Immer et al. (1934) conducted an experiment to compare the yield of four varieties of barley (manchuria, velvet, trebi and peatland) when paired with two different fertilizers (“A” and “B”). Four locations in Minnesota were selected for the experiment. At each location, 8 plots were established, and the variety fertilizer combinations were randomized to the plots such that each unique variety fertilizer combination appeared exactly once at each location. The yield of each plot was measured at the end of the growing season. The data are contained in the file barley.txt, which can be found on the course website. The data set contains the following variables:
loc The [loc]ation: St. Paul, Waseca, Morris, or Duluth
var The [var]iety of barley
fertilizer The type of fertilizer provided
yield The response.
The investigator is interested in characterizing the differences among the barley varieties, between the fertil- izer treatments, and any possible interaction between barley variety and fertilizer. The location is considered a blocking factor. The investigator is interested in drawing inferences that apply to these four specific loca- tions, suggesting that the blocking factor should be modeled using a fixed effect. Use PROC GLM to answer question 1, and also answer question 2.
An experiment compared the effects of two different fertilizer application methods (broadcast vs. band) and two different fertilizer application rates (low vs. high) on watermelon yield. Application methods and application rates were crossed to form four unique treatment combinations. Treatment combinations were assigned to a total of sixteen (16) experimental units arranged in a Latin-squares design. You can find the data in the file melon.txt on the course website. The data set contains the following variables:
rblock The row block.
cblock The column block.
method The method of fertilizer application.
rate The rate of fertilizer application.
yield The response.
Jan proposes to fit an ANOVA model to these data that includes the following terms:
• Full factorial effects (main effects and interaction) for the method and rate factors.
• A fixed effect for the row block.
• A fixed effect for the column block.
• Residual error.
Answer question 3 on the basis of this proposed model. (You do not actually have to do any model fitting for this question, although you are welcome to do so if you wish.)
A plant biologist is interested in characterizing the effects of 4 concentrations of a growth hormone (0, 1x, 2x, 3x) on the growth of seedlings of two pine species (A and B). Species A and B were of specific interest to the researcher (A was known to be tolerant to acid rain whereas B was not tolerant). In this experiment, 24 petri dishes (also called plates) were prepared, 6 for each of the 4 growth hormone concentrations. Each plate contained 2 embryos from each species, for a total of 4 embryos per plate. The 24 plates were placed in randomly assigned locations in an incubator, and after 2 weeks the length of the primary shoot was measured for every embryo in every plate. The data set thus includes 96 records (24 plates 4 embryos per plate.) The response of interest is the length of the primary shoot. A schematic of the design is shown below
The data are contained in the file pine.txt, which can be found on the course website. The data set contains the following variables:
enzyme The enzyme concentration of the plate
plate A variable to distinguish the replicate plates assigned to each enzyme concentration
species The species of the seedling
logy The log of the length of the primary shoot, the response.
Use these data to answer questions 4 – 7.
Here is an alternative version of the same experiment. This experiment also investigates the effects of 4 concentrations of a growth hormone (0, 1x, 2x, 3x) on the growth of seedlings of two pine species (A and B). Species A and B are again of specific interest to the researcher. This experiment also involved 24 petri dishes. However, in this experiment, 3 plates were assigned to each of the 8 unique combinations of growth-hormone concentration and pine species. Each plate contained 4 embryos, all of the same species. This data set also includes 96 records (24 plates 4 embryos per plate.) The response of interest is the length of the primary shoot. A schematic of this modified design is shown below.
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