Due Thursday, February 6, 2003 at 12:40pm. Late homework will not be accepted.
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.
Writeups 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 your colleagues, but your writeup must be your own.
Students requesting regrades of assignments or exams must make these requests within one week of receiving the graded material. Attach a note explaining the regrade issue to your assignment or exam and submit to instructor. The instructor or TA has the option to regrade the entire assignment or exam.
Adapted from Sleuth exc. #29, page 203-204
Full text of article by M. Soler et al. "Weight lifting and health status in the black wheater," Behavioral Ecology 10(3) (1999):281-86. Their analysis is different from the one you will do.
Text writeup, Page 1:You will investigate the question of whether health as measured by T-cell response (mm) is associated with stone mass. You will need to cover the following points in your writeup.
Perform an exploratory analysis of the data, giving appropriate summary statistics and the linear correlation coefficient. Make a summary stats table and use a scatterplot (regression line plot below) to discuss in a few sentences the features of the data.
Regress T-cell response (response variable) on stone mass (explanatory variable), and report regression results. State assumptions needed in terms of the problem at hand. Underline the sentences on assumptions.
Test for evidence of a linear association between T-cell response and stone mass and give p-value for your result. Interpret the slope in terms of the problem and give a 95% confidence interval for the slope.
For a future observation of a bird carrying a 7g stone, find a 95% prediction interval for a the T-cell response. Discuss in terms of the problem at hand.
Use plots of residuals vs. fitted values and a qqplot of residuals to examine the fit of the regression model.
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: 1.5 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.
Soler et al. comment that the "Average mass of stones was positively correlated with the response to injection with phytohemagglutinin [Figure 1; F = 9.27, df=1,19, r-sq=.33, p=.0067; mean stone mass (g)=(4.00 +/- 1.10) + [(9.98 +/- 3.28)xT-cell response] (mm)]." (page 283, 2nd to last paragraph)
In your own words, what is the null hypothesis being tested with the p-value they give? How did they decide whether to do a one-sided or a two sided test?
The number after the "+/-" sign is the standard error of each estimate. From the information they provide, could you calculate a 95% confidence interval for the intercept? Why or why not? Interpret such a confidence interval in terms of these variables. Is this a useful confidence interval to calculate?
Why do they make a Bonferroni correction in the "Health Status vs. Reproductive Success" section of the paper? How does this change their conclusions?
With their experimental design, can we conclude that higher T-cell responses cause the mean stone mass to increase? Why or why not?
Why might we be concerned that they are using mean stone mass as a response variable? (Use what you know about the relationship between the slope and correlation coefficient.)
Required Format for answers to supplemental exercises: 2 pages max, 1.5 spaced, 11pt font, 1 inch margins all around, Times New Roman.
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. But also, 8 significant digits is unacceptable as well. Carefully choose the level of precision in your final answer. My rule of thumb is 1 or 2 digits more than the precision of the data for things like p-values. Often, it may be appropriate to round an important figure to the number of significant digits in the data.
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.