three-way anova help please!


i'm currently performing a practical in R requiring 3-way fixed effects ANOVA for my maths degree. There are 2 quantitative factors - analysis temperature (AT) at 7 equally spaced levels and growth temperature (GT) at 2 levels. the qualitative factor is variety at 2 levels. there are 3 replicates at each combination of factors

i have performed the anova and found that 3-way interaction is not significant, the only 2-way significant interaction is GT-variety and the significant main effects are AT and variety.

I have been asked to maximise the response (amy - short for amylase activity). In doing this i need to perform 3-way anova (as i have done), analyse residuals, analyse interactions, fit polynomial models and produce contour plots.

I'm struggling to adapt my knowledge of 1 and 2 way ANOVA to this data and hence perform the analysis as required. i have a number of questions and would be very grateful if someone could guide me with them please.

1. looking at the plot of residuals against fitted values and the qq-plot of the residuals it is not obvious whether or not the ANOVA assumptions hold. i'd like to perform the shapiro-wilks test and bartlett's test and conclude from these. however, i am not sure exactly what to perform them on. what would you suggest please?

2. If I can show that one variety statistically yields better results, can I then discard the other variety from the data and only proceed on analysis with the superior variety? what would be the best way to show one variety was better than another?

I'll probably encounter more questions and post as I do. I'd be so grateful if anybody would be able to help me.


btw, it appears that one variety produces better results irrespective of growth temperature. it just appears that one variety prefers one growth temperature and one variety prefers the other (this is all based on the interaction plots).


TS Contributor
Basically, in order to optimize the response, or at least gain insight as to how it could be optimized after doing ANOVA, is to:

(1) remove insignificant main effects and interactions from the model, and
(2) do response-surface or contour plots on the reduced model

From the reduced model ANOVA, you should be able to get a regression equation or at least an output that shows model coefficients...

....there's no fixed procedure for this - you need to examine the remaining significant main effects and interactions and do some exploratory stuff with the plots.

I'm not familiar with the R software program, but as long as you can show that the data from each treatment group reasonably follows a normal distribution, that the treatment groups show reasonably equivalent variances, and that the residuals from the model are normal (i.e., use a normal probability plot), then the assumptions probably hold.
thanks John!

i'm gonna give those things a go. I did ask my tutor whether or not it was ok to remove insignificant variables and interactions and her reply was "no, this isn't regression analysis, removing variables and interactions won't give you any more insight into the data". then she asked us to model a regression polynomial by omitting insignificant terms and well, i got quite confused.

but yeah, im gonna just get stuck into it and do the best i can. i don't really understand how you can model a polynomial on 3 factors, one of which isn't even numerical or odered and then display it in a 2-dimensional graph. the idea of the response surface makes sense if there are 2 quantitative variables but when there are 3, surely it would be extending into 4-d space.

but like i say, im just gonna do whatever i can and hope for the best. thanks again for your help



TS Contributor
Your tutor's comments are a bunch of baloney.

Of course you can gain insight by removing insignificant factors - it makes the model simpler, and easier to explore and interpret.

You can model a polynomial on anything - it won't necessarily be a good fit, however....