ANOVAs or what they did not tell you at Uni

Yesterday I taught a course to MASH Statistical advisors on ANOVA. All their advisors have a statistical background, quite a number of them are doctoral students in Probability and Statistics department here. So why was I giving a course on such a simple technique as ANOVA which is normally taught first or second year undergraduate.

Well I was not teaching them how to do the mathematics, which is what they get at University, that and a couple of neat examples to have a go at. What I was teaching was the application in a research (non-statistical) environment.  This meant I had to cover:

1. The assumptions that ANOVA makes and which are important
2. How to check these assumptions and why some of the ways people are taught to check these assumptions are wrong!
3. What to do if the analyses do not meet the assumptions (transformation, non-parametric, robust methods)
4. Extra worries when the ANOVA is multi-way
5. Carrying out more complex analyses with statistical packages in this case SPSS

At no point would I say I was an expert, but I am an experienced user. I have learnt from my years of consultancy but even so I was doing some indepth revision in order to prepare for the course. Sometimes there are no real answers so you make the best decision you can on the information you have to hand. It is not helped by the fact that research statistical packages are about thirty years behind the literature and products like Excel and noddy statistical packages are even worse. If you want to do a modern analysis by Statistical standards then you really need to look at something like R but if you want something more user friendly try something similar to  Stata or maybe Statistica which seem to be aimed at Statisticians. However in the non-statistical research environment we are not often going to find people prepared to use them, as they require a significant investment in knowledge of statistics and often programming. Rather the attitude is something along the lines of "if T-tests were good enough for Prof they are good enough for me".  In such an environment all we can try to do is move people up a stage accepted techniques and explain why t-test are not good enough. They normally get it when you start explaining multi-comparisons to them. You can then move them onto ANOVA, but then you have to know about ANOVA and that is where this course comes in. Researchers data is habitually more complex than they think and so often the ANOVA is not straightforward. Hopefully I have started a lot of people into sorting their own advice out and we will thereby get a higher level of statistics at the University.