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.
Maine Learning Results learning standard: HSS.ID.B.5; HSS.ID.C.9 · two-way tables, conditional relative frequency, 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 Maine
In the Maine Learning Results, 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.
Source: Maine Department of Education
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
What percent of the "Grade 8" row are "Walks to school"?
Getting to school Walks to school Rides to school Total Grade 8 10 10 20 Grade 9 16 9 25 Total 26 19 45 - 38.5%
- 60%
- 22.2%
- 50%
50%
Hint: 10 out of 20 = 10 ÷ 20 × 100.
Question 2
People who carry umbrellas are more likely to have wet shoes. What is the best conclusion?
- The data must be wrong
- One must cause the other
- There is no link at all
- 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.
Question 3
How many in the "Doesn't like reading" row are in the "No library card" column?
Reading survey Has a library card No library card Total Likes reading 18 2 20 Doesn't like reading 11 14 25 Total 29 16 45 - 14
- 25
- 2
- 11
14
Hint: Find the row, then move across to the column.
Question 4
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 39 11 50 Doesn't like reading 4 16 20 Total 43 27 70 - You can't tell from a two-way table
- Yes, the percents are very different
- Not much, the percents are close
Yes, the percents are very different
Hint: Likes reading: 78%. Doesn't like reading: 20%.
Question 5
Students who own more books tend to have higher reading scores. What is the best conclusion?
- They are linked, but this does not prove one causes the other. Something else, like time spent reading at home, could explain both.
- The data must be wrong
- There is no link at all
- One must cause the other
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 6
Compare the percent of each row that is "Walks to school". Is there evidence of an association?
Getting to school Walks to school Rides to school Total Grade 8 33 17 50 Grade 9 12 8 20 Total 45 25 70 - Yes, the percents are very different
- Not much, the percents are close
- You can't tell from a two-way table
Not much, the percents are close
Hint: Grade 8: 66%. Grade 9: 60%.