## Misconception Mutt extract from chapter 15

The Misconception Mutt was spinning around in circles. In the lecture he’d been taken to, the lecturer kept rambling on about circularity, which had reminded the mutt how much fun it was to chase his tail. A ginger mist arose like a tornado from the epicentre of his spinning body, forming into a feline cloud above him. The cloud raised its eyebrows at him and muttered ‘Stupid dogs!’ The mutt stopped to throw the cat a look of disgust.

‘What are you doing?’ said the cat disapprovingly.

‘I learnt about circularity today,’ the dog wheezed, ‘about how you need to look for sphericity when you compare two related means, and you use Mauchly’s test, and if it’s significant then sphericity can’t be assumed but if it’s non-significant then you can assume it …’

The cat’s paw reached towards the mutt’s lips and gently closed them. The dog looked puzzled. ‘Shhh …’, said the cat, throwing him a patronizing look.

‘Where to begin?’ the cat whined. ‘First, sphericity is not relevant if you’re comparing only two means. The assumption is that the variances of difference scores between pairs of treatment levels are equal, and with only two conditions you have only one set of difference scores, and only one variance. You need at least three conditions for sphericity to be an issue. Second, Mauchly’s test is, essentially, pointless. In large samples a significant Mauchly’s test could mean a small departure from sphericity that we have a lot of power to detect, and in small samples a non-significant Mauchly’s could mean a large departure from sphericity that we didn’t have the power to detect. Mauchly’s test can’t be interpreted without the context of the sample size. Also, if sphericity is violated then you can apply a correction proportionate to the extent of the violation (for example, the Greenhouse–Geisser

correction) so you may as well ignore Mauchly’s test and always apply the correction. When the data are spherical no correction is made, for small violations a small correction is made, and for large violations a large correction is made.’

The mutt started spinning furiously in the opposite direction, chasing his tail as though his life depended on it. As he spun he created a reverse vortex that sucked the cat back into the ether. ‘That’ll learn him,’ he thought to himself.