# 5.1 Descriptive Statistics: Some popular Displays of Data 5.1.4 Cross-Tabulations

Cross-Tabulations are tables that reflect the joint distribution of two (or more) variables with a limited number of categories or distinct values.

• help to understand how one variable (e.g., brand loyalty) relates to another variable (e.g., sex)
• a cross-tabulation table contains a cell for every combination of categories of two (or more) variables

Examples:

• How many brand-loyal users are males?
• Is product use (heavy users, medium users, light users, and non-users) related to outdoor activities (high, medium and low)?
• Is familiarity with a new product related to age and education levels?
• Is product ownership related to income (height, medium, and low)?

Does education influence ownership of expensive automobiles?

Ownership of Expensive Automobiles by Education Level

 Education Own Expensive Automobile College Degree No College Degree yes 32 % 21 % no 68 % 79 % Column total 100 % 100 % Number of cases 250 750

Sometimes introducing a third variable can reveal

• spurious relationship
• suppressed association
• no change in initial relationship

1. Spurious relationship

Does education influence ownership of expensive automobiles?

Ownership of Expensive Automobiles by Education and Income Levels

 Low Income High Income Own Expensive Automobile College Degree No College Degree College Degree No College Degree yes 20 % 20 % 40 % 40 % no 80 % 80 % 60 % 60 % Column total 100 % 100 % 100 % 100 % Number of cases 100 700 150 50

### Does it?

2. Suppressed association

Does age influence desire to travel?

Desire to Travel Abroad by Age

 Ages Desire to travel abroad Less than 45 45 or more yes 50 % 50 % no 50 % 50 % Column total 100 % 100 % Number of cases 500 500

Desire to Travel Abroad by Age and Sex

 Male Female Desire to travel abroad < 45 ≥ 45 < 45 ≥ 45 yes 60 % 40 % 35 % 65 % no 40 % 60 % 65 % 35 % Column total 100 % 100 % 100 % 100 % Number of cases 300 300 200 200

3. No change in initial relationship

Does family size influence frequency of eating in fast-food restaurants?

Eating Frequency in Fast-Food Restaurants by Family Size

 Eat frequently in fast-food restaurants Family size Small Large yes 50 % 50 % no 50 % 50 % Column total 100 % 100 % Number of cases 500 500

Eating Frequency in Fast-Food Restaurants by Family Size and Income

 Eat frequently in fast-food restaurants Low income High income Small Large Small Large yes 50 % 50 % 50 % 50 % no 50 % 50 % 50 % 50 % Column total 100 % 100 % 100 % 100 % Number of cases 250 250 250 250