# Exercises: Contingency tables - Risk, Odds and χ2 tests

##### Question 6.1

The following data are taken from the paper Caries prevalence in northern Scotland before and 5 years after, water defluoridation (Stephen et al., 1987, BDJ 163: 324-326). They show the social composition of children recruited to two arms of the study one before and one after water defluoridation. What is the probability that we don't know the social class of a child in the fluoridated arm? What is the probability that a child in the defluoridated arm is from social class III?

Social class Fluoridated Defluoridated
I & II 16 32
III 45 53
IV & V 32 22
Not known 13 19
Total 106 126

##### Question 6.2

A recent MDentSci project was looking at a number of risk factors thought to be associated with the health of oral implants in a population of elderly patients. One factor considered was smoking. The table below shows the number of healthy and non-healthy implants for smokers an non-smokers. Calculate and interpret the risk ratio and the odds ratio. The patients were selected for the study on the basis of the health of their implants (a case-control study). Which of the two ratios you have calculated would you use to report your results? Why?

A χ2 test was performed on these data, the results were: χ2 = 2·023, d.o.f. = 1, P = 0·16. Interpret these results.

 Healthy implant Yes No Total Smoker 32 48 80 Non-smoker 10 7 17 Total 42 55 97

##### Question 6.3

A study (Erosion of dental enamel among competitive swimmers at a gas-chlorinated swimming pool, Centerwall et al., 1986, Am. J. Epid. 123: 641-647) was carried out to see if swimming in chlorinated water was linked to erosion of dental enamel. 49 swimmers with erosion of dental enamel (cases) were recruited along with 245 swimmers without erosion (controls). The data are summarised below.

 Erosion of dental enamel Hours of swimming per week Yes No Total 6 or more 32 118 150 less than 6 17 117 134 Total 49 235 284

Calculate the appropriate ratio to show the effect of excessive swimming on erosion of dental enamel. A test was performed on these data, the results were: χ2 = 4·802, d.o.f. = 1, P = 0·03. Interpet these results.