Two-Way Tables
Construct and read two-way tables that sort the same people by two categories at once (e.g., year group against preferred sport); use row and column totals and relative frequencies to judge whether the two categories are associated
What a learner can do afterwards
- Build a two-way table from raw data on two categories collected from the same people
- Read off joint and total frequencies (e.g., how many students both walk to school and pack their lunch)
- Compare row or column relative frequencies to say whether two things seem linked (e.g., do pet owners do more sport?)
1 · Read
You already know how to read a table. A two-way table does one more job: it sorts the same group of people by two questions at once, not just one.
Ms. Ito asked 50 students two questions: do you have a pet, and do you play a sport? She put the answers in a two-way table.
| Plays sport | No sport | Total | |
|---|---|---|---|
| Has a pet | 18 | 6 | 24 |
| No pet | 10 | 16 | 26 |
| Total | 28 | 22 | 50 |
The box where a row meets a column is called a cell. The 'Has a pet' row meets the 'Plays sport' column at 18. That means 18 students both have a pet and play a sport.
The 'Total' row and column tell you about just one question at a time. At the bottom of the 'Plays sport' column, 28 students play a sport in total, no matter whether they have a pet. In the right-hand 'Total' column, 24 students have a pet, no matter what sport they play.
Row totals are not always equal (24 pet owners, 26 without). That is why you compare percentages, not raw counts, when you want to know if two categories are linked.
A two-way table sorts the same people by two questions at once; compare relative frequencies, not raw counts, to see if the two are linked.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.