Chi Square Significance Level problems, someone, change, tables

king_kong

L1V1 Reading 11 Example 7 (Page 617) and Problem 13 (Page 630)
Regarding chi square (for the two problems above), for a significance level of 0.05, the idea is to look under the 0.95 column.
This seems counterintuitive to what we do for the rest of the tests. Which is, if we know the alpha, we simply look for that significance level in the tables (alpha/2 for the equality based hypotheses).
Can someone throw some light on this change of behavior for chi square? I want to make sure I am understanding properly so that I know when to look under which column.
Thanks as usual!

kmf229

Chi square table gives you the probability in ‘RIGHT’ tail only. This means if you want .05 in left tail, you have to look at .95 in the table (if probability in left tail is .05, right tail will have .95)

skycfa

OK, I went back and read some of the CFA material with a fresh mind. It seems to have stuck. I was able to decipher (please confirm, anish) that for the “less than” test, the lower alpha point is (1  alpha).
This was based on the BOK’s representation of the “Not equal to Halternative”: it recognizes that the lower (alpha/2) point is ((1  alpha)/2).
Given all this, can you confirm this example: Assume an “equal to/not equal to” test. Significance level = 0.10. DF = 10.
This implies (alpha/2) = 0.05
This also means that the upper (alpha/2) point is 18.307 and that the lower (alpha/2) point is the value at the intersection of DF=10 and alpha=0.475.
Thanks!

kseniaru

I don’t give much thought to the formulas. Just the concept of distribution. Think of the shape of the chi square distribution (like normal but lower limit is 0 and it is right skewed… hence it is not symmetrical)
Now for df = 10, significance level = .10, two tailed, you will have .05 in the left tail and .05 in the right tail.
.05 in the left tail means .95 in the right tail so lower limit is 3.94
.05 in the right tail is straight forward .05 with a value of 18.307 (as you suggested)

pimpineasy

Yea, messed up the calculation in the example  alpha shouldn’t be 0.475. It should be 0.05.
Thanks for the input, as usual.