to say, I should select several units

再去抽取若干个单位进行调查
from each selected cluster for investigation

那当然可能二阶段
Of course, the whole sampling process

可能三阶段
may be completed

可能四阶段等等
in two stages

才能完成这样一个
three stages

整体的这样一个抽样过程
four stages … and so on

那么我们说最常见的例子
The most common example

就是我国的这个农产量的这个调查
is the investigation of agricultural production in our country

我国的这个农产量的调查
in the investigation of agricultural production in our country

我们先是比如说从
For instance

从我们全国所有的省里面
we sample cities

先去抽市
from all provinces in our country first

对抽中的市
then sample villages

我们再从它的这个市里面
from the cities we have sampled

再去抽乡

对抽中的乡我们再去抽村

然后接下来到了村这一步
and finally sample-specific plots of land

我们再去抽具体的这个地块
from the villages we have sampled

进行农产量的调查
to investigate agricultural production

大家看你完成这样一个抽样过程
As we can see, we complete such a sampling process

需要多个阶段
in many stages

这就是多阶段抽样的这个做法
This is multi-stage sampling

那么多阶段抽样我们说在现实当中
Multi-stage sampling is widely used

它是用的比较多的
in reality

那么多阶段抽样
The advantage of

它的优点就是
multi-stage sampling

它的样本相对集中
is that its sample units are relatively concentrated

这跟整群抽样是非常相似的
which is very similar to that of cluster sampling

那么也就在实践当中
so in practice

是比较节约调查费用的
multi-stage sampling is relatively cost-effective

但是我们在具体做的过程
However, in the specific process

要包含所有第一阶段
we should get the sampling frame of

抽样单位的抽样框
all sample units in first stage

就你每一步每一步去抽的时候
that is, we should be supported by

都要有相应的这个抽样框的支持
the corresponding sampling frame to each sampling

那么这个就是多阶段抽样
This is multi-stage sampling

所以我们一般的大规模的
Therefore, generally speaking

抽样调查
large-scale sampling investigations

经常都是采取
are often completed

多阶段抽样的这个方式
through multi-stage sampling