Chi Square

c2 Test of Independence
& Goodness of Fit

Great news! There are only two big ideas in Chi- Square!

1st Big Idea - How Do You Say Chi-Square!

Many people embarrass themselves by saying CHEE - Square.
Ha Ha - you will be laughed at!
Later - you'll be scorned as a loser!
The following illustration will give you the correct pronunciation! It's like the beginning of kite.

2nd Big Idea - It's All About Whether Or Not Proportions Differ.

Chi-square is incredibly useful.
What is does is compare whether one set of proportions is different from another.
It does this on the basis of comparing frequencies.

Let's get right to a real example.

Discrimination at the Work Place

(Goodness of Fit - Remember this)

You are hired as a statistician by a disgruntled employee who says that the company discriminates on the basis of gender.

The employee's evidence - there are 6 male mangers and 4 females.

This is the classic situation of comparing proportions using the frequencies.

The complainant says:

There are 10 mangers.

If there was perfect equality based on Gender - then one would expect 5 males and 5 females. That would be the 50- 50 split based on equal proportions of .5 and .5 or 50% vs. 50%

Expected Males = 5, Expected Females = 5.

However, she observed 6 males and 4 females. This is a 60-40 split

So she said that the observed is different from the expected.

In other words.

O (observed) (E)Expected

or

O (observed) - (E)Expected 0

{what are the boxes for? Should be not equals?}