Child obesity 'in proportion' to popularity?

The concept of two variables being 'in proportion' is fairly fundamental in mathematics, so it is a little disturbing when it is used in error in a respectable newspaper. The Times last Tuesday reported some research that had shown apparently that child obesity in children was 'in proportion' to their popularity with other children. I don't think so.

We have two variables here, the level of obesity and the level of popularity. The point of the report was that the more obese the children the less popular they are with their peers. Some correspondents to The Times suggested therefore that the report should have said that the variables were in 'inverse proportion'. Wrong again.

We are dealing with statistical data here, which cannot therefore be described as either direct or inverse proportion. There is not a simple 'formula' (like y = kx for direct proportion or y = k/x for inverse proportion) which will convert obesity level (x) to popularity level (y). The evidence here can only indicate a statistical trend – that the more obese children tend to be less popular – not a precise rule.

The mathematical concept needed here is 'correlation'. We could say that the evidence suggests a negative correlation between level of obesity and level of popularity. This means that in general the greater values of one variable tend to be linked with the smaller values of the other, and vice versa.