Abstract The principles of replication, randomization and local control as put forward by R.A. Fisher a century ago are all well known and adhered to in most experiments. In some applications, however, lack of randomization is still practiced. One particular area where this is common is on-farm experimentation. Hence, revisiting these important principles seems useful. In this paper, we particularly consider the use of uniformity trial data to empirically assess the validity of experimental designs in terms of the estimation of error and empirical Type 1 error rates. We compare classical designs such as the completely randomized design and the randomized complete block design to systematic designs. Moreover, following a suggestion in Fisher’s 1925 book, we propose a design optimized for a positional covariate of the plots. These designs are compared to two systematic designs. In addition to simple linear models, we consider a specific kind of spatial model for analysis systematic designs. Our results show that properly randomized designs yield valid inferences, whereas with systematic designs there is a risk of biased estimates of error. The design optimized for the positional covariate, while entailing some mild restriction on randomization, still provided valid inferences. In conclusion, our recommendation is to always use properly randomized designs.
Piepho et al. (Mon,) studied this question.