STAT 5303 Assignment 5

An Orange Tree Growth Experiment

An experiment was set up to compare the effect of different soil pH values and calcium additives on the increase in trunk diameters for orange trees. Annual applications of elemental sulfur, gypsum, soda ash, and other ingredients were applied to provide pH value levels of 4, 5, 6, and 7. Three levels of a calcium supplement (100, 200, and 300 pounds/acre) were also applied. All factor-level combinations of these two variables were used in the experiment. At the end of a 2-year period, three diameters were examined at each factor-level combination. The data appear here:

pH Calcium
Value 100 200 300
4.0 5.2 7.4 6.3
5.9 7.0 6.7
6.3 7.6 6.1
5.0 7.1 7.4 7.3
7.4 7.3 7.5
7.5 7.1 7.2
6.0 7.6 7.6 7.2
7.2 7.5 7.3
7.4 7.8 7.0
7.0 7.2 7.4 6.8
7.5 7.0 6.6
7.2 6.9 6.4

Your task is to analyze these data using the techniques of Unit 5. In the process, you should do/answer the following:

  1. Construct a profile plot. What do these data suggest regarding the effects of pH and calcium on the increase in mean trunk diameters for orange trees?
  2. Identify the experimental design used here. Write down the linear model corresponding to an appropriate analysis of variance.
  3. Fit this analysis of variance model and draw conclusions. Are the assumptions behind the model satisfied?
  4. Use Tukey's W procedure to determine the significant differences in mean increase in diameters among the three calcium rates. Summarize this by comparing either: the 3 calcium means (main effects of calcium), or by comparing the 3 calcium means within each level of pH, whichever you think is most appropriate given the model you fitted above. Also identify which treatment combination seems to be the most effective at increasing trunk diameter. (Use alpha=0.05.)