Independence based on contingency tables

CFA Level I Quant
#1

Hi all,

my question of the day :smiley: is:
Why do I use a two-tail test if my null hypothesis is:

H0 = two characteristics are independent
Ha = two characteristics are dependent = two characteristics are not independent

I understood everything until the point in the Schweser Notes as they us alpha/2 in the upper tail
and alpha/2 in the lower tail.
There are just these two possibilities (independent and not independent).
So why do I use the two tail test ?

Many thanks!

Cheers

#2

Are you testing their correlation coefficient?

#3

Well, I have the contingency table of the both categories and calculated the ChiSq-Test-Statistic X².
The LOS 6.m asks for independence based on contingency tables.
So I would like to compare my X² to a critical value. The significance level is 5% with 4 degrees of freedom.

The table states:

df = 4 and prob = .025 => 11.143
df = 4 and prob = .05 => 9.488

The solution mentioned in the Schweser notes used a CV of 11.143.
I am just wondering why to use this one and not the 9.488.

H0 = independent
Ha = dependent (or do I state it as Ha <> independent and therefore “two-sided” test)?

#4

Is this in the 2022 curriculum?

(I haven’t a copy of that yet, alas.)

#5

Yes it is.
I just contacted Schweser as the example was nealry the same as in the CFA Curriculum.
They confirmed that it should be 9.488.

Sorry for the confusion.

Cheers