6.1.1 Sampling survey: definition and several groups of concepts 抽样调查：定义与几组概念在线视频

爸爸 你还记得吗
Daddy, do you remember

上次我和二妞想帮妈妈了解
last time, younger sister and I wanted to help mom understand

道路的交通状况时
the traffic condition of roads

知道了许多调查方法
I knew a lot about investigation methods

最近我们学校要举行一场
our school will hold

实践技能大比拼的比赛
a competition of practical skills recently

这次我想实践一下
This time I want to

提交一份调查报告
submit an investigation report

您看可以吗
Do you agree on that

当然好
Of course yes

选好主题了吗
Have you chosen the theme

最近我们班同学
Recently, my classmates

老抱怨说
often complain

学校食堂的饭菜越来越贵
that the food in the school canteen was increasingly expensive

做的也不如原来好吃了
and is not as good as it used to be

我想调查我们学校的学生
I want to investigate

对学后勤服务的满意程度
the satisfaction of students in our school with logistics services provided by our school

我想采用抽样调查这种方式
I'd like to take a sampling survey

可是具体要怎么去抽学生呢
but how will I select students

据我了解通常是随机抽样
As far as I know, the usual practice is

通常是随机抽样
random sampling

难道还有不随机的抽样
Is non-randomized sampling existing

当然有
Of course yes

它具体又有很多种组织形式
It has many kinds of organization forms

使用灵活
and its use is flexible

爸爸你好像很了解的样子
Dad, you seem to know much

能给我介绍介绍吗
Can you introduce more to me

我记得上次看到一个
I remember last time I saw

很好的抽样的例子
a good example of sampling

我来找找看
I'll look for it

找到了
I get it

我们一起看看吧
Let's have a look

我国南部邻邦越南
Vietnam, a southern neighbor of China

在二十世纪中叶爆发了
suffered a long-standing civil war

旷日持久的内战
in the middle of the 20th century

美国当时的几届政府
Several American governments at that time

都卷入了这场战争
were involved in this war

但在越南战争后期
but in the late Vietnam War

美国国内反战情绪与日俱增
the anti-war sentiments in America were increasing

如何向前线补充兵源
How to supplement the sources of soldiers

让当时的美国政府伤透了脑筋
gave a headache to American governments at that time

美国国会1969年12月批准的
According to the new law

新法规定
approved by the United States Congress in December 1969

所有18到25岁的美国籍公民
all 18 to 25-year-old American citizens

都被列为征兵预选对象
are all listed as candidates for conscription

为保证公平性
to ensure fairness

应征对象用抽签方法确定
Candidates were determined by drawing lots

具体步骤是
The specific steps are

将1到366的号码考虑了闰年
Write the dates from the 1st day to the 366th day (a leap year considered)

分别写在外观一样的乒乓球上
on ping-pong balls that look the same

放在一个大容器里进行搅拌
Put them in a large container for mixing

然后逐个随机抽出
Then randomly draw out them one by one

记录次序
and record the order

按指派号码先后顺序
in order of assigned dates

把生日与之对应的年轻人征召入伍
The youths whose birthdays correspond to the dates should be drafted into the service

结果第一次抽到是9月14日
It turned out that the first number drawn out was September 14

所有生日在9月14日的青年
All youths whose birthdays were on September 14

第一批入伍
should join the army first

依此类推
and so on

事后统计学家发现
After the event, statisticians found that

前183个号码中
of the first 183 numbers drawn out

有73个对应的日子在前半年
73 corresponded to the first half of the year

有110个日子在后半年
and 110 to the second half of the year

也就是说
That is to say

生日在后半年的合格青年
the qualified youths whose birthdays were in the second half of the year

服兵役的机会
have more opportunities to perform military service

大于前半年的合格青年
than those whose birthdays were in the first half of the year

造成事实的不公平
thus resulting in factual unfairness

但如果抽样是完全随机的
However, if sampling was completely random

前半年和后半年的日子
the days corresponding to the first half and those to the second half of the year

应该各占一半
should be half and half

73和110的差距太大了
The gap between 73 and 110 was too big

已经不是随机性所能解释的范围
which was beyond the extent that can be explained with randomness

为什么呢
Why?

