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.  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 !