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vee · 2022年11月28日

做对了

NO.PZ2017092702000133

问题如下:

Which of the following statements is correct with respect to the p-value?

选项:

A.

It is a less precise measure of test evidence than rejection points.

B.

It is the largest level of significance at which the null hypothesis is rejected.

C.

It can be compared directly with the level of significance in reaching test conclusions.

解释:

C is correct.

When directly comparing the p-value with the level of significance, it can be used as an alternative to using rejection points to reach conclusions on hypothesis tests. If the p-value is smaller than the specified level of significance, the null hypothesis is rejected. Otherwise, the null hypothesis is not rejected.

对于一个分布而言,每个概率面积在横轴上都有一个对应点,例如significance level α对应的分位点就是临界值critical value(假设正态分布下α=95%,双尾检验,则右尾就会对应critical value=1.96)。

而p-value也是一个概率面积,对应的点就是计算出来的检验统计量的那个点。所以当p-value<α时,就等价于检验统计量>critical value,也就是拒绝原假设。

能不能翻译一下每个选项?不怎么了解

1 个答案
已采纳答案

星星_品职助教 · 2022年11月28日

同学你好,

A选项:拒绝原假设有两种等价的方法:1)p-value<significance level; 2)|critical value|<|test statistic|,其中critical value就是rejecttion point。

所以A选项说rejection points的方法不如p-value的方法精确就错了,两种方法是一样的。

B选项:正确的定义为p-value是能拒绝原假设的smallest significance level,也就是说如果significance level比p-value还小,那么就无法拒绝原假设。换个方向,这就是在说如果要拒绝原假设,significance level就必须比p-value大。说的还是拒绝原假设的条件应该是p-value<significance level。B选项的largest说反了。

C选项:p-value可以和significance level直接相比从而得到假设检验的结论。这个描述是正确的,仍然说的是拒绝原假设的原则为p-value和significance level相比,p-value小的时候拒绝原假设。三个选项实质上都在考这一点。

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