1

Many people embarrass themselves by saying
CHEE
- Square.
Well, how many people really use this in regular conversation?
The following illustration will give you the correct pronunciation!
It's like the beginning of
KI
TE
.
Chi-square is an incredibly useful
statistic. What it does is
test whether
one set of
proportions
is different
from another. It does this by
comparing
frequencies
.
2

3
Up to this point, the inference to the population
has been concerned with “scores” on one or
more variables, such as SAT scores, mathematics
achievement, and hours spent on the computer.
We used these scores to make the inferences
about population means. To be sure not all
research questions involve score data.
Today the data that we analyze consists of
frequencies; that is,
the number of individuals
falling into categories
. In other words, the
variables are measured on a
nominal
scale.
The test statistic for frequency data is Pearson
Chi-Square. The magnitude of Pearson Chi-
Square reflects the amount of discrepancy
between observed frequencies and expected
frequencies.

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 female
managers
.
Let's look at the complaint
:
There are 10 managers. If there were perfect gender equality - then
you would
expect 5 males and 5 females
. That would be a 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 and the observed is different from the expected. In other words:
4

But, you tell your client that's not good
enough evidence.
You make up the following chart:
It's just chance.
The office could be 5 males or 5
females and the change of one
person would make it 6 to 4. It could
have just as easily been 4 males or 6
females.
Intuitively, you can see that it would
be hard to convince someone that
this 60 - 40 split is discrimination. It's
too easy to be just luck.
5

What if the company only had 5
managers in the office?
With an odd
number of
managers, there
will always be one
more male OR
female.
So, this
ISN’T
discrimination,
mostly because
our numbers are
too small.
6

If you understand these pictures, you understand
chi-
square's purpose
. You have a set of proportions that you
think should be true
(Expected)
and you test them
against
a
set that you have observed
(Observed)
.
In this case, the differences between the proportions of male
and female managers could easily be chance as the value of O
- E is very small
Your client won't give up. She says "I will get data from all the
company's offices across the city.
I will measure 100
people
–
not just ten!"
Ok.
If there were no discrimination, you should get the
following picture with 50 men and 50 women
.

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- Spring '18
- Donald Sweeney
- Chi-Square Test, Statistical tests, Chi-square distribution, Pearson's chi-square test, Non-parametric statistics