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 |
