8.6.1 P value: another test criterion P值：另一个检验准则在线视频

大家好
Hello, everyone

欢迎回到轻松学统计的课堂
Welcome back to the Easy Learning Statistics Class

这一讲
In this lecture

我们要给大家讲一讲P值
we will talk about the P value

为什么要给大家讲P值呢
Why shall we talk about the P value

是因为我们在做一些
Because when conducting

计量经济学检验的时候
some tests about econometrics

大家在软件输出结果里面
everyone often sees several P values

经常会看到几个P值
in the output result in the software

那么P值
So what exactly is

它究竟是什么呢
the P value

我们为什么可以根据P值
Why can we make judgment on the test result

对检验的这个结果作出判断呢
in accord to the P value

那么P值它事实上
Well, the P value is in fact

就是一个实际的显著性水平
an actual significance level

那么又叫
also called

观察到的显著性水平
the observed significance level

如果原假设是正确的话
If the null hypothesis is correct

那么我们得到
then how high is the probability

目前的这个样本
that we get

它的可能性有多大
the current sample

当然如果这个可能性很小的话
Of course, if this probability is very small

那么我们就应该拒绝原假设
then we should reject the null hypothesis

所以利用P值做假设检验
So the P value is used for hypothesis testing

它的决策规则
Its decision-making rule

就是如果P值小于显著性水平α
is: If the P value is smaller than α, the significance level

那么我们就拒绝原假设
then we simply reject the null hypothesis

这里我们当然还可以
Of course, here we can also

根据P值的大小
judge how strongly we reject the null hypothesis

来判断我们拒绝原假设的力度
depending on the magnitude of the P value

P值越小
The smaller the P value

我们拒绝原假设的力度越大
the more strongly we reject the null hypothesis

为什么呢
Why

大家想一想
Everyone has a think

在我们假设检验当中
in hypothesis testing

我们事先规定了
we have prespecified

小概率事件的概率
the probability of small probability event

就是显著性水平
namely the significance level

我们认为
We believe

一旦小概率事件发生
once the small probability event happens

我们就有理由拒绝原假设
we have the reason to reject the null hypothesis

而P值
While the P value

它是说你实际观测到的
indicates the probability that

这个样本统计量的取值
the value of the sample statistic you have actually observed

它发生的概率
occurs

当然这样说
Of course

并不是非常严谨
this does not sound quite rigorous

因为我们说取到
Since we say

在连续型随机变量的
under the premise that

这个前提下
the random variable is continuous

那么这个随机变量取到
it follows that the probability

任何一个点的概率应该是0
of this random variable at any point should be zero

所以我们P值的定义当中
So the P value

是这样讲的
is defined this way

它是说你取到
Once you get the probability

现在得到的这个点
at the point

以及比这个点更极端
as well as at the more extreme point

更不可能发生的这个概率
where the event is even unlikely to happen

那么这个就是P值
this is the P value

P值的定义中
The definition of P value

蕴含了显著性检验的
contains the basic thinking method

基本思维方法
of significance test

这种思维方法
which

几乎被运用到所有主流的
is almost applied in all mainstream

统计学分析之中
statistical analyses

对它的准确理解
Accurate understanding of it

不仅是通向掌握各种具体的
is not a mere gate leading to various specific

统计学测试的大门
statistical tests

更影响着
but it also affects

我们对统计分析结果的解读
our interpretation into the result of statistical analysis

下面我们大家看几张图
Below let’s see a few graphs

在这几张图中
In them

我们会理解P值的含义
we will understand the connotation of P value

大家看第一张图
Let’s look at the first graph

在这张图上
In it

我们说
we say

这是一个双侧检验的情形
this is a circumstance of two-sided test

那么我们刚才给出
Just now we presented

双侧检验的检验规则
the testing rules of two-sided test

就是如果检验统计量的取值
namely if the value of the test statistic

处在我们两侧的拒绝域的话
is located on either side of the rejection region

那么我们就要拒绝原假设
then we shall reject the null hypothesis

那么这里P值
So what does the P value

指的是什么呢
refer to here

大家看
Everyone notices

我们两个红色的这个箭头
the two red arrows

也就是说
In other words

如果我们检验统计量的取值
if the value of the test statistic

取到了某一个点
falls at a certain point

那么取到这个点
then the probability of reaching this point

以及比这个点
as well as falling in the region

更不可能的区域的概率
more impossible than this point

就是P值
is the P value

所以大家在这张图上
