9th grade · Math · Unit 16 of 17
Two-Way Tables & Causation
Relative frequency and correlation
What your child practices
Reading two-way frequency tables, finding conditional relative frequencies, spotting associations, and knowing that correlation does not prove causation.
Minnesota K-12 Academic Standards benchmark: 9.1.2.5; 9.1.1.5 · two-way frequency tables, and correlation versus causation
How we explain it
Children can open this short lesson before they practice.
- A joint frequency is one cell. A row total is a marginal frequency.
- A conditional percent is a cell ÷ its row total.
- Two things changing together does not prove one causes the other.
Example: Of 40 students who ate breakfast, 30 felt rested. What percent is that? 30 ÷ 40 = 0.75. Answer: 75%
Two-Way Tables & Causation in Minnesota
In the Minnesota K-12 Academic Standards, this is unit 16 of 17 in 9th grade Math, after Rearranging Formulas and before Sequences.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Compare the percent of each row that is "Has a library card". Is there evidence of an association?
Reading survey Has a library card No library card Total Likes reading 11 9 20 Doesn't like reading 27 13 40 Total 38 22 60 - Not much, the percents are close
- You can't tell from a two-way table
- Yes, the percents are very different
Not much, the percents are close
Hint: Likes reading: 55%. Doesn't like reading: 68%.
Question 2
Students who own more books tend to have higher reading scores. What is the best conclusion?
- One must cause the other
- The data must be wrong
- They are linked, but this does not prove one causes the other. Something else, like time spent reading at home, could explain both.
- There is no link at all
They are linked, but this does not prove one causes the other. Something else, like time spent reading at home, could explain both.
Hint: Correlation shows two things change together. It does not prove that one causes the other.
Question 3
What percent of the "Plays sports" row are "Has a pet"?
Sports and pets Has a pet No pet Total Plays sports 14 26 40 No sports 43 7 50 Total 57 33 90 - 24.6%
- 35%
- 45%
- 15.6%
35%
Hint: 14 out of 40 = 14 ÷ 40 × 100.
Question 4
How many in the "Grade 9" row are in the "Rides to school" column?
Getting to school Walks to school Rides to school Total Grade 8 17 3 20 Grade 9 10 15 25 Total 27 18 45 - 3
- 25
- 10
- 15
15
Hint: Find the row, then move across to the column.
Question 5
How many in the "No sports" row are in the "No pet" column?
Sports and pets Has a pet No pet Total Plays sports 34 6 40 No sports 9 11 20 Total 43 17 60 - 11
- 20
- 9
- 6
11
Hint: Find the row, then move across to the column.
Question 6
People who carry umbrellas are more likely to have wet shoes. What is the best conclusion?
- One must cause the other
- There is no link at all
- The data must be wrong
- They are linked, but this does not prove one causes the other. Rainy weather could cause both.
They are linked, but this does not prove one causes the other. Rainy weather could cause both.
Hint: Correlation shows two things change together. It does not prove that one causes the other.