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.
Arizona Academic Standards learning standard: A1.S-ID.B.5; A1.S-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 Arizona
In the Arizona 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.
Source: Arizona 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
Students who own more books tend to have higher reading scores. What is the best conclusion?
- 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.
- One must cause the other
- 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 2
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 29 11 40 Doesn't like reading 14 36 50 Total 43 47 90 - 50
- 36
- 14
- 11
36
Hint: Find the row, then move across to the column.
Question 3
What percent of the "Plays sports" row are "Has a pet"?
Sports and pets Has a pet No pet Total Plays sports 11 29 40 No sports 24 26 50 Total 35 55 90 - 27.5%
- 12.2%
- 37.5%
- 31.4%
27.5%
Hint: 11 out of 40 = 11 ÷ 40 × 100.
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 7 18 25 Doesn't like reading 20 5 25 Total 27 23 50 - Not much, the percents are close
- Yes, the percents are very different
- You can't tell from a two-way table
Yes, the percents are very different
Hint: Likes reading: 28%. Doesn't like reading: 80%.
Question 5
What percent of the "Ate breakfast" row are "Felt rested"?
Morning survey Felt rested Felt tired Total Ate breakfast 9 16 25 No breakfast 16 4 20 Total 25 20 45 - 37%
- 36%
- 46%
- 20%
36%
Hint: 9 out of 25 = 9 ÷ 25 × 100.
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 2 18 20 Grade 9 10 30 40 Total 12 48 60 - Yes, the percents are very different
- You can't tell from a two-way table
- Not much, the percents are close
Not much, the percents are close
Hint: Grade 8: 10%. Grade 9: 25%.