Chapter 9 Handout – Analyzing Contingency Tables

MTH 207 Elementary Statistics

Contingency tables – or crosstabs – display data so we can see if one variable seems to be having an effect on a second variable (does the independent variable effect the dependent variable?)

independent variable: displayed across the top (column)

dependent variable: down the sides (rows)

Contingency Tables by Hand

How are the smoking habits of students related to their parents’ smoking? Here are data from a survey of students in eight Arizona high schools:

Both parents smoke / One Parent Smokes / Neither parent smokes
Student Smokes / 400 / 416 / 188
Student does not smoke / 1380 / 1823 / 1168

Which would be the dependent variable and which would be the independent variable? Why?

Calculate the proportion of students who smoke in each of the three parent groups. Then describe in words the association between parent smoking and student smoking.

According to research reported in the Journal of the National Cancer Institute (Apr. 1991), eating foods high in fiber bay help protect against breast cancer. The researchers randomly divided 120 laboratory rats into four groups of 30 each. All rats were injected with a drug that causes breast cancer, then each rat was fed a diet of fat and fiber for 15 weeks. However, the levels of fat and fiber varied from group to group. At the end of the feeding period, the number of rats with cancer tumors was determined for each group. The data are summarized in the contingency table below. Is there a relationship between diet and cancer?

Diet
High-Fat/ No-Fiber / High-Fat/ Fiber / Low-Fat/ No-Fiber / Low-Fat/ Fiber / Totals
Cancer Tumors / Yes / 27 / 20 / 19 / 14 / 80
No / 3 / 10 / 11 / 16 / 40
Totals / 30 / 30 / 30 / 30 / 120

Contingency Tables on SPSS

Here is an example taken from a data set of students in a college calculus course. You don’t have this data set, but the next example will be from your class data.

Does your grade in Calculus depend on the size of your class?

Now try this example with your class data set: Are males happier at the Mount than females? Use the class data set.

What is the dependent and what is the independent variable?

Analyze – Descriptive Statistics - Crosstabs

Row:

Column:

Click the cells box on the bottom, and then choose check the box for ‘column percents’. Hit continue and OK. What trends to you see?

Contingency Table

Level of Job Satisfaction

Income
Under $40,000 / $40,000-$59,000 / $60,000-$89,000 / $90,000+ / Total
Satisfied / 31 / 71 / 32 / 65
Dissatisfied / 9 / 32 / 8 / 13
Total

Would you favor paying higher taxes to further promote the availability of quality childcare in Orange County?

Higher Taxes for Quality Child Care

Political Affiliation
Republican / Democrat / Independent / Total
Yes / 9 / 22 / 6
No / 27 / 12 / 10
Total