Statistical Conundrum

My friend Tamzin and I decided to go to a statistics lecture at a conference we attended recently. My stats knowledge used to be quite ropey but has improved considerably over the last few months and I thought at least I would understand the majority of what was being talked about. Tamzin however is very good at statistics and teaches it (and very well I’ve heard). It was a great lecture and we learned about what the ‘p value’ really means, cluster analysis (which I might have a go at) plus loads of other really interesting stuff. At the end the lecturers had a Q&A session. There’s a statistical query I’ve had for quite a while and haven’t been able to find the answer from anywhere and, suffice to say, these lecturers didn’t know the answer either.

The question is –

“There are three ways to save scores from a Principal Components Analysis. The first is the Regression option, the second is the Anderson-Rubin way (which is the one I use so I can use the scores to do ANOVA), and the third is the Bartlett’s option. What is the Bartlett’s option? What does it assume? When would it be used?

If anyone knows the answer please tell me. It’s driving me bonkers not knowing. But explain it in jellyhead terms please.