Two-way tables with a third variable: Simpson's paradox, relative risk, lurking variables
licensing
Restricted-licence practical test results for one year at two testing centres, P and Q, split by the type of vehicle the candidate used:
| Centre | Vehicle | Passed | Tests |
|---|---|---|---|
| P | Manual | 360 | 450 |
| P | Automatic | 30 | 50 |
| Q | Manual | 85 | 100 |
| Q | Automatic | 260 | 400 |
Figure 1 shows the number of tests at each centre by vehicle type.
Stacked bar chart of the number of restricted-licence practical tests at each centre: Centre P had 450 manual and 50 automatic tests; Centre Q had 100 manual and 400 automatic tests.Facts you may need
(a)
Calculate the overall pass rate at each centre. A news site says 'Centre P is the easier place to pass.' Does the overall data support this?
(b)
Calculate the pass rates by vehicle type at each centre, and use Figure 1 to explain why they contradict the conclusion in (a).
(c)
At Centre Q, calculate the relative risk of failing for automatic compared with manual candidates, and suggest a reason for the difference that is not about the vehicle itself.
(d)
Explain what further information would be needed before concluding which centre is easier.
Driving-test pass rates at two centres — Scholarship Statistics | Xametric
