Two-Way Streets

Learning Focus

Read two-way frequency tables and use joint, marginal, and conditional relative frequencies to look for association between categorical variables.

Big idea

A two-way table counts individuals by two categories.

• Joint frequency: both conditions together.
• Marginal frequency: row or column totals.
• Conditional relative frequency: a fraction within one row or column.
• If conditional percentages differ across groups, there is an association.

Worked example

Survey of $100$ students on liking pizza:

• Grade 9: $30$ like, $10$ do not (total $40$).
• Grade 10: $20$ like, $40$ do not (total $60$).

P(likes | grade 9) $=\frac{30}{40}=0.75$; P(likes | grade 10) $=\frac{20}{60}\approx0.33$. The difference shows an association.

Takeaways

• Use the right denominator for conditional frequencies.
• Different conditional rates suggest association.
• Describe the result in context.