In a pharmacological experiment on eating behavior in rats, 18 rats are to be randomly allocated to three treatment groups: T1, T2, and T3 While under observation, the animals will be kept in individual cages in a rack. The rack has three tiers with six cages per tier. In spite of efforts to keep the lighting uniform, the lighting conditions vary somewhat from one tier to another (the bottom tier is darkest), and the experimenter is concerned about this because lighting is thought to influence eating behavior in rats. The following three plans are proposed for allocating the rats to positions in the rack (to be done after the allocation of rats to treatment groups):
Plan I. Randomly allocate the 18 rats to the 18 positions in the rack.
Plan II. Put all T1 rats on the first tier, all T2 rats on the second, and all T3 rats on the third tier.
Plan III. On each tier, put two T1 rats, two T2 rats, and two T3 rats.
Put these three plans in order, from best to worst. Explain your reasoning.