Unbalanced two way ANOVA

[#1]

Hello,

Please could I get help to analyse the following dataset. 

Birds were provided with two different feed pellets (long versus short) at three different concentrations of protein (100%, 80% and 60%). I want to consider the effect of protein concentration and feed type both together and separately. I was planning to do a two way ANOVA to consider the separate and interactive effects of these factors.

However, during the trial, a feeder malfunction meant that some pens had to be excluded, and the trial was no longer balanced, as there are different numbers of replicates in each treatment. Can I still do the two way ANOVA? And is there any way to perform a linear regression to see the stepwise effect of drop in protein concentration?

The experimental unit here is "Pen". Each week a sample of birds in each pen were weighed for bodyweight. So some of the parameters are recorded at different time points in each trial, and some paramters i.e. gross margin are recorded only at the end.

Thank you

Abbie

[#2]

You can absolutely still do the analysis the way you intended.  Equal sample sizes for each treatment is a nice-to-have property, maximizes power for the total sample size, and can make things mathematically simpler.  You're in a less ideal situation, but you are in no way impeded from being able to do a 2-way ANOVA.  However, since you're data is longitudinal, you may want to consider doing a more sophisticated analysis using the Mixed personality in Fit Model if you have JMP Pro (I don't, so I can't show you how to construct the analysis), but you will need to stack the columns of for the weight at different time periods and fit random intercepts/slopes model.  I think an AR(1) correlation structure would be most appropriate for this data.

[#3]

Thank you for this. I don't have JMP Pro either so I will just do the 2 way ANOVA in the meatime.

Thanks very much

Abbie