Derived linear model 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.Hinkelmann and Kempthorne (2008, Volume 1, Section 6.3: Completely Randomized Design; Derived Linear Model) 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.Hinkelmann and Kempthorne (2008, Volume 1, Section 6.6: Completely randomized design; Approximating the randomization test) However, there are differences. For example, the randomization-based analysis results in a small but (strictly) negative correlation between the observations.Bailey (2008, Chapter 2.14 "A More General Model" in Bailey, pp. 38–40)Hinkelmann and Kempthorne (2008, Volume 1, Chapter 7: Comparison of Treatments) 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!
Derived linear model 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.Hinkelmann and Kempthorne (2008 ,Volume 1, Section 6.3: Completely Randomized Design; Derived Linear Model) 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.Hinkelmann and Kempthorne (2008, Volume 1, Section 6.6: Completely randomized design; Approximating the randomization test) However, there are differences. For example, the randomization-based analysis results in a small but (strictly) negative correlati,on between the observations.Bailey (2008, Chapter 2.14 "A More General Model" in Bailey, pp. 38–40)Hinkelmann and Kempthorne (2008, Volume 1, Chapter 7: Comparison of Treatments) 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!