Identifying associations using relative frequencies
Relative frequencies in two-way tables reveal associations between categorical variables when the percentages differ significantly across categories — a statistics skill in enVision Algebra 1 Chapter 11 for Grade 11. If 80% of students who play an instrument take music class but only 15% of non-players do, the large 65-percentage-point difference strongly suggests an association between playing an instrument and taking music class. In a cafe, if 65% of morning customers order coffee but only 30% of afternoon customers do, the time of day is associated with drink choice. When relative frequencies are nearly equal across categories, no association exists.
Key Concepts
Relative frequencies in two way tables can reveal associations between categorical variables. When the relative frequencies for one variable differ significantly across categories of another variable, this suggests an association exists between the two variables.
Common Questions
How do relative frequencies in a two-way table reveal associations?
Calculate relative frequencies for each category and compare them. If the percentages differ significantly across categories (e.g., 80% vs. 15%), an association likely exists between the two variables.
80% of instrument players take music class vs. 15% of non-players. Is there an association?
Yes, there is a strong association. The 65-percentage-point difference is large and suggests that playing an instrument and taking music class are related.
When is there no association between two categorical variables?
When the relative frequencies are approximately equal across categories. For example, if 50% of instrument players and 48% of non-players take music class, the difference is negligible — no association.
How do you calculate relative frequencies for rows in a two-way table?
For each row, divide each count by the row total and multiply by 100%. This gives the percentage distribution within that category.
What is the difference between association and causation in a two-way table?
Association means the two variables tend to occur together. Causation means one directly causes the other. Two-way tables can reveal association but cannot establish causation — other factors may explain the relationship.