11/29/2010
1
χ
2
(Chi-Square) Test of
Independence
1
2
χ
2
Test Overview
•
Up to this point, we have focused on
statistical tests that examined mean
differences among two or more groups on
the value of an outcome variable
•
We used scores in the sample data to
make the inferences about population
means
•
Obviously, not all research questions
involve continuous outcome measures
and/or sample means
χ
2
Test Overview
•
The
χ
2
is used to examine relationships
between two categorical variables when
the
outcome variable is nominal
•
Recall that nominal variables only allow for
qualitative classification--- i.e., they are
measured in terms of whether the subjects
belong to distinctively different categories
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11/29/2010
2
χ
2
Test Overview
•
More on nominal variables
:
–
You do not quantify or rank order the
categories of a nominal variable--- no one
category is better/worse or higher/lower
–
You cannot say that a given individual has
more or less of the quality represented by the
variable
–
All you can say is that individuals are different
in terms of the variable (e.g., two individuals
are of different race or gender)
4
χ
2
Test Overview
•
With nominal (i.e., categorical) outcome
variables, you test a null hypothesis that
the frequency, or percentage, of people in
each category is the same for two or more
different groups
•
This is conceptually the same as an
independent t-test or an ANOVA, except
the dependent variable is nominal--- and
thus evaluated in terms of frequencies
5
χ
2
Test Overview
•
You examine observed frequencies in the
data to see how many individuals fall in
each category
•
The magnitude of the
χ
2
test statistic
reflects the amount of discrepancy
between the observed frequencies you
see and the frequencies that you would
expect to see if the null hypothesis were
true ( i.e. if the variables are
not related to
one another).
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