Question

In the cornfield An agriculture researcher wants to compare the yield of five corn varieties: A, B, C, D, and E. The field in which the experiment will be carried out increases in fertility from north to south. The researcher therefore divides the field into twenty five plots of equal size, arranged in five east–west rows of five plots each, as shown in the diagram.

(a) Explain why a randomized block design would be better than a completely randomized design in this setting.

(b) Should the researcher use the rows or the columns of the field as blocks? Justify your answer.

(c) Use technology or Table D to carry out the random assignment required by your design. Explain your method clearly.

Short answer

(a) Randomized block design allows us to consider one or more extra variables as here we can subject group subjects into blocks having common characteristics.

(b) The researchers should use the rows.

(c) For each block, go to table E, record five unique numbers ranging $1$through $5$. Plant corn variety from left to right. Repeat for each block.

Step-by-step solution

Given Information

The researcher wants to compare the corn fields in five fields A, B, C, D, E. The field in which the experiment will be carried out increases in fertility from north to south. The researcher therefore divides the field into twenty five plots of equal size, arranged in five east–west rows of five plots each.

To explain randomized block design would be better than a completely randomized design

Randomized block design allows us to consider one or more extra variables as here we can subject group subjects into blocks having common characteristics. In completely randomized design, it is able to take into account changes in predictor variables. Hence randomized block design is preferred.

To explain if researcher should use the rows or the columns of the field as blocks

Since, randomized block design is preferred, researcher should use rows of the fields as block so that, within each block, location north or south does not vary.

To use a technology or Table D to carry out the random assignment required by design.

The random assignment is as follows:

• Label corn varieties A through E as $1$through $5$.
• For every block, go to table, chose a starting point and record five unique numbers from $1\mathrm{through}5$.
• Plant corn variety from left to right going from left to right in same order as their corresponding numbers were chosen.
• Repeat for every block.