STAT170 Workshop Notes prepared by Nan Carter for Numeracy ...

Week 12 Questions on ODDS RATIO TESTS prepared for
Stat170 workshop held at the Numeracy Centre, Macquarie
University. Prepared by Nan Carter with examples from
various sources and adapted for Stat170.
ODDS RATIO TESTS
The χ 2 test of independence showed that wearing a helmet and
receiving a head injury in a bicycle accident are associated,
but does not indicate how strong, or weak, the association is.
To get that information we need to look at odds ratios.
DEFINITION: if p is the probability of an event occurring,
and (1-p) the probability of it not occurring, then p/(1-p) is
the odds of it occurring.
We can show that the odds of a cyclist wearing a helmet will
receive a head injury is [17/147]/[130/147], which simplifies
to 17/130.
Similarly, we can show that the odds that a cyclist not
wearing a helmet will receive a head injury is
[218/646]/[428/646], which simplifies to 218/428.
So, the odds ratio of a cyclist receiving a head injury if
wearing a helmet relative to a cyclist receiving a head injury
if not wearing a helmet is [17/130]/[218/428], which can be
written [17x428]/[218x130] = 0.26.
Similarly, a cyclist receiving a head injury if not wearing a
helmet relative to a cyclist receiving a head injury if
wearing a helmet, is [218/428]/[17/130], which can be written
[218x130]/[17x428]= 3.89.
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Nan Carter: workshop notes prepared for Numeracy Centre Macquarie University.