Chapter 2.8, Problem 20E

In Exercises 2.20–2.22, identify whether the design is a completely randomized design, randomized complete block design, or Latin square design. If there is a factorial structure for the treatments, specify whether it has a two-factor or three-factor structure. If the measurement units are different from the experimental units, identify both.

2.20. The researchers design an experiment to evaluate the effect of applying fertilizer having varying levels of nitrogen, potassium, and phosphorus on the yields of orange trees. There were three, four, and three different levels of N, P, and K, respectively, yielding 36 distinct combinations. Ten orange groves were randomly selected for the experiment. Each grove was then divided into 36 distinct plots, and the 36 fertilizer combinations were randomly assigned to the plots within each grove. The yield of five randomly selected trees in each plot is recorded to assess the variation within each of the 360 plots.