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猪排吕小沛 · 2022年10月08日

想请问t-statistic和P-value是什么关系

NO.PZ2021061603000047

问题如下:

An economist collected the monthly returns for KDL's portfolio and a diversified stock index. The data collected are shown in the following table:


The economist calculated the correlation between the two returns and found it to be 0.996. The regression results with the KDL return as the dependent variable and the index return as the independent variable are given as follows:


When reviewing the results, Andrea Fusilier suspected that they were unreliable. She found that the returns for Month 2 should have been 7.21% and 6.49%, instead of the large values shown in the first table. Correcting these values resulted in a revised correlation of 0.824 and the following revised regression results:


Explain how the bad data affected the results.


选项:

解释:

The Month 2 data point is an outlier, lying far away from the other data values.

Because this outlier was caused by a data entry error, correcting the outlier improves the validity and reliability of the regression. In this case, revised R2 is lower (from 0.9921 to 0.6784). The outliers created the illusion of a better fit from the higher R2; the outliers altered the estimate of the slope. The standard error of the estimate is lower when the data error is corrected (from 2.861 to 2.0624), as a result of the lower mean square error. However, at a 0.05 level of significance, both models fit well. The difference in the fit is illustrated in Exhibit 1:


何老师总说有P-value的话就不用看t统计量,又说P是在跟不上切得的面积,那么面积就是百分比,是和α进行对比的?但题目里p-value都是值,t-statistic不也是算出来的检验统计量的值吗?这两个有什么区别呢?请老师帮忙解答,谢谢!

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星星_品职助教 · 2022年10月08日

同学你好,

p-value的值对应的是概率面积,可以用小数或者百分数表示。t-statistic计算出来的值对应的是横轴上的点。

拒绝原假设有两种等价的方法:

① p-value<significance level,这是面积之间的对比。

② |test statistic|>|critical value|,这是横轴上的值的对比。

p-value和significance level都不用计算,题目会直接给出。但test statistic需要算(critical value还需要查表)。所以当存在p-value时,首选上面的方法①,节省了计算的时间。

猪排吕小沛 · 2022年10月08日

棒呆,谢谢老师!

星星_品职助教 · 2022年10月08日

@猪排吕小沛 学习加油~

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