2-1 Designed Experiments

We are interested in the relationship between the amount of fertilizer applied and the yield of wheat. We are interested in three levels of fertilizer: low, medium, and high. There are eighteen similar plots, numbered 1 through 18, available and the plots are located on an experimental farm at Midwestern University. The fertilizer is called a factor and there are three levels of interest for this factor. The plots are numbered as shown in Table 2-1.

The fertilizer levels are applied randomly as follows. Six random numbers are chosen between 1 and 18. The numbers are 1, 13, 8, 10, 16, and 12 and a low amount of fertilizer is applied to these plots. From the remaining twelve numbers, six more are randomly chosen. They are 2, 14, 9, 4, 11, and 6. A medium amount of fertilizer is applied to plots with these numbers. A high amount is applied to the remaining plots.

L represents a plot with low application of fertilizer, M a plot with medium application, and H a plot with high application. L, M, and H are levels of fertilizer. They are also called treatments. Table 2-2 shows the random assignment of treatments to experimental units or plots.