有人注意到
Someone noticed that

标注日期的乒乓球
ping-pong balls marked with dates

是按1到12月的先后顺序
were put into the container

放入容器的
in the order from January to December

366个球入箱后
After entering the container

没混合均匀
366 balls were not mixed evenly

标有1月份生日的球容易在底下
The balls marked with date numbers of January were easy to be at the bottom

标有12月生日的球容易在上面
and the balls marked with date numbers of December were easy to be at the top

从而导致了非随机性
thus leading to non-randomness

吸取前一年的教训
Drawing lessons from this year

第二年再度组织抽签前
before re-organizing the draw next year

美国国家标准局咨询了统计学家
American National Standards Institute (ANSI) consulted statisticians

具体实施如下
The specific implementation steps were as follows

第一步
Step 1

按随机数表决定的顺序
In the order determined by the table of random numbers

把1到365的数字
put the numbers from 1 to 365

放进365个相同的塑料球里
into 365 identical plastic balls

用同样的方式再把一年365个日期
In the same way, put 365 dates of a year

放入另外365个同样的塑料球里
into another 365 identical plastic balls

第二步把两类365个塑料球
Step 2: Put two types of 365 plastic balls

分别放进各自的滚筒里
into their respective rollers

滚动一小时
and roll them for an hour

这样一人把手伸入日期滚筒
Then a person put his hand into the roller of plastic balls marked with dates

抽出9月16日
to take out September 16

再把手伸入数字滚筒
and then he put his hand into the roller of plastic balls marked with numbers

抽出139号
to take out 139

于是第一轮确定
In this way, it was decided by the first round of draw

9月16号出生的人
that people born on September 16

对应征兵序号139号
correspond to No. 139

依此类推
and so on

步骤虽然复杂
Although the steps were complicated

但充分保证了随机性
The randomness is fully guaranteed

这样的抽样方法
such a sampling method

就是简单随机抽样
is simple random sampling

大家好
Hello, everyone

欢迎来到轻松学统计的课堂
Welcome to the Easy Learning Statistics Class

今天我要给大家讲的是
What I'm going to teach you today is

第六章的内容
the contents of Chapter VI

第六章是抽样与抽样分布
Chapter VI is Sampling and Sampling Distribution

大家都知道
As you all know

抽样是一种常用的统计技术
sampling is a common statistical technique

通常的抽样调查是指
The usual sampling survey refers to

随机抽样调查
random sampling survey

随机抽样调查
Random sampling survey

就是按随机原则
means that some units are taken

从调查对象当中
from the respondents

抽取部分单位
according to the principle of randomization

作为样本进行观察
aas samples for observation

它的目的在于利用样本
Its purpose is to use samples

来推断总体的特征
to infer the characteristics of population

这一章
In this chapter

我先给大家介绍一些
let me introduce you some

常用的抽样方法
common sampling methods

然后回顾几种常见的概率分布
and then review some common probability distributions

最后给大家介绍样本统计量的
Finally, I will introduce the sampling distribution of

抽样分布
sample statistics

这些内容
These contents

主要是为后续的推断统计
are mainly to provide theoretical preparation

做理论上的准备
for the following inferential statistics

今天我们的第一个问题是
Our first question today is

为什么要抽样
why we do sampling

在第二章当中
In the second chapter

我们讲过
we talked about

一些调查的方法
some investigation methods

比如说普查
Including census

再比如说典型调查
typical investigation

重点调查
and key-point investigation

那么我们在讲各种调查方法的时候
When we talk about various investigation methods

说统计调查
statistic survey

按照他所覆盖范围的不同
can be divided into overall investigation

可以分成全面调查
and non-overall investigation

和非全面调查
according to the different coverage

那么抽样调查是属于全面调查
So, a sampling survey is an overall investigation

还是非全面调查呢
or an non-overall investigation

当然
Of course

抽样调查是属于非全面调查的一种
a sampling survey is

调查方式
an non-overall investigation

那么我们为什么要在实践当中
Why should we

采取抽样调查的方式呢
take a sampling survey in practice

因为总体所包含的单位数
Because a population

往往很多
often includes a lot of units

对总体当中的每一个单位
It is unrealistic

都进行观测
time-consuming

往往很不现实
and untimely

费时费力
to observe

而且不及时
every unit in the population

比如说大学生恋爱观的调查
For example, in the investigation of college students' views of love

