Fisher gave us three fundamental principles for designed experiments: replication, randomization and local control. Consonant with this, Brien et al. (2011) [Brien, C. J., Harch, B. D., Correll, R. L., & Bailey, R. A. (2011) Multiphase experiments with at least one later laboratory phase. I. Orthogonal designs. Journal of Agricultural, Biological, and Environmental Statistics, 16, 422-450.] exhort the use of randomization in multiphase experiments via their Principle 7 (Allocate and randomize in the laboratory). This principle is qualified with ‘wherever possible’, which leads to the question ‘when is randomization not possible?’.
Situations where randomization is not applicable will be described for both single-phase and multiphase experiments. The reasons for not randomizing include practical limitations and, for multiphase experiments, difficulty in estimating variance parameters when randomization is employed. For the latter case, simulation studies canvassing a number of potential difficulties will be described. A Nonrandomization Principle, and an accompanying analysis strategy, for multiphase experiments will be proposed.