Answers

a) i: Student’s t test

b) g: Cox regression

c) h: Correlation coefficient

d) f: Fisher’s test of exact probability

A visual analogue scale produces a continuous measure, so it is sensible to compare the mean improvement of each patient. Student’s t test is used to compare means and is safe to use on large samples such as that in the example here.

Fever resolved eventually in all of the children in example b, so traditional risk measures or cure rates are hard to apply. The effect of the drugs was captured by measuring how quickly fever was reduced. Time to event is well suited to survival analysis. Cox regression is one method for comparing survival between two groups.

Comparing the supply of doctors with infant mortality rates across countries will require an ecological study design, the results of which are often best represented in a scatter plot. The degree of association can be judged by eye and quantified with a correlation coefficient. Ideally, both axes of the scatter plot should show continuous measures.

Although comparing death rates is about survival, the study in this example is not suited to analysis by survival methods. The time to event was not measured because survival is measured only once at 30 days. The comparison is between the proportion dying within 30 days of hip surgery and the proportion dying within 30 days of cataract surgery. At first sight, a simple comparison within a 2x2 table using a Chi square test might work. It is likely that very few people will die within 30 days of cataract surgery, however, leaving a cell of the table with 1 or 2 (or worse 0) people in it. With low numbers like this, an exact test is required such as Fisher’s test of exact probability or a Binomial test. The Chi square test is certainly appropriate when all the expected cell numbers are above 10.

None of the pairings given above are absolute and it is probably possible to work out a way to use each test in each study. For example, Fisher’s exact test could be used to compare pain scores in example a by dichotomising the outcomes into those who improve and those who do not. This approach would not be the most efficient use of the available data, however.

Cite this as: BMJ 2009;339:b2702