1. ## Chi square distribution

If we want to evaluate P(chi square with n degrees of freedom>=k)=0.05

should I say k=chi square(n,0.05) or k=chi square (n, 1-0.05)?

I am not sure since I don't know if >= or <= makes a difference in chi square distribution as it does in normal distribution (which is symmetric), but chi square is not!

Any help would be appreciated, thank you

2. ## Re: Chi square distribution

Originally Posted by Darkprince

I am not sure since I don't know if >= or <= makes a difference in chi square distribution as it does in normal distribution (which is symmetric), but chi square is not!
You are correct to say $\chi^2$ is not symmetric.

Your 0.05 value is a probability, the region under the curve. The left hand critical value which gives p=0.05 (region under the curve) will be different to the critical value for the right hand side p= 0.05

3. ## Re: Chi square distribution

Originally Posted by pickslides
You are correct to say $\chi^2$ is not symmetric.

Your 0.05 value is a probability, the region under the curve. The left hand critical value which gives p=0.05 (region under the curve) will be different to the critical value for the right hand side p= 0.05

So which value I should use? k=chi square(n,0.05) or k=chi square(n,0.95)?

If I had to evaluate P(chi square with n degrees of freedom<=k)=0.05 would it be different, obviously, but how do I know which value I take each time?

4. ## Re: Chi square distribution

Depends on the table/technology you are using.

To find a critical value, let's say df=15

In ms-excel
CHIINV(0.95,15) = 7.26 (left tail)
CHIINV(0.05,15) = 25.00 (right tail)

Draw a picture of the curve with these values on it, does it help?

5. ## Re: Chi square distribution

Originally Posted by pickslides
Depends on the table/technology you are using.

To find a critical value, let's say df=15

In ms-excel
CHIINV(0.95,15) = 7.26 (left tail)
CHIINV(0.05,15) = 25.00 (right tail)

Draw a picture of the curve with these values on it, does it help?

Basically I have the following (which is a part from a problem I solved):

Under Ho (null hypothesis)
P(Sum from i=1 to 50 of Xi >= k) = P(Sum from i=1 to 50 of 4*Xi >=4k) = P(chi square with 200 df >= 4k) since I had deduced in the problem that the sum follows that distribution.

But at the same time P(Sum from i=1 to 50 of Xi >=k) = 0.05 (0.05 is the power of my test)

The problem had to do with most powerful test and region. The thing is that P(Sum from i=1 to 50 of Xi >=k) = 0.05 if and only if 4k = chi square with 200 df but looking at 0.05 or 0.95? This was my question!

If I had P(Sum from i=1 to 50 of Xi <= k) = 0.05 it would be a different case? So this is my question, if my sum >=k or my sum <=k would change the value of chi square with 200 df I should look in my tables.

I hope I got clear this time with my question

In my problem I have the sum >=k, not <=k!