Editing Analysis of variance (section)

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

The randomization-based analysis has the disadvantage that its exposition involves tedious algebra and extensive time. Since the randomization-based analysis is complicated and is closely approximated by the approach using a normal linear model, most teachers emphasize the normal linear model approach. Few statisticians object to model-based analysis of balanced randomized experiments.