4 - Correlation and association

Summary

Arguing that the trial judge had failed to explain clearly the use of Bayes' theorem, the defence lodged an appeal. But in a bizarre irony, the Appeal Court last month upheld the appeal and ordered a retrial – on the grounds that the original judge had spent too much time explaining the scientific assessment of evidence. In their ruling, the Appeal judges said: ‘To introduce Bayes’ theorem, or any similar method, into a criminal trial plunges the jury into inappropriate and unnecessary realms of theory and complexity'.

(Robert Matthews, New Scientist 1996)

When we make a set of measurements, it is instinct to try to correlate the observations with other results. One or more motives may be involved in this instinct: for instance we might wish (1) to check that other observers' measurements are reasonable, (2) to check that our measurements are reasonable, (3) to test a hypothesis, perhaps one for which the observations were explicitly made, or (4) in the absence of any hypothesis, any knowledge, or anything better to do with the data, to find if they are correlated with other results in the hope of discovering some new and universal truth.

4.1 The fishing trip

Take the last point first. Suppose that we have plotted something against something, on a fishing expedition of this type. There are grave dangers on this expedition, and we must ask ourselves the following questions.