那么我们往往没有必要
we often don't have to

对我们全国的每一名大学生
to investigate

都展开调查
every college student in our country

这样我们会花费太多的时间和精力
Because we need to spend too much time and energy

那么如果我们展开抽样调查的话
Then if we carry out a sampling survey

我们说首先他非常经济
First of all, we think it's very economical

其次呢
Secondly

我们说时效性更高
we think it's more time-effective

准确性也能够保证
and its accuracy can also be guaranteed

因为科学的抽样调查
Because scientific sampling

事实上是非常准确的
in fact, is very accurate

操作起来也很灵活
and its operation is also very flexible

正如俗话所讲
As the saying goes

如果想知道梨子的味道
if you want to know the taste of a pear

就要亲口尝一尝
you have to taste it yourself

还有一句俗话
There is another saying

你不必吃完整一头牛
you don't have to eat a whole cow

才知道它的肉是咬不动的
only to know that its meat is tough

当然
Of course

还有一些极端的情况
There are some other extreme cases

有一些调查是具有破坏性的
Some investigations are destructive

在这种情况下
under these circumstances

我们就必须采取抽样调查的方式
we have to take the way of sampling survey

比如说对灯管 炮弹的质量调查等等
For example, quality investigation of lamps, shells, etc.

下面我要给大家介绍
Next I want to introduce

抽样涉及的一些基本的概念
some basic concepts involved in sampling

这在后续的学习当中
which we may encounter

我们都可能会遇到
in the following study

第一组概念
The first group of concepts

是总体和样本的概念
are the concepts of population and samples

总体呢
Population

就是根据研究目的
is the whole of things to be researched determined

所确定的所要研究事物的全体
according to the research purpose

那么在抽样当中呢
Then in sampling

我们把总体往往也称其为全集总体
we often call a population a whole population

样本呢
Samples

是按照一定的抽样规则
are a collection of

从总体当中
some elements extracted

抽取的一部分元素
from a population

构成的集合
according to certain sampling rules

那么也叫做样本总体
So they are also called sample population

比如说
For instance

我要从在座的40位同学当中
I want to select 5 students

抽取5名同学出来
from the 40 students in this class

那么我们的总体呢
Then the population

就是我们这个班的40名同学
is the 40 students in this class

而样本呢
And the samples

就是我要抽取的这5名同学
are the 5 students I want to select

那么接下来
Next

第二组概念呢
The second group of concepts

是重置抽样和非重置抽样
are resetting sampling and non-resetting sampling

重置抽样呢
Resetting sampling

也叫回置抽样重复抽样
is also called sampling with replacement, repeated sampling

有放回的抽样
or sampling with return

它是指我们当从总体当中
It means that

去抽取样本单位的时候
when we are taking sample units from the population

我们每抽到一个样本单位
after we

进行观察
have observed and recorded

记录之后呢
every sample unit

我们再放回总体当中
we should put it back into the population

然后再去抽取下一个单位
and then take the next sample unit

这样呢
In this way

我们在整个的抽样过程当中呢
during the whole sampling process

我们总体的单位数
the total number of units in the population

始终没有减少
will never be reduced

总体各个单位
and the probability of

被抽中的可能性
each unit in the population being selected

前后都是相同的
is same all along

那么这个例子呢
For example

比如说我在全班40名同学当中
I want to select

按重置抽样的方式
5 students from the 40 students in the class

抽取5名同学
by resetting sampling

那么我开始先抽取一名同学
Then after I select a student

那么记录好它的信息之后呢
and record his information

那么它参不参加我下一次的抽取呢
will he participate in my next selection

当然参加
Yes, of course

这就是重复抽样
This is repeated sampling

那么不重置抽样呢
Non-resetting sampling

我们又把它叫做无放回抽样
is also called sampling without return

不回置抽样
or sampling without replacement

不重置抽样呢
Non-resetting sampling

是从总体当中
means that after we take

每抽取一个单位之后呢
every unit from the population

不将其放回总体当中
We will not put it back into the population

那么这样的话呢
In that case

也就是说
That is to say

我如果在40名同学当中
If I want to select 5 students

抽5名同学出来
from the 40 students

首先我抽第一名同学之后
After I select the first student

我记录好他的信息之后
and record his information

他还是否参加下一次的抽取呢
will he participate in the next selection

我们说当然它不再参加
Of course not

这就是非重置抽样
This is non-resetting sampling

第三组概念呢
The third group of concepts

是概率抽样和非概率抽样
are probability sampling and non-probability sampling

概率抽样呢
Probability sampling

是依据随机原则抽取样本
Probability sampling is based on the principle of randomization

样本统计量的理论分布存在
Because the theoretical distribution of sample statistics exists

那么我们就可以根据调查的结果
we can infer the population

来推断总体
according to the investigation results

那么关于概率抽样呢
About probability sampling

我们后续会给大家介绍
later we will introduce

简单随机抽样
simple random sampling

分层随机抽样
stratified sampling

以及等距抽样等等
systematic sampling, etc.

