Chapter 6. Two-Way Tables
Topics covered in this chapter:
•
•
•
Creating a Two-Way Table
Marginal Distribution
Conditional Distribution
Creating a Two-Way Table
Example 6.1: I think I’ll be rich by age 30
The Problem: A sample survey of young adults asked, “What do you think are
the chances you will have much more than a middle-class income at age 30?”
Create a two-way table showing the results of this survey.
1. Open the data set ta06-01.por.
2. Go to the Data and scroll down to Weight Cases.
3. The following window appears:
4.
5.
6.
7.
Click on Weight cases by.
Highlight Count and click the arrow next to the Frequency Variable box.
Click OK.
Go to the Analyze menu, click on Descriptive Statistics, and then click
on Crosstabs. You will see the following window:
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8. Highlight Chance and click on the arrow to the left of the Row(s) box.
9. Highlight Sex and click on the arrow to the left of the Column(s) box.
10. Click OK.
11. Your table will appear in the Output window. It will be labeled
Chance*Sex Crosstabulation.
Marginal Distribution
Example 6.3: Creating a marginal distribution
The Problem: A sample survey of young adults asked, “What do you think are
the chances you will have much more than a middle-class income at age 30?”
Find the Marginal Distribution young adults opinions of their chances of getting
rich.
To find the Marginal Distribution of the variable Chance, we need only to look at
the subtotals for each of the “Chance” options divided by the total number of
young adults surveyed. We can also do this by using SPSS.
1. Follow instructions 1 through 9 for Example 6.1 above to create the twoway table.
Two-Way Tables 60
2. Click on the Cells button to the right of Row(s). You will see the
following window:
3. Under the Percentages box, select Total. Click Continue.
4. Click the OK button. A table of counts and percentages will appear in the
Output window.
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The marginal distribution of Chance may be found by looking at the percentages
for each value of Chance under the Total column at the right hand side of the
table.
To get the Marginal Distribution of Sex, just look at the percentages for each
value of Sex in the Total row at the bottom of the table.
Conditional Distribution
Example 6.3:Comparing women and men
Problem: How do young men and young women differ in their responses to the
question, “What do you think are the chances you will have much more than a
middle-class income at age 30?”
Find the Conditional Distribution of the student’s opinions given that the student
is male. If we know that the student is male, we need to look only at the “Male”
column of the two-way table. To find the distribution of the students’ opinions of
their chances of getting rich given that the student is male, divide each count in
the Male column by the column total. We can do this also by using SPSS.
1. Follow instructions 1 through 9 for Example 6.1 above to create the twoway table.
2. In the Crosstabs window, click on the box labeled Cells at the right side
of the window.
3. To get the conditional probabilities of Chance given Sex, check the
Column box under Percentages, since Sex is the column variable.
Two-Way Tables 62
4. Select Continue and then click OK.
5. The following output will appear:
Crosstabs
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The Chance * Sex Crosstabulation gives the conditional distribution of Chance
given Sex for all Sex groups. To find the conditional distribution of Chance
given that a young person is a male, just look at the percentages for each group in
the Male column. The probability that a young person believes they will have “a
good chance” of getting rich given that the person is male is 30.8%. The
probabilities in this column should sum to 100% since all males surveyed fall into
one of these 5 “Chance” groups.
Likewise we can find the conditional distribution given that a young person is a
female by looking at the percentages in the Female column.
Chapter 6 Exercises
6.1
6.3
6.19
6.27
6.29
Attitudes towards recycled products.
Attitudes towards recycled products.
Helping cocaine addicts.
Life at work.
College degrees.
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Chapter 6 SPSS Solutions
6.1
The
table
represents
the
opinions
of
20 + 7 + 9 + 29 + 25 + 43 = 133 people. Of these, 36 were
buyers of recycled paper coffee filters. The marginal
distribution of opinions is 49/133 = 36.8% think the quality
is higher, 32/133 = 24.1% think the quality is the same, and
52/133 = 39.1% think the quality is lower. 60.1% think the
quality is the same or higher than other filters.
6.3 SPSS does not like data tables already summarized. To find the conditional
distributions, we’ll simply divide each cell count by the total number of buyers (36) and
non-buyers (97). There should be no surprises – more than half the buyers think the
quality of the recycled filters is higher; almost half of the non-buyers think the quality of
the recycled filters is lower.
6.19 The percents of relapsed subjects are 10/24 = 41.7% for the Desipramine group,
18/24 = 75% for the Lithium group, and 20/24 = 83.3% for the Placebo group. Enter
these percents and the treatments into two variables. Then click Graphs, Legacy
Dialogs, Bar and define a simple bar chart where Data in Chart are Values of Individual
Cases. The bars represent the relapse percentages and the treatment type is the category
variable. Give the graph a title, then click OK to generate the graph.
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6.27 Open data file ex06-27. We’ll create a stacked
bar chart to display these data and examine the effect
of education on freedom at work. Click Graphs,
Legacy Dialogs, Bar. Select a Stacked chart with
Summaries for groups of cases. Click Define to
continue.
Move the button to Other statistic and enter Count; enter Degree as the Category axis
and Define Stacks by Work. Give your graph an appropriate Titles.
The intial graph is shown below. The bars are not all the same height because there were
different numbers of individuals with a given education level. We’ll use the Chart Editor
to make all the bars extend to 100%.
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Double-click in a bar to bring up the Chart Editor. Click Options, Scale to 100%. You
can also click on the Y axis label to change this label to Percent (type the new label in the
box). To change from color fill to a black-and-white Pattern, click in a bar for a
Properties window. Click the Variables tab and change the drop-down box entry for
Work from Style:color to Style pattern. Apply your changes and Close the Chart Editor.
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This chart clearly shows that individuals with more education have more freedom to
organize their own work. Less than 10% (7.78%) of those with Bachelor’s degrees have
no freedom while almost 40% (37.01%) of those with less than a high school diploma
have no freedom.
6.29 Follow the instructions given in
Exercise 6.27 to create another stacked bar
chart after entering the data as shown at
right. Our finished chart is below.
While the projection is for women to earn far more degrees than men, the conditional
distributions are remarkably similar. Men are slightly more likely to pursue professional
and doctor’s degrees than women.