# Refer to Exercise 19.1. Use the least significant difference criterion to identify which pairs of…

Refer to Exercise 19.1. Use the least significant difference criterion to identify which pairs of methods of irrigation have significantly different mean yields.

Exercise 19.1

In Exercise 15.1, we described an experiment in which a horticulturist was investigating the effectiveness of five methods for the irrigation of blueberry shrubs. The methods are surface, trickle, center pivot, lateral move, and subirrigation. There are 10 blueberry farms available for the study representing a wide variety of types of soils, terrains, and wind gradients. The horticulturist wants to use each of the five methods of irrigation on all 10 farms to moderate the effect of the many extraneous sources of variation that may impact the blueberry yields. Each farm is divided into five plots, and the response variable will be the weight of the harvested fruit from each plot of blueberry shrubs. During the study, a problem occurred on the plot irrigated using the surface method on farm 1, and no yield was obtained. The yields in pounds of blueberries over a growing season are given here.

a. Estimate the yield value for the missing plot.

b. Analyze the data by replacing the missing value with the estimate obtained in part (a), and then perform an analysis of variance using the formulas for a randomized block design with no missing observations.

c. Is there a significant difference in the mean yields for the different methods of irrigation? Use   0.05.

Exercise 15.1

A horticulturist is designing a study to investigate the effectiveness of five methods for the irrigation of blueberry shrubs. The methods are surface, trickle, center pivot, lateral move, and subirrigation. There are 10 blueberry farms available for the study, representing a wide variety of types of soil, terrains, and wind gradients. The horticulturist wants to use each of the five methods of irrigation on all 10 farms to moderate the effect of the many extraneous sources of variation that may impact the blueberry yields. On each farm, five 1-acre plots are randomly selected, and a method of irrigation is randomly assigned to each plot. The response variable will be the weight of the harvested fruit from each of the plots of blueberry shrubs.

a. Show the details of how you would randomly assign the five methods of irrigation to the plots.

b. How many different arrangements of the five methods of irrigation are possible in each of the farms?

c. How many different arrangements are possible for the whole study of 10 farms?

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