#### my first AAS. III. ANOVA

Believe it or not, I saw ANOVA (ANalysis Of VAriance) from a poster at AAS. This acronym was considered as one of very statistical jargons that one would never see in an astronomical meeting. I think you like to know the story in detail.

I was browsing posters; there were so many but the acronym ANOVA couldn’t miss my eyes. I decided to take a look. The poster was made by an education graduate student who designed experiments on children and performed a statistical analysis (ANOVA) with collected data to find a factor that affects children (testing the significance of a factor via the F-test). Frankly, I didn’t read it through but was desperate to know the occasion in astronomy where ANOVA can be utilized. I was half excited because ANOVA appeared in the AAS meeting and half disappointed because ANOVA was not performed as a part of astronomical research. A train of thoughts, nonetheless, came along.

ANOVA or statistical methods from design of experiments may be of no use in astronomical experiments (collecting data by observations, i.e. collecting random incidents seems to not allow experiment designing stages). However, these methods can be used in evaluating proposals, summaries of projects’ quality, standardizing decision making processes, improving usages of instrument times, and so on. These statistical experiment design tools could be a servant to improve the procedures of collecting data and allocating time slots, and could amplify already tremendous efforts of renovating/creating expensive instruments.

Experiment design has never been of my interest because I could not see any chance of using them in astronomy. Upon finding ANOVA at the AAS, my second thought combined with my experience at CfA is now quite opposite to my first thought. There are plenty of rooms where well sought experiment design can be adopted in the astronomical society.

## TomLoredo:

Thanks, Hyunsook, for the comments on ANOVA. Just thought I’d point out for astronomers that ANOVA is not at all limited to design of experiments. It’s a kind of umbrella term for a group of methods that try to study parameters in groups (perhaps of size one), to see whether and where they are important across a set of subjects. ANOVA arises in inferential statistics as well as in experimental design and exploratory data analysis.

The nicest overview of ANOVA I’ve come across is a lovely article by Andrew Gelman from

06-27-2008, 11:29 pmAnnals of Statisticsin 2005: Analysis of variance–why it is more important than ever. I especially like the connections it makes between ANOVA and hierarchical (multilevel) modeling and regression, and the Bayesian flavor Gelman gives to ANOVA (normally considered frequentist territory) I think will appeal to a physical scientist’s intuition more than the treatments in stats texts.## hlee:

I’m always very much obliged to have your comments! My slow reading delayed showing my gratitude, though. I never ponder on ANOVA from a Bayesian perspective. I only have a notion that it’s a great way to see regressions or (generalized) linear models whose components are not necessarily ruled by physics but needs interpretations in terms of their significance in model contribution. The challeges comes in when the structures of components for mutli-way ANOVA and MANOVA.

Once I tried to understand ARF, RMF, PSF in X-ray observations from the ANOVA perspective. For example, one’s best fit depends on a source model within which ARF is nested. I wanted to see ARF as random effect but was not sure how things were crossed. Overall, the nested structure was not clear to me. If the structure becomes clear, I guess Bayesian modeling is naturally incorporated for fitting (factoring statistical and systematical uncertainties as by product) and testing source models (Bayes factor instead of goodness of fits).

It is a very good read (Gelman is a very good writer and speaker) but I’m afraid how many astronomers will bother to learn ANOVA and related statistics. The lexicons in design of experiments and consequent statistical inference seem very absurd for astronomers, at least I felt that way when I just began to learn statistics.

07-02-2008, 3:30 pm