Question

5 a farmer wants to investigate the effectiveness of two types of irrigation for increasing the growth of his crops. he has 12 plots of land available for the study. some plots border a stream that runs from the farmhouse to the southern edge of the property. he plans to use a randomized block design to randomly assign half of the plots to one irrigation type and the other half of the plots to the other irrigation type. two options for blocking are shown in the diagram. for each option, one block is identified by the gray shaded region and the other block is identified by the white shaded region. a. which blocking plan, option 1 or option 2, will better determine the effectiveness of the two types of irrigation? explain. b. draw an outline of the randomized block design for this experiment. c. what is the purpose of randomly assigning within each block?

Explanation:

a. Option 2 is better. Blocks should group similar plots. The stream might affect soil moisture (a confounding variable). Option 2 blocks by proximity to the stream (plots in a block are more homogeneous regarding stream - related factors).

b.

• Block 1 (plots near stream):
• Randomly assign half of Block 1 plots to Irrigation Type A and half to Irrigation Type B.
• Block 2 (plots far from stream):
• Randomly assign half of Block 2 plots to Irrigation Type A and half to Irrigation Type B.
• Measure crop growth in all plots.

c. Random assignment within blocks reduces bias. It ensures that any differences in crop growth within a block are more likely due to the irrigation type (treatment) rather than other lurking variables.

Answer:

a. Option 2. Because it groups plots by proximity to the stream (a potential confounding variable), making blocks more homogeneous.
b.

• Block 1 (near - stream plots): Randomly assign half to Irrigation A, half to Irrigation B.
• Block 2 (far - stream plots): Randomly assign half to Irrigation A, half to Irrigation B.
• Measure crop growth.

c. To reduce bias and ensure differences in growth within a block are due to irrigation (treatment).