My Math Forum (http://mymathforum.com/math-forums.php)

 iranch December 4th, 2015 01:50 PM

2 Attachment(s)
Hello,
Could you explain why we have http://mymathforum.com/attachment.ph...1&d=1449269305 ? why alpha minus from 1 ?

The right in diagram have alpha/2 , and center is 1 - alpha, now the left of diagram 1 - alpha/2?!

 Country Boy December 13th, 2015 05:38 AM

The total area/probability under the curve (for any probability density curve) is 1. Two values have been chosen so that the area to the left of the first line is [math]\alpha/2[/imath] and to the right of the second line is $\displaystyle \alpha/2$. Of course, the area between the two lines is $\displaystyle 1- \alpha/2- \alpha/2= 1- \alpha$.

The parts you are asking about seem to have the notation reversed. What I see in the graph is $\displaystyle \chi^2_{1-\alpha/2}(n-1)$ and $\displaystyle \chi^2_{\alpha/2}(n-1)$ when I think it should be $\displaystyle \chi^2_{n-1}= 1-\alpha/2$ and $\displaystyle \chi^2_{n-1}= \alpha/2$.

That is because, typically, the subscript is the number of "degrees of freedom" minus 1, an integer. If I am correct then the first, $\displaystyle 1- \alpha/2$ is just the area/probability to the right of the first line, 1 minus the area/probability to the left.

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