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December 4th, 2015, 02:50 PM  #1 
Newbie Joined: Nov 2015 From: japan Posts: 15 Thanks: 0  Explain about chisquared
Hello, Could you explain why we have ? 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?! Last edited by iranch; December 4th, 2015 at 02:56 PM. 
December 13th, 2015, 06:38 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
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 $\displaystyle \chi^2_{1\alpha/2}(n1)$ and $\displaystyle \chi^2_{\alpha/2}(n1)$ when I think it should be $\displaystyle \chi^2_{n1}= 1\alpha/2$ and $\displaystyle \chi^2_{n1}= \alpha/2$. 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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