The chi-square test evaluates how likely an observed distribution is due to chance, typically referred to as a 'goodness of fit' test. It includes the chi-square goodness of fit test for single measurement variables and the chi-square test of independence for comparing two measurement variables. Both tests assess whether the observed data fits expected patterns and require categorical or nominal data but are not suitable for continuous data.

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Chi-square Test

2. The Chi-square test is intended to test how likely it is
that an observed distribution is due to chance. It is also
called a "goodness of fit" statistic, because it measures
how well the observed distribution of data fits with the
distribution that is expected if the variables are
independent.
Chi-square Test

3. Chi-square test the same as a χ², χ is the Greek
symbol Chi.
If you have a single measurement variable, you use
a Chi-square goodness of fit test. If you have two
measurement variables, you use a Chi-square test
of independence. There are other Chi-square tests,
but these two are the most common.
Chi-square Test

4. You use a Chi-square test for hypothesis tests
about whether your data is as expected. The basic
idea behind the test is to compare the observed
values in your data to the expected values that
you would see if the null hypothesis is true.
There are two commonly used Chi-square tests:
the Chi-square goodness of fit test and the Chi-
square test of independence. Both tests involve
variables that divide your data into categories. As
a result, people can be confused about which test
to use.
Types of Chi-square tests

5. 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.
You can use the test when you have counts of
values for a categorical variable.
This test is same as Pearson’s Chi-square test.
Chi-Square Goodness of Fit Test

6. The Chi-square goodness of fit test checks whether
your sample data is likely to be from a specific
theoretical distribution. We have a set of data values,
and an idea about how the data values are
distributed. The test gives us a way to decide if the
data values have a “good enough” fit to our idea, or if
our idea is questionable.
Using the Chi-square goodness of fit test

7. Data values that are a simple random sample
from the full population.
Categorical or nominal data. The Chi-square
goodness of fit test is not appropriate for
continuous data.
A data set that is large enough so that at least five
values are expected in each of the observed data
categories.
Application

8. 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.
You can use the test when you have counts of
values for two categorical variables.
If you have only a table of values that shows
frequency counts, you can use the test.
Chi-Square Test of Independence

9. The Chi-square test of independence checks whether
two variables are likely to be related or not. We have
counts for two categorical or nominal variables. We
also have an idea that the two variables are not
related. The test gives us a way to decide if our idea is
plausible or not.
Using the Chi-square test of independence

10. Data values that are a simple random sample
from the population of interest.
Two categorical or nominal variables. Don't use
the independence test with continous variables
that define the category combinations. However,
the counts for the combinations of the two
categorical variables will be continuous.
For each combination of the levels of the two
variables, we need at least five expected values.
When we have fewer than five for any one
combination, the test results are not reliable.
Application

11. Non-Probability methods
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