而非概率抽样
Not-probability sampling

它是指
is not

不是依据随机原则抽取样本
based on the principle of randomization

样本统计量的分布是不确定的
Because the distribution of sample statistics is uncertain

无法使用样本的结果
we can not infer the population

推断总体
according to the sample results

那么这个部分呢
About this part

我也给大家举了几个例子
I also give you a few examples

比如说我们的方便抽样
such as convenience sampling

滚雪球抽样等等
snowball sampling, etc.

那么下面呢
Next

我们来介绍概率抽样当中的
let me introduce simple random sampling

简单随机抽样
In probability sampling

简单随机抽样
simple random sampling

也被称为单纯随机抽样
just as its name

它是指从总体大N个单位当中
means that we randomly select n units from N units

随机的收取小n个单位作为样本
from the population as samples

使得每一个单位都有相同的机会
so that each unit has the same chance

被抽中
to be selected

简单随机抽样呢
There are many ways

它抽取样本的方法
to take samples

多种多样
by simple random sampling

但它的基本的要求呢
But it has a basic requirement

是要把总体各个单位
that all units of the population

全部编号
must be numbered

然后呢
Then

可以采取抽签 摇号
we can determine the units selected

或者查随机数字表的方式
by draw, lottery

来确定所抽的单位
or random number table lookup

简单随机抽样
Simple random sampling

在抽样理论中
in sampling theory

是作为其它抽样
serves as the basis of

组织方法的基础的
other sampling organization methods

它的理论发展是最成熟的
Its theoretical development is most mature

抽样效率和估计精度
and its sampling efficiency and estimation accuracy

也很理想
are also ideal

但简单随机抽样
However, simple random sampling

也有它的局限性
also has its limitations

首先呢
First of all

从我们刚才介绍的简单随机抽样的
from the implementation methods for simple random sampling

实施方法当中
that we just introduced

大家可以看出
you can see

它有一个前提
its basic requirement

就是要求呢
that

我们对总体当中的
we should

每一个单位
number

都要编号
every unit of the population

这意味着
which means

我们必须有包含所有总体单位的
that we must have

一个完整的抽样框
a complete sampling frame including all units of the population

那么这里呢
Here

我们提出了一个概念
we put forward a concept

就是抽样框的概念
the concept of sampling frame

那么抽样框呢
Sampling frame

在抽样调查当中
serves as the basis of sample taking

它就是我们抽样的依据
In sampling survey

它的形式呢
its forms include

有名单抽样框 区域抽样框
list sampling frame, area sampling frame

时间表抽样框等等
schedule sampling box, etc.

那么当N很大的时候
When N is very big

这个抽样框常常是不具备的
this sampling frame is often not available

或者呢
or

我们要准备这样的抽样框很费事
it's very difficult for us

难以做到
to prepare such a sampling frame

其次呢
Secondly

我们用简单随机抽样
the samples

抽到的样本呢
that we take by simple random sampling

往往很分散
are often highly scattered

要找到每一个样本单元
It is very difficult

并且实施调查
to find every sample unit

在实际当中呢
and carry out an investigation on it

会遇到很多的困难
In practice

例如2015年
for example, in 2015

我们国家进行了1%人口的抽样调查
our country conducted a sampling survey of 1% of the population

如果采取简单随机抽样的方式
If simple random sampling is adopted

我们要对我们国家13亿多的人口
we need to number

每个人都编上号
more than 1.3 billion people in our country

这样编制一个完整的抽样框
In that case, it's actually impossible

实际上是不可能的
to prepare a complete sampling frame

即使有这种可能性
Even if there is such a possibility

那么我们抽到1300多万人
then we will take a sample

构成的样本
consisting of more than 13 million people

那么我们要落实到
It is also unimaginable

每一个被抽中的人
for us to carry out an investigation on

这个工作也是难以想象的
everyone who has been selected