## Misconception Mutt extract from chapter 8

The Misconception Mutt had just come out of a lecture on correlation with his owner. It had made him think about the relationships between certain important variables in his life. There seemed to be a correlation between him getting under his owner’s feet in the kitchen and being fed, staring lovingly at his owner seemed to get him strokes, and walking nicely and not chasing squirrels got him treats.

As his mind wandered, he thought about how much he liked the campus. It was full of trees, grass and squirrels that he really wanted to chase if only it didn’t stop the supply of treats. ‘I really like treats,’ he thought, ‘and I really like chasing squirrels. But chasing squirrels is negatively correlated with treats, so if I chase the squirrel it will cause the number of treats to go down.’

He was hungry, so he started walking extra nicely. A squirrel darted up to him and jumped on his head as if trying to goad him into a chase. It started to grow, becoming heavier and more ginger until the grinning Correcting Cat stared down into the mutt’s eyes from on top of his head.

‘Correlation coefficients give no indication of the direction of causality,’ he said to the dog. ‘You might think that chasing squirrels causes fewer treats, but statistically speaking there’s no reason why fewer treats isn’t causing you to chase squirrels.’

‘That’s ridiculous,’ replied the mutt.

‘It may be less intuitive to think of fewer treats causing you to chase squirrels more, but statistically speaking the correlation between those variables provides no information about cause: it is purely a measure of the degree to which variables covary. Think back to the lecture: the correlation measures whether differences between scores on one variable and its mean correspond to differences between scores on a second variable and its mean. Causality does not feature in the computation.’

‘Another issue,’ the cat continued, ‘is that there could be other measured or unmeasured variables affecting the two things that correlate. This is known as the third-variable problem or the tertium quid (Section 1.7.2). Perhaps the time of day affects both how many treats you get and how many squirrels you chase.’

Annoyingly, the cat had a point, so the mutt shook him from his head and, after watching his feline form shrink back to that of a squirrel, chased him across campus.