Hello Charles,

Thank you very much for your reply!

1) For experiment 1, both data sets that failed the normality test (p= and p=) are not symmetric, according to the box plot. Therefore, a nonparametric test should be used for the analysis, right?

2) For experiment 2, there are two experimental groups. I only have three values for each group. The data for group A are: , , (normality test P<). The data for group B are: , , (normality test P=). The results from t-test (p=) and Mann-Whitney Rank sum test (p=) are very different.

Thank you!

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. [29] 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. [30] However, there are differences. For example, the randomization-based analysis results in a small but (strictly) negative correlation between the observations. [31] [32] 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* !

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.

Kind regards

Gerard