In an experiment to compare six different fertilizers for tomatoes, 36 individually potted seedlings are to

be used, 6 to receive each fertilizer. The tomato plants will be grown in a greenhouse, and the total yield of

tomatoes will be observed for each plant. The experimenter has decided to use a randomized blocks design:

The pots are to be arranged in six blocks of 6 plants each on the greenhouse bench. Two possible arrangements of the blocks are shown in the accompanying figure.

One factor that affects tomato yield is temperature, which cannot be held exactly constant throughout the

greenhouse. In fact, a temperature gradient across the bench is likely. Heat for the greenhouse is provided by a

steam pipe that runs lengthwise under one edge of the bench, and so the side of the bench near the steam pipe is likely to be warmer.

(a) Which arrangement of blocks (I or II) is better? Why?

(b) Prepare a randomized allocation of treatments to the pots within each block. (Refer to Example 11.6.4 as a

guide; assume that the assignments of seedlings to pots and of pots to positions within the block have

already been made.)

Example 11.6.4:

Blocking in an Agricultural Field Study When comparing several varieties of grain, an agronomist will generally plant many field plots of each variety and measure the yield of each plot. Differences in yields may reflect not only genuine differences among the varieties, but also differences among the plots in soil fertility, pH, waterholding capacity, and so on. Consequently, the spatial arrangement of the plots in

the field is important. An efficient way to use the available field area is to divide the field into large regions—the blocks—and to subdivide each block into several plots.Within each block the various varieties of grain are then randomly allocated to the plots, with a separate randomization done for each block. For instance, suppose we want to test four varieties of barley. Then each block would contain four

plots.The resulting randomized allocation might look like Figure 11.6.2, which is a schematic map of the field. The “treatments” T1, T2, T3, and T4 are the four varieties of barley. _

Figure 11.6.2: