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橘子皮橙子心儿🍊 · 2022年05月17日

老师为什么p-value值越小，越拒绝啊，一直理解不了

  1. FRM I
  2. Quantitative

NO.PZ2018122801000062

问题如下：

For a sample of 400 firms, the relationship between corporate revenue (Yi) and the average years of experience per employee (Xi) is modeled as follows:

Y i = β 1 + β 2 X i + ε i ,i=1,2,...,400  

You wish to test the joint null hypothesis that at the 95% confidence level. The p-value for the t-statistic for β1 is 0.07, and the p-value for the t-statistic for β2 is 0.06. The p-value for the F-statistic for the regression is 0.045. Which of the following statements is correct?

选项：

A.

You can reject the null hypothesis because each β is different from 0 at the 95% confidence level.

B.

You cannot reject the null hypothesis because neither β is different from 0 at the 95% confidence level.

C.

You can reject the null hypothesis because the F-statistic is significant at the 95% confidence level.

D.

You cannot reject the null hypothesis because the F-statistic is not significant at the 95% confidence level.

解释：

C is correct.

考点 ： Regression Coefficient Confidence Interval and Significance test

解析 ： The T-test would not be sufficient to test the joint hypothesis. In order to test the joint null hypothesis, examine the F-statistic, which in this case is statistically significant at the 95% confidence level. Thus, the null can be rejected.

老师为什么p-value值越小，越拒绝啊，一直理解不了

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1 个答案

DD仔_品职助教 · 2022年05月17日

嗨，爱思考的PZer你好：


p-value代表的是检验数据尾部的概率，如果p-value越小，那么落入拒绝域的可能性越大，就越容易拒绝。

比如p-value是1%，代表该检验值所对应的z值的尾部概率，当假设检验是5%时，p-value小于5%，就落入了拒绝域，拒绝原假设，同理，pvalue如果越小，尾部概率越小，落入拒绝域的可能性就会越大。

如下图：

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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