Homework #1: Due 18 Jan, 5pmNote: Your response to question 1 goes to me. Your answers to questions 2 and 3 go to the grader, Senniang Chen (firstname.lastname@example.org). On future HW, all answers go to Senniang. If you want to print your answers and bring them to Friday lecture, I will give them to Senniang. If you want to print your answers and deliver them to Senniang's office (3211 Snedecor), that's also fine.
1) Please read the syllabus. If you have any questions, please e-mail them to me (email@example.com). If not, please e-mail me a short statement saying something like “I have read the syllabus, understand its contents, and have no questions”.
2) The data in handicap.txt are from a randomized study of the influence of handicaps on perception of job applicant’s suitability for a managerial job. A single actor was taped responding to questions in a mock job interview. In one tape, he had no visible handicap (code=1), in a second tape he behaved as if his leg had been amputated (code=2), in a third tape he arrived using crutches (code=3), in a fourth tape he behaved as if he had a hearing difficulty (code=4), and in a fifth tape he arrived in a wheelchair (code=5). Seventy undergraduate students were recruited to read the job description, view a tape and report on the suitability of the candidate for the job. 14 students were randomly assigned to view each tape. The response (score) is the student’s evaluation of the suitability of the candidate for the job (high values = more suitable).
a) Test the null hypothesis that there is no influence of handicap on mean rating (i.e. all five groups have the same mean). Report the null hypothesis, your test statistic, its distribution if the null hypothesis is true, and write a one sentence conclusion
b) Estimate the mean difference in suitability score between no handicap and the average of any handicap (amputee, hearing, wheelchair, or crutches). Report your estimate, its se and a test of whether the population estimate = 0.
c) Estimate the mean difference in suitability score between permanent handicaps (amputee, hearing, and wheelchair) and temporary handicaps (crutches). Report your estimate, its se and a test of whether the population estimate = 0.
d) Are quantities in parts b) and c) contrasts? Explain (briefly) why or why not.
e) Are the quantities in parts b) and c) orthogonal? Explain (briefly) why or why not.
f) How many orthogonal contrasts are needed to create the test statistic in part a?
g) Write down the coefficients of one set of orthogonal coefficients that will, when the SS are summed, lead to the test statistic in part a.
3) This problem is based on a carefully controlled study of the long-term effectiveness of three diet plans. Most studies of long-term effectiveness are flawed by dropout (subjects leaving the study) and poor compliance (subjects not sticking with their assigned diet). These data came from a study where the main meal of the day was provided by the employer, so there was (relatively) little dropout and good compliance.
322 overweight employees were randomly assigned to one of three diet plans: low fat, low carb, and mediterranean. Details of the diets are not important. The response is the kg lost per subject 24 months after the start of the diet for the 272 people who completed the study. The data are in dietstudy.csv. Ask if the comments in oneway.r or oneway.sas are not sufficient for you to read .csv files from Excel into SAS or R.
a) Test the null hypothesis that the mean weight loss is the same in the
three diets. Report your test statistic, its theoretical distribution when the
null hypothesis is true, the p-value, and a short conclusion (no statement of
b) The low-fat and Mediterranean diets both have 1800 kcal/day for men and 1500 kcal/day for women. Use a t-test to test whether these two diets have the same mean (remember to estimate the pooled error variance from all individuals). Report the p-value. (No conclusions needed in 3b).
c) The hypothesis of equality of means for the low-fat and Mediterranean diets can also be tested by comparing an intermediate model with 2 groups (A: low-carb and B:either low-fat or mediterranean) to a full model with different means for all 3 diets. The p-value from the F test comparing the intermediate to the full model is 0.1264. Is this the same as the p-value from part 3b? Briefly explain why the two p-values should (or should not) be the same.
d) Compared to other long-term diet studies, dropout was low in this study. Even so, 50 of the initial 322 subjects did not complete the study. Why might dropout be a concern?
Note: We haven't talked about this. I want you to think about it. It may help to know that some folks fail to complete a study because they move out of the area or change employers; other folks decide on their own to stop following their assigned diet. Experience with weight loss studies indicates that folks are more likely to stop following their assigned diet if they believe it is not working.