The chi-square test is a statistical hypothesis testing method used to determine if observed frequencies in categories match expected frequencies, serving to assess relationships between variables. Two primary types are the chi-square goodness of fit test for single-variable analysis and the chi-square test of independence for examining relationships between two categorical variables. Each test has specific applications, hypotheses, and required data structures for valid analysis.

1. CHI-SQUARE TEST
THEA G. NOPAT
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2. Definition
•A Chi-square test is a hypothesis testing
method. Two common Chi-square tests involve
checking if observed frequencies in one or
more categories match expected frequencies.
•A statistical test used to compare observed results
with expected results.
•Represented as the 22nd
letter of the Greek
alphabet, Χ(Chi) with a square, Χ2
hence the
name Chi-Square.

3. PURPOSE
•The purpose of this test is to determine if a difference
between observed data and expected data is due to
chance, or if it is due to a relationship between the
variables you are studying.

4. What Chi-Square Test to use?
The two most common Chi-Square tests are:
1. Chi-square goodness of fit test.
2. Chi-square test of independence.
When measuring only a single variable, the Chi-square
goodness of fit test is used. And the use for the Chi-square test
of independence is when two measurement variables are used.

5. What is the Chi-square goodness of fit
test?
The Chi-square goodness of fit test is a statistical hypothesis test
used to determine whether a variable is likely to come from a
specified distribution or not. It is often used to evaluate whether
sample data is representative of the full population.
When can I use the test?
You can use the test when you have counts of values for a categorical
variable.

6. What is the Chi-square test of
independence?
The Chi-square test of independence is a statistical hypothesis test
used to determine whether two categorical or nominal variables are
likely to be related or not.
When can I use the test?
You can use the test when you have counts of values for two
categorical variables.

7. Chi-Square
Goodness of Fit
Test
Chi-Square Test of
Independence
Number of
variables
One Two
Purpose of
test
Decide if one variable is likely to
come froma given distribution or
not
Decide if two variables might be related or
not
Example
Decide if bags of candy have the
same numberof pieces of each
flavorornot
Decide if movie goers' decision to buy
snacks is related to the type of movie they
plan to watch

8. Ch
i-
Squ
ar
e
Goodn
ess
of Fit T
est
Ch
i-Squ
ar
e T
est of
I
n
depen
den
ce
Hypotheses in
example
Ho: proportion of
flavors of candy
are the same
Ha: proportions
of flavors are not
the same
Ho: proportion of people who buy snacks is
independent of the movie type
Ha: proportion of people who buy snacks is different for
different types of movies
Theoretical
distribution used
in test
Chi-Square Chi-Square
Deg
rees of
freedom
Number of
categ
ories minus
1
 In our
example,
number
of flavors
of candy
minus 1
Number of categ
ories for first variable minus 1,
multiplied by number of categ
ories for second variable
minus 1
 In our example, number of movie categ
ories
minus 1, multiplied by 1 (because snack
purchase is a Yes/No variable and 2-1 = 1)

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