I have a question about the way to code nested factor in the data. Should each level be identified with a unique code (I think this is required for lmer) or each factor should be repeated. Example:

3 treatments (enrichment), repeated 3 times (different places, uniques):

enrichment place place_unique

A 1 1

A 2 2

A 3 3

B 1 4

B 2 5

B 3 6

I really enjoyed your threads and am amazed with the way you explain things that is understandable even to a beginner like me. Came across your website by accident while looking for chi-square vs logistic regression explanations. Thank you! A quick question: The place where I work is currently using a tool to categorize feeding difficulties in children and it has never been validated. BUT it has been widely used world wide (~8 countries) with studies proving its efficacy. Is it feasible to make a research using this tool without going through a validation study? Thanks very much !

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. [30] 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. [31] However, there are differences. For example, the randomization-based analysis results in a small but (strictly) negative correlation between the observations. [32] [33] 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* !