Warm-up
Three quick questions from earlier lessons.
Discover
70% of students who sleep 8+ hours passed a test, and 40% of those who sleep less passed. Is there an association between sleep and passing?
- Yes, the pass rates differ
- We cannot tell without an experiment
Key idea
Compare conditional distributions.
Two categorical variables are associated if the conditional distribution of one differs across the groups of the other. If the conditional proportions are all equal, there is no association. Association in observational data does not show causation.
Worked example
Of 50 phone users, 30 sleep badly; of 50 non-users, 10 sleep badly.
60% vs 20% sleep badly
Within each group.
Association between phone use and sleep
A big difference.
It does not prove phones cause bad sleep
Observational data.
Your turn, guided
Your turn: the difference in proportions (users − non-users).
0.6 − 0.2.
Practice ★
- Of 40 drivers who texted, 30 had a near-miss; of 40 who did not text, 10 had one. Is there an association between texting and near-misses in these data?
- Yes: 75% of texters vs 25% of non-texters had a near-miss
- No: both groups have 40 drivers
- Yes, and it proves texting causes near-misses
- In a school, 50 of 125 girls and 100 of 250 boys walk to school. What does this suggest?
- No association: 40% of each group walks
- Boys are more likely to walk: 100 > 50
- Girls are more likely to walk
Watch out!
Practice ★★
- A survey asked 135 people whether they exercise weekly. Under 30: 44 yes, 40 no. Age 30 or over: 18 yes, 33 no. Find the proportion of under-30s who exercise minus the proportion of those 30 or over who exercise.
- A survey asked 163 people whether they exercise weekly. Under 30: 45 yes, 37 no. Age 30 or over: 48 yes, 33 no. Find the proportion of under-30s who exercise minus the proportion of those 30 or over who exercise.
Exit ticket
Three questions to check you have got it.
- A survey asked 135 people whether they exercise weekly. Under 30: 44 yes, 40 no. Age 30 or over: 18 yes, 33 no. Find the proportion of under-30s who exercise minus the proportion of those 30 or over who exercise.
- A survey asked 163 people whether they exercise weekly. Under 30: 45 yes, 37 no. Age 30 or over: 48 yes, 33 no. Find the proportion of under-30s who exercise minus the proportion of those 30 or over who exercise.
- A survey asked 112 people whether they exercise weekly. Under 30: 28 yes, 48 no. Age 30 or over: 13 yes, 23 no. Find the proportion of under-30s who exercise minus the proportion of those 30 or over who exercise.
Summary card
Association
- Compare conditional proportions across groups.
- Different: associated. Equal: not associated.
Watch out: association is not causation; counts are not rates.
End of the lesson
Next lesson: Scatterplots and correlation Back to the chapter