Lesson 19
Chi-Square
Outline
Categorical Data
Goodness of Fit Test
-observed frequency
-expected frequency
-X2 statistic
Example
-hypothesis testing
Categorical Data
As mentioned at the start of the lesson with correlation, all of the data we have been
working with so far involve measurement data. We actually took measurements from
units in our sample to create our distribution. Often times, however, we will want to
analyze categorical or qualitative data as well. For categorical data we will not have a
measure of individual units in the sample. Instead, we will analyze frequencies or counts
of people falling into different categories or groups. When analyzing categorical data we
say the test is non-parametric. Thus, all the tests we have learned before this point were
parametric tests.
Chi-Square Goodness-of-Fit Test
We will learn two different Chi-square tests. The first of these is the goodness-of-fit test.
With the goodness-of-fit test we will test whether the data “fit good” with what we would
expect if only chance factors were operating. For example, if I measured the number of
insurance claims for different car types, I might have the following data:
High Performance Compact Mid Size Full Size
20 14 7 9
Notice that our data is now frequency values or how many values in our sample fit into
different categories. The test will tell us whether there is a difference in how many
values fall at different levels of the single variable (car type). Is there a difference in
number of claims for different car types?
The values we observe in our sample are the observed frequencies ( 0
f). What we want
to know is if they differ from the frequencies we would observe by chance. The values
we would expect if there really was no difference in the number of claims made for
different car types are what we call the expected frequencies ( e
f). If there really was no
difference in the frequencies for each level of the variable, then we would expect equal
numbers of claims for each car type. Since there a total of 50 claims in our sample, and
