Three-set Venn reconstruction, exposure-adjusted risk, solving for a count
transport safety
An online survey of 2400 regular cyclists in New Zealand asked whether, in the past 12 months, they had experienced a crash (C), a near miss with a motor vehicle (M), or a 'dooring' incident (D — hitting or swerving to avoid an opening car door).
- 1130 reported at least one of the three; 990 reported a near miss, 315 a crash and 150 a dooring incident.
- 865 reported exactly one type, 205 exactly two types, and 60 all three.
- 40 reported a dooring incident and nothing else; 15 reported a crash and a dooring incident but no near miss.
Figure 1 is a partly completed Venn diagram of these results.
Of the 2400 cyclists, 520 mainly ride e-bikes and 1880 mainly ride conventional bikes. 94 e-bike riders and 221 conventional riders reported a crash (Figure 2). E-bike riders rode a mean of 2900 km in the year; conventional riders 1800 km.
Three-set Venn diagram for crash (C), near miss (M) and dooring (D) among 2400 cyclists; D only is 40, C and D only is 15, all three is 60, and the other regions, including outside all three, are marked with question marks.
Stacked horizontal bar chart of the number of riders who did and did not report a crash: 94 of 520 e-bike riders and 221 of 1880 conventional riders.Facts you may need
(a)
Complete the Venn diagram in Figure 1. Of the cyclists who reported a crash or a dooring incident (or both), what proportion also reported a near miss?
(b)
A cycling advocate claims e-bikes are more dangerous than conventional bikes. Calculate the relative risk of a crash for e-bike riders compared with conventional riders, then use the distance information to evaluate the claim.
(c)
For the 520 e-bike riders, the probability that two randomly chosen (different) e-bike riders both reported a near miss is 0.1802. Find how many e-bike riders reported a near miss, and compare the near-miss rate for e-bike and conventional riders.
(d)
Discuss TWO reasons why these survey results may not represent all New Zealand cyclists.
