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:
- 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?
- Identify the experimental design used here. Write down the linear
model corresponding to an appropriate analysis of variance.
- Fit this analysis of variance model and draw conclusions. Are the assumptions behind the model satisfied?
- 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.)
Instructions:
- Here is the data as a plain text file.
- Typeset your results as a report, using the same
format, template, and general instructions as for Assignment 2.