So in this graph

可以看到两侧蓝色的
everyone can see the areas

这个区域 这个面积
of the regions in blue on both sides

我们说
We say

加起来就一共就是P
they add up to P

两侧各为P/2
P/2 on each side

那么单侧检验的情况
The same goes with

道理是一样的
the case of one-sided test

大家看我们这张图
Let’s look at another graph

我们这张图
This graph

是一个左侧检验的例子
is an example of left-sided test

在这个例子当中
In this example

我们刚才说
we have just said

我们在左侧检验的时候
the rejection region is on the left side

我们拒绝域在左边
in the case of left-sided test

我们确定了我们的临界值
Now that we have determined the critical value

那么我们检验统计量的取值
as long as the value of the test statistic

只要落在这个拒绝域里面
falls in the rejection region

那么我们就要拒绝原假设
we shall reject the null hypothesis

那么P值指的是什么呢
So what does the P value refer to?

就是你取到某一个点
It means when you get a point

以及比这个点
as well as the region

还不可能的这个区域
more impossible than this point

那么大家看
Everyone notices

当然在我们这个图上
it is definitely the region in blue

就是这个蓝色的这个区域了
in this graph -

那么这一块的面积
then this area

就是P值
is the P value

大家想 我这个P值
Everyone imagines, if the P value

如果小于α
is smaller than α

事实上就意味着
it in fact means

小概率事件发生了
the small probability event happens

所以我们要拒绝原假设
and thus we shall reject the null hypothesis

反过来
Conversely

如果P值大于α的话
if the P value is greater than α

那事实上
then in fact

检验统计量的取值
the value of the test statistic

一定是取在了接受域里面
must fall in the acceptance region

所以我们不能拒绝原假设
so we cannot reject the null hypothesis

下面我们看右侧检验的这个例子
Now let’s look at an example about right-sided test

在右侧检验这张图当中
In the graph of right-sided test

我们的拒绝域在右边
the rejection region is on the right side

那么如果检验统计量的取值
So if the value of the test statistic

取在了拒绝域里面
falls in the rejection region

我们就拒绝原假设
we simply reject the null hypothesis

那么大家也可以看到
Everyone can also notice

当检验统计量的取值
if the value of the test statistic

取在了拒绝域的时候
falls in the rejection region

那么我们的这个P值
then the P value

它肯定是小于α的
must be smaller than α

所以我们决策的规则
So our decision-making rule

就是只要P小于α
is, as long as P is smaller than α

那么我们就有理由
we have the reason

拒绝原假设
to reject the null hypothesis

下面我们总结一下
Below let’s have a summary

总而言之
In sum

我们P值
the P value

它是一个关于数据的概率
is a probability about data

它反映的
What it reflects

就是在某一个总体的
is, among a lot of samples

许多样本当中
from a population

某一类数据出现的经常程度
the frequency that a certain kind of data occurs

也就是说
In other words

当原假设正确的时候
when the null hypothesis is correct

我们得到目前
the P value is

这个样本数据它的概率
the probability of the sample data for the moment

当然P值越小
Of course, the smaller the P value

我们拒绝原假设的理由就越充分
the more sufficient the reason we have for rejecting the null hypothesis

下面的这张图
In the following graph

我们是把用P值决策
we make a comparison

和用检验统计量决策
between decision-making using the P value

做一个比较
and decision-making using the test statistic

那么在这张图中
In this graph

我想问一下大家
I have a question to ask everyone

统计量1和统计量2
We use statistic 1 and statistic 2

我们用它来判断原假设
to judge whether the null hypothesis

是否成立
is true

那么当然
Of course

我们的结论
our conclusion

都是要拒绝原假设
is always to reject the null hypothesis

但是哪一个力度更大呢
But which one coincides with greater strength?

当然是统计量2
Statistic 2, certainly

因为统计量2
Because the probability

它出现的概率更小
that statistic 2 occurs is smaller

换句话说
In other words

就是一个非常非常不可能
it is the case that the event that is extremely unlikely to

发生的这个事件发生了
happen does happen

当然在原假设成立的情况下
Of course, under the circumstance that the null hypothesis holds

那么这个非常非常
it is quite abnormal that

不可能发生的事件发生了
the event extremely unlikely to happen

那么这个是很违反常理的
does happen

所以我们有充分的理由
So we have sufficient reason

去拒绝原假设
to reject the null hypothesis

这就是我们要给大家讲的
That is all about the P value problem

P值的问题
I shall relate to everyone

那么这一讲
So much

我们就讲到这里
for this lecture

谢谢大家
Thank you everyone