<P> The assumption of unit treatment additivity usually cannot be directly falsified, according to Cox and Kempthorne . However, many consequences of treatment - unit additivity can be falsified . For a randomized experiment, the assumption of unit - treatment additivity implies that the variance is constant for all treatments . Therefore, by contraposition, a necessary condition for unit - treatment additivity is that the variance is constant . </P> <P> The use of unit treatment additivity and randomization is similar to the design - based inference that is standard in finite - population survey sampling . </P> <P> 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! </P> <P> 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 . </P>

A factorial anova is this type of analysis