Cogito
Probability and Statistics · Chapter 4 · Lesson 3
Two-Way Tables and Association
Two categorical variables at once.
12 problems · about 21 minutes · TEKS P.S.2.E, S-CP.A.4
What this lesson teaches
The student builds two-way tables, computes marginal and joint frequencies, and judges association.
- A two-way table cross-classifies by two categorical variables.
- Inner cells are joint counts; margins give each variable alone.
- Compare conditional distributions, as percentages, to judge association.
Warm Up
Straightforward practice. Get the method working first.
5 problemsA row has 18 yes out of 24. What proportion said yes, as a decimal?
Answer 0.75
Why 0.75.
Why compare percentages rather than counts across groups?
Answer The groups may be different sizes, making counts incomparable.
Why Unequal group sizes make raw counts misleading.
A row has 15 yes and 5 no. Proportion yes, as a decimal?
Answer 0.75
Why 15 ÷ 20.
Cells 10, 10, 20, 20. Grand total?
Answer 60
Why Add them.
Row 1 rate 0.6, row 2 rate 0.6. Is there association? 1 yes, 0 no.
Answer 0
Why The rates match.
Build It Up
The same ideas with more to keep track of.
3 problemsRow 1 rate 0.8, row 2 rate 0.3. Is there association? 1 yes, 0 no.
Answer 1
Why The rates differ sharply.
A row has 9 yes out of 12. Proportion, as a decimal?
Answer 0.75
Why 9 ÷ 12.
Where do marginal frequencies appear? 1 inner cells, 2 row and column totals.
Answer 2
Why In the margins.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each term with where it lives in a two-way table.
Answer Joint frequency → An inner cell; Marginal frequency → A row or column total; Conditional distribution → A row divided by its own total
Why Only one of these involves dividing.
A row has 7 yes out of 28. Proportion, as a decimal?
Answer 0.25
Why 7 ÷ 28.
The Row: A row has 30 yes and 20 no. What proportion said yes, as a decimal?
Answer 0.6
Why 0.6.
The Margin: Cells hold 12, 8, 5 and 15. What is the grand total?
Answer 40
Why 40.