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上小学 · 2023年02月03日

请详细解释下什么是Pvalue. 如何计算？F 检验中如何应用pPvalue

  1. FRM I
  2. Quantitative

NO.PZ2018122801000062

问题如下：

You estimate a regression model

Yi=α+β1X1i+β2X2i+εi Y_i=\alpha+\beta_1X_{1i}+\beta_2X_{2i}+\varepsilon_i

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.

Pvalue. 在不同检验方法中如何应用？概念非常模糊 碎片化。谢谢

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1 个答案

李坏_品职助教 · 2023年02月03日

嗨，努力学习的PZer你好：


P值（P value）就是当原假设H0为真时，比所得到的样本观察结果更极端的结果出现的概率。

如果P值很小，说明原假设H0情况的发生的概率很小，根据小概率原理，我们就有理由拒绝原假设。P值越小，我们拒绝原假设的理由越充分。


在5%的显著性水平下，如果p value小于0.05，那就可以拒绝H0。本题中告诉我们F statistic的p value是0.045，这就说明F检验的结论应该是：拒绝原假设H0，F statistic是显著的。


不管在什么检验中，p value都是越小越显著。一般认为p value小于0.05就足够显著了。

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

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