The allocation of experimental units to completely random positions in an experiment, normally by using tables of random numbers. This form of experimental design is used when the units are very similar and they are being observed under particularly controlled conditions as, for example, a pure line of plants in a growth chamber. It has the advantage over *randomized block
and *Latin square
designs in that it increases the number of degrees of freedom, which consequently reduces the error variance. If, however, the experimental units or the environment are variable then a completely random design is less likely to pick up significant differences between treatments.