# Suggested answer to exercise: Socioeconomic status and tumour stage

Question: What is wrong with their analysis?

The analysis does not take into account the ordering of the categories. The deprivation group is clearly ordered and so is the tumour size. Thus the data could have been analysed with a method which takes these orderings into account, such as the chi-squared test for trend.

To do this we must omit the 'unknown' row, of course. When we do, the chi-squared test for trend yields the following P values:

trend chi-squared = 5.16, d.f. = 1, P = 0.02
about trend chi-squared = 0.49, d.f. = 3, P = 0.9
total chi-squared = 5.65, d.f. = 4, P = 0.2

Hence we have a significant trend and inspection of the table shows that more deprived subjects tend to have bigger tumours. We can see this if we omit the unknowns from the table:

Tumour size (mm): Deprivation group Total
Affluent Middle Deprived
0-20 271 (66.3) 730 (61.4) 166 (57.6) 1167 (61.9)
21-50 124 (30.3) 409 (34.4) 109 (37.8) 642 (34.1)
>50 14 (3.4) 49 (4.1) 13 (4.5) 76 (4.0)
Total 409 (100.0) 1188 (100.0) 288 (100.0) 1885 (100.0)

The authors disagree with me, and you can judge for yourself from the BMJ Rapid Responses.