Thank you for your extremely useful website.
I have a question. I want to know whether a specific chicken feed affects height, length and weight of chickens. So I have a team of three raters, each recorded weight, length and height of each 50 chicken at time 0, 1 and 2 months after this specific feed.
How should I analyse these data?
I plan to do intraclass correlation coefficient first to ensure the reliability of different raters. Should I use one factor at one time-point (such as weight at time 0)?
How do I test for normality? Do I average weights of each chicken and test for normality, then do the same for length and weight?
If I want to look at one factor (such as height), I shall then do repeated measures ANOVA. But if I want to look at three factors (height, weight and length), do I do repeated measures ANOVA for each factor separately? Is there a better way? From my understanding, two-factor ANOVA with replication does not apply to this situation.
If I reject the null hypothesis, do I then do repeated measures ANOVA for each factor separately?
If I reject the null hypothesis of weight alone, how do I do post-hoc analysis in this situation?
I hope my question is not too troublesome. I look forward to hearing from you in due course and than you in advance for your help.
Kempthorne uses the randomization-distribution and the assumption of unit treatment additivity to produce a derived linear model , very similar to the textbook model discussed previously.  The test statistics of this derived linear model are closely approximated by the test statistics of an appropriate normal linear model, according to approximation theorems and simulation studies.  However, there are differences. For example, the randomization-based analysis results in a small but (strictly) negative correlation between the observations.   In the randomization-based analysis, there is no assumption of a normal distribution and certainly no assumption of independence . On the contrary, the observations are dependent !