distribution of the responses: Independence of observations – this is an assumption of the model that simplifies the statistical analysis. Normality – the distributions of the residuals are normal. Equality (or "homogeneity") of variances, called homoscedasticity—the variance of data in groups should be the same. The separate assumptions of the textbook model imply that the errors are independently, identically, and normally distributed for fixed effects models, that is, that the errors () are independent and Randomization-based analysis In a randomized controlled experiment, the treatments are randomly assigned to experimental units, following the experimental protocol. This randomization is objective and declared before the experiment is carried out. The objective random-assignment is used to test the significance of the null hypothesis, following the ideas of C. S. Peirce and Ronald Fisher. This design-based analysis was discussed and developed by Francis J. Anscombe at Rothamsted Experimental Station and by Oscar Kempthorne at Iowa State University. Kempthorne and his students make an assumption of unit treatment additivity, which is discussed in the books of Kempthorne and David R. Cox. Unit-treatment additivity In its simplest form, the assumption of unit-treatment additivity states that the observed response from experimental unit when receiving treatment can be written as the sum of the unit's response and the treatment-effect , that is The assumption of unit-treatment additivity implies that, for every treatment , the th treatment has exactly the same effect on every experiment unit. 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. The use of unit treatment additivity and randomization is similar to the design-based inference that is standard in finite-population survey sampling. 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. 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