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* !

Would it ever be the case that the significance tests of the regression coefficients would come out non-significant when the overall F-test did come out significant? What if, for example, you had a factor with three levels, A, B, and C, with means 3, 5, and 4. If C is the reference level, could it be the case in the regression model that neither the coefficient comparing A to C nor the coefficient comparing B to C would be significantly different from 0, but that the F-statistic would be significant due to the difference between A and B?