So, thanks to Math for the Masses I can now do equations using LaTeX, a typesetting language I have avoided learning to date, if only because so many people have told me that I simply *must* learn LaTeX.

To return to the problem at hand, why do we get a negative correlation between preoperative score & health gain?

The reason is that ‘health gain’ is a *change score*, calculated from the postoperative score *minus* preoperative score:

**Health Gain = Postoperative Score – Preoperative Score**

I haven’t worked out how to make LaTeX do ‘friendly’ equations so we will have to simplify this to:

**c = b – a**

The correlation between preoperative score (**a**) and health gain (**c**) is clearly the same as the correlation of **a** with **b-a**. We can write the equation for this as follows:

The important thing about this equation the top part. The standard deviations of pre- and postoperative scores are likely to be very similar: we have the same people filling in the same questionnaire on both occasions. Similarly, r_{ab} is likely to be positive because it’s the correlation between pre- and postoperative scores, and less than 1.0.

This means that r_{ab} × sd_{b} will be almost always be smaller than sd_{a} so the expression will be negative, making the correlation between a and c negative.

Note also that the corrleation between pre- and postoperative scores might be quite small if the questionnaire is unreliable so the greater the measurement error, the greater the negative bias.

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