Assignment 6
Due Date
Friday, October 12, 2012
Data Source
The data for this assignment is fisheggs.txt, a tab-delimited text file.
Background
The data are from Zar (1999), p. 302. The file fisheggs.txt records the sodium content (μmol/g dry weight) of freshly laid fish eggs that were collected from six ponds in three seasons and at two water depths for two fish species. Six measurements were obtained from each of the six ponds. Fish species 1 was used in ponds 1, 2, and 3 while fish species 2 was used in ponds 4, 5, and 6. The organization of the data is shown below.
| Table 1 Sodium content (μmol/g) of fish eggs from six different ponds |
| Species |
Pond |
Season |
| Early |
Middle |
Late |
| Shallow |
Deep |
Shallow |
Deep |
Shallow |
Deep |
| 1 |
1 |
254 |
257 |
249 |
246 |
236 |
241 |
| |
2 |
261 |
268 |
257 |
263 |
249 |
252 |
| |
3 |
248 |
253 |
239 |
242 |
226 |
221 |
| 2 |
4 |
227 |
226 |
221 |
218 |
219 |
226 |
| |
5 |
233 |
239 |
229 |
235 |
222 |
224 |
| |
6 |
212 |
220 |
214 |
220 |
203 |
205 |
Questions
- Explain the experimental design that was used here. Clearly identify the different kinds of experimental units and treatments using the language that is appropriate for this design.
- Analyze the manner in which species, depth, and season affected the sodium content of fish eggs.
- Bonus question. Because the data of this experiment are perfectly balanced the analysis can also be done using the aov function of R. Show how your starting model in Question 2 can be fit using the aov function.
- Prepare a graph that summarizes the results of your analysis.
- Assume that the three values of the season variable are equally spaced in time. Refit your final model from question 2 but this time treat season as a continuous variable with equally spaced values. Superimpose your final continuous season model on the graph of Question 4.
- Interpret your final model of Question 5. In terms of this model how does the sodium content of the eggs of the two species differ? Give both a qualitative and a quantitative answer.
Hints
- By the way I've constructed Table 1 I mean for you to assume that there is no connection between the season and the depth, i.e., in each of the three seasons two new random locations were selected—one deep and one shallow—in each of the six ponds. Thus you can view season and pond as crossed factors.
- Question 3 is a bonus question; it is not required. If you manage to fit both the aov model and the starting model in Question 2 correctly, the results should match exactly. Be sure when you're fitting the aov model that any categorical variable that has numeric levels is declared to be a factor.
Cited references
- Zar, Jerrold H. 1999. Biostatistical Analysis (4th edition). Upper Saddle River, New Jersey: Prentice Hall.
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