6.3 An agronomist conducted a field trial to compare the relative effects of five par- ticular fertilizers on the yield of Trebi barley. Thirty homogeneous experimental plots are available and six were assigned at random to each fertilizer treatment. At harvest time, three sample quadrats were taken (at random) from each exper- imental plot and the yield was obtained for each of the 90 quadrats. (i) What is the name of the experimental design used? Give an appropriate model for analyzing the data from this experiment. (ii) The agronomist has consulted two "statisticians" for the analysis of the data. He wants to know whether there are differences among the fertilizer effects. He is confused by the three SAS printouts (see Tables 6.16

a, b,

c) and he comes to you for help to find out which analysis is correct. Based on the information provided explain how an appropriate test should be carried out. (iii) What is the variance of a single observation [express as a formula based on your model statement in (i)] and how much of this variance is due to experimental error and to observational (sampling) error (use the numerical information provided). (iv) Give the standard error for a simple treatment comparison.