Chi-square Test

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Chi-square Test
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Chi-square Test
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.
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Chi-square Test
Chi-square test the same as a ?², ? 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.
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Types of Chi-square tests
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.
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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. You can
use the test when you have counts of values for
a categorical variable. This test is same as
Pearsons Chi-square test.
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Using the Chi-square goodness of fit test
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.
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Application

• 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.

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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.
• 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.

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Using the Chi-square test of independence
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.
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Application
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.
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