# Question

Refer to Exercise 19.11.

In Exercise 19.11

A horticulturist is interested in examining A horticulturist is interested in examining the yield potential of three A horticulturist is interested in examining the yield potential of three new varieties of asparagus. She designed a study to evaluate the three new varieties relative to the standard variety. There were 16 plots available on a large test field for the study, but the plots were not homogeneous in that there was a distinct sloping from north to south throughout the field. Also, a soil analysis revealed a discernible nitrogen gradient, which ran from west to east across the field. Therefore, the horticulturists decided to assign the varieties V1, V2, V3, and V4, with V1 being the standard variety, to the plots in a Latin square arrangement. The values for marketable yield per plot (in kg/ ha) are given in the following table. Note that there is a missing yield for variety V4 in row 4 and column 1. This was due to a problem that occurred during one of the harvesting periods.

a. Identify nitrogen level and slope level as either fixed or random effects.

b. How would you test for a significant difference in the mean marketable yields due to differences in nitrogen levels?

c. How would you test for a significant difference in the mean marketable yields due to differences in the amount of slope in the plots?

In Exercise 19.11

A horticulturist is interested in examining A horticulturist is interested in examining the yield potential of three A horticulturist is interested in examining the yield potential of three new varieties of asparagus. She designed a study to evaluate the three new varieties relative to the standard variety. There were 16 plots available on a large test field for the study, but the plots were not homogeneous in that there was a distinct sloping from north to south throughout the field. Also, a soil analysis revealed a discernible nitrogen gradient, which ran from west to east across the field. Therefore, the horticulturists decided to assign the varieties V1, V2, V3, and V4, with V1 being the standard variety, to the plots in a Latin square arrangement. The values for marketable yield per plot (in kg/ ha) are given in the following table. Note that there is a missing yield for variety V4 in row 4 and column 1. This was due to a problem that occurred during one of the harvesting periods.

a. Identify nitrogen level and slope level as either fixed or random effects.

b. How would you test for a significant difference in the mean marketable yields due to differences in nitrogen levels?

c. How would you test for a significant difference in the mean marketable yields due to differences in the amount of slope in the plots?

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