Anova results

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?

Anova results

anova results


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