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.

Thanks

Alex