Data set: Corn
Split-plot designs were often originally used in agricultural experiments, where one factor was randomly applied to plots of land and then each plot was split up into smaller sections and a second treatment was randomly assigned to the smaller subplots. There are many reasons for using split-plot designs in agriculture. For example, a farmer can hire an airplane to spray herbicides or pesticides over large areas of land, and smaller plots within the larger plots can be used to plant rows of different species of a crop. Another example is growing strawberries in a greenhouse, where a factor, such as temperature, is applied to an entire greenhouse while another factor, such as water level, is applied to certain areas within the greenhouse. A study was conducted to determine if different species of corn or amounts of nitrogen would impact yields. 8 Nitrogen is available in the soil as the result of natural and biological processes; however, farmers often add a nitrogen fertilizer to corn crops in order to increase yields. A nitrogen deficiency can considerably decrease yields. Fertilizer is expensive; thus, many farmers will choose to plant a species of corn that grows well with less nitrogen. Soil types vary with each plot of land. The amount of nitrogen can also vary from year to year, depending on the type of crop (e. g., wheat, oats, hay, soybeans, or corn) planted the previous year. Thus, the amount of nitrogen needed will be different for different plots. Researchers often conduct studies for a county or entire state, so they are primarily interested in measuring the variability between plots instead of how well a specific plot does compared to another. Determining the right species to plant as well as the right amount of fertilizer can dramatically impact a farmer’s profit. In fact, a quick Google search will show that many agricultural states provide corn-nitrogen productivity calculators on the web. Many seed companies and state-sponsored agricultural research centers have large testing areas that have been shown to be similar to other plots of land throughout their state. In a large testing area, eight 20-acre plots of land were randomly assigned to a nitrogen application rate (0, 70, 140, or 210 pounds of nitrogen per acre). Each of these 20-acre plots was also subdivided into five 4-acre subplots. Within each 20-acre plot, the subplots were assigned to be planted with one species of hybrid corn (A, B, C, D, or E). At the end of the season, the fields were harvested and the yield in bushels per acre was recorded.
a. Specify whether each factor in the study is fixed or random and whether each factor is crossed or nested.
b. Calculate an appropriate ANOVA for this study using Yield as the response. State your conclusions, taking into account random sampling and random allocation. Provide appropriate plots.
c. Check the model assumptions. Create a plot to check if the data appear to be skewed or have outliers. Is there reason to doubt the equal variance assumption? Are the error terms approximately normally distributed?
d. Draw a Hasse diagram corresponding to this study.
e. Draw a picture of an aerial view of a possible 160-acre test area plot. There should be a total of 40 small plots in the final picture. Demonstrate how corn species and nitrogen rates could possibly have been randomly assigned.