STA242/ENV255

STA242/ENV255 Assignment 2

Due Friday, March 7 at 5pm. Late homework will not be accepted.

Policies for this assignment:

The Nicholas School of the Environment and Earth Sciences (NSEES) advocates the highest standards of professional ethics and academic integrity. Students and faculty have developed an honor code for the school which is distributed to all students prior to matriculation and discussed during orientation. Students in this course are expected to follow the honor code.
All work must be done independently. This includes computations, Splus output, graphs, answers to questions and discussion of results. Copying will not be tolerated, and will be treated as a violation of the NSEES honor code.
You may discuss issues and concepts with the instructor or TAs only.

Assignment: Factors Affecting Extinction. This assignment has 2 parts.

One-page writeup, 2 pages of supporting material (graphs, etc) 80%
Supplemental questions 20%

Link to Dataset
Adapted from Sleuth exc. #27, page 299-300
Full text of article by Pimm et al. is available via E-journals at Duke Pimm et al.'s analysis is different from the one you will do.

Three Page Written Assignment:

Page 1: Text writeup. See new format below.
Page 2 & 3: Figures, Tables.

Text writeup, Page 1:The main question we will answer is whether after accounting for average number of nesting pairs, size is a significant determinant of average extinction time. The analysis will consist of fitting 3 models that describe:

The effect of body size on average time to extinction after accounting for the average number of nesting pairs
Migratory birds: the effect of body size on average time to extinction after accounting for the average number of nesting pairs
Resident birds: the effect of body size on average time to extinction after accounting for the average number of nesting pairs

What is the role of size (Large or Small) in this analysis? Is the relationship between extinction time and average number of nesting pairs the same for the large and small birds, or does it change according to size? For whatever model you choose, give confidence intervals for the slope for both sizes. Do the same relationships hold when we consider migratory birds alone? What about resident birds?

Perform an exploratory analysis of the data, giving appropriate summary statistics in a summary stats table. Make 3 coded regression line plots to for the 3 models above and discuss features of the data using these. (You can refer to these again when you discuss fitted models).
Report regression results. State assumptions needed in terms of the problem at hand. Underline the sentences on assumptions.
Interpret the slopes of the models to describe the role of size on time to extinction after accounting for nesting pairs. Give CI's. Put these sentences in italix.
Use plots of residuals vs. fitted values and qqplots of residuals to examine the fit of the regression models. You'll need to examine residuals vs. fitted and normal QQ plots at each step as you investigate the relationship. Coded scatterplots will be very helpful in choosing a model. Coded residual plots may also be helpful. You can save the residuals and fitted values from a fitted model and plot them against the fitted values by making slight adjustments to the commands for coded scatterplots (replace X1 and Y with your fitted values and residuals, respectively, and again code by bird size).
As you write up your exploratory data analysis and statistical analysis section, briefly describe the features of the data that lead to your modeling choice. The majority of the statistical analysis section should focus on interpretations of the model you have chosen (and answers to the specific questions above).
DO NOT waste space talking about transformations and models you tried that did not work. Focus on your final model.
You will make most efficient use of your time by working on this problem incrementally, and spreading your work/discussion with TAs over a few days. Spend some time exploring the data, models, transformations.
Comment on scope of inference: generalizability and causality/association. Describe any issues in experimental design/data collection that might lead to violations of assumptions.
Required Format for page 1: single spaced, 11pt font, 1 inch margins all around, Times New Roman. Points will be deducted if the format is not followed exactly. Name on each page.

Supporting figures, tables, equations, Page 2 & 3: Refer to these in your writeup.

Provide a Table of Summary Statistics that you will briefly discuss in your writeup. Provide a caption.
Summarize all regression results in the format at bottom of page 185. Provide a caption.
Provide 3 carefully labelled regression line plots with captions.
Provide a plots of residuals vs. fitted values with caption for the final models you choose.
Provide a QQ-normal plot of residuals with caption for the final models you choose.
You can also use this sections to give any other technical details or discussion that does not belong in the 1-page writeup. Remember, your analysis will be judged just on page 1.

An easy way to get figures to fit on a page is to put them inside the cells of a table (with no visible border lines) and then reduce the size of the picture.

Sample writeup for a simple linear regression problem.

Components of a writeup

Note a mistake in the Sleuth dataset as printed on p. 301: Note that the data presented in Display 10.22 have had 1.0 added to years. There are 7 species for which average extinction time was 0, meaning that these populations survived without extinction for the entire census. These are called "censored" data, meaning that there is an extinction time, and we know it is greater than the greatest value in the dataset, but we do not know how much greater. Thus, the Sleuth's idea to say the extinction time is "1" year for these makes no sense. The dataset link provided above has omitted these observations. You do not need to discuss these in your writeup. We will discuss how to handle these later.

Supplemental Exercises Skim through the Pimm et al. paper so that you can answer the following questions.

Read "Technical Comments" on page 767-8. What is the Y variable that Pimm et al. use in mathematical terms and in terms of the problem. Give one of the justifications for its use.
Again under the "Technical Comments" on page 767-8, why might our analysis be biased by excluding those species for which a time to extinction was not observed?
Read the "Effects Related to Body Size" section on p. 771, particularly the paragraph beginning "The regression analysis also illustrated that...." Do his comments on "7 pairs" apply to your results for model 1 (the effect of body size on average time to extinction after accounting for the average number of nesting pairs)? Could you adapt this type of statement for your data? If yes, do so. If no, explain why.
Under "Effects of Migratory Status" on page 771, do you support the finding that for migrant species, time to extinction is not affected by the number of nesting pairs? Use a statistical argument.
For model 1, (the effect of body size on average time to extinction after accounting for the average number of nesting pairs) give a prediction interval for time to extinction for a future observation of a Wood Pidgeon, using the value of average nesting pairs and size from Table 10.23 on page 301.

General format hints:

Raw Splus output is not acceptable. Edit the output to show the most relevant results.
Give exact p-values using Splus. You'll only use the tables for exams.
Be careful with rounding. If you round too much, you propogate errors.
STAPLE your pages in the correct order PRIOR to turning them in. TAs do not grade unstapled homework.
Please type your answers.
Written interpretations and conclusions are at least as important if not more important than generation of data summaries, statistics, tests, etc. Clear, careful writing and interpretation of results are critical components of this course.

Last modified: Sat Mar 1 16:05:01 EST 2003