Example 10: Chi-Square Test
The goal of this example is to determine the relationship between two
categorical variables. We want to know if these two categorical variables
are independent. If not, we will further explore the relationship between
For this example, the Smoking habits.sta
data set, included with the Statistica examples, is used. In this data,
observations were recorded from 50 people about their age and whether
they smoke cigarettes. With this study, we want to answer the question,
"does a significant relationship exist between a person’s age
category and smoking?" The null hypothesis is that the variables
AGEGROUP and SMOKING
are independent. A chi-square
test for independence will help to answer this question. A partial
view of the data is shown in the next image.
Open the data file Smoking habits.sta
and start the Basic Statistics module.
Following are instructions to do this from the ribbon bar and from the
bar. Select the Home tab.
In the File group, click the Open arrow and select Open
Examples to display the Open a
Statistica Data File dialog box. Smoking
habits.sta is in the Datasets
On the Statistics tab, in the
Base group, click Basic
Statistics to display the Basic Statistics and Tables
menus. From the File menu,
select Open Examples to display
the Open a Statistica Data File
dialog box. The data file is located in the Datasets
From the Statistics menu, select
Basic Statistics/Tables to display
Statistics and Tables dialog box.
On the Quick tab, select Tables and banners.
Click the OK button to display
the Crosstabulation Tables
Click the Specify tables (select variables)
button to display a variable selection dialog box. Select AGEGROUP
in List1 and SMOKING
in List2 as shown in the next
Click OK in the variable selection
Click OK in the Crosstabulation
Tables dialog box to display the Crosstabulation Tables
Results dialog box. Select the Options tab.
This tab contains several statistics options from which to choose for
two-way tables. For this example, we will use the Pearson Chi-Square
test for Independence. In the Statistics
for two-way tables group box, select the Pearson
& M_L Chi-square check box.
To create the output, select the Advanced tab.
Click the Detailed two-way tables
button to create the 2-Way Summary Table
and a separate output spreadsheet containing the Pearson Chi-Square and Maximum Likelihood Chi-Square tests.
The Pearson Chi-square test
is 4.065393 with a p-value of
0.13098. Because the p-value
is greater than alpha = 0.05,
the null hypothesis (Smoking
and Age category are independent)
is not rejected. This can be interpreted by saying that a significant
relationship does not exist between a person’s smoking status and
To further explore this relationship, in the Crosstabulation
Tables Results dialog box, click the 3D
histograms button. A bivariate histogram shows the frequencies
broken down across the categories of the two variables. Although some
relationship appears to exist in the plot, namely that the age category
< 20 has fewer smokers than non-smokers, which is opposite of the relationship
in the other two categories, the statistical test did not detect a relationship.
Note that you can use the Interactive
Graphics Controls at the bottom of the graph window to rotate the
graph and/or adjust the transparency of the plot areas to view different
aspects of the plot.