Solution to question 6.3
Which ratio to use?
As this is a retrospective study (the subjects were selected on the basis of the outcome - erosion of dental enamel - rather than exposure - hours of swimming) so we have to use the odds ratio.
Odds ratio
The odds of a frequent swimmer having erosion are: 32÷118 = 0·27
32 frequent swimmers have erosion, 118 do not.
The odds of an infrequent swimmer having erosion are: 17÷117 = 0·15
17 infrequent swimmers have erosion, 117 do not.
The odds ratio for having erosion for frequent swimmers compared to infrequent swimmers is 0·27÷0·15= 1·87
Frequent swimmers have more than one and three-quarters the chance of having dental erosion compared to infrequent swimmers
The χ2 test
As P < 0·05 the χ2 test leads us to reject the null hypothesis of no association. We would conclude that there is a significant association between frequency of swimming and erosion of dental enamel. We would expect that if we calculated a 95% confidence interval for the odds ratio above that it would not include 1.
