STA 6205 Syllabus
Fall 2012 -- Design of Experiments

Text:
Design and Analysis of Experiments, Montgomery, D. C. (8th Edition)
Recommended: SAS/ STAT User's Guide, Vol. 1 & 2
Instructor: Dr. Sen

Office: 14/2706 | Phone: 620 - 3724

Office Hours: 4:00 - 5:00 P.M. on Tuesdays and Thursdays, 4:30 - 5:30 P.M. on Mondays and Wednesdays, other times by appointment only.


Materials to be covered:
Simple Experiments and Experiments with a single Factor (Chapters 2 & 3)
  Randomized Blocks, Latin Squares, Balanced Incomplete Block Designs (Chapter 4)
  Factorial Designs (Chapter 5)
  The 2k Factorial Design, Blocking and Confounding (Chapters 6 & 7)
  Experiment with Random Factors (Chapter 13)
   

Grading: Final grades will be calculated based on a number of assignments, a midterm and a final
exam. You will need to use SAS for your homework. The assignments should be typed most of the times. I will accept some hand written assignments if done neatly on regular papers. If computer output is used, cut and paste the results.

I will not accept any late assignment.
Assignments are listed below so that you can plan ahead.
35% of your final grade will be based on the assignments (it is very important that you turn in your
assignments on time). You will have one project in the end of the semester. The rest of the final grade
is calculated based on 10% for project, 25% is for the midterm, and 30% is for the final exam.

Important Dates:
Holidays: Sept 3(Monday), Nov. 12 (Monday), Nov. 22 - 25 (Thur - Sat)
  Midterm: October 9 (Tuesday)
  Last day to withdraw: November 2, 2012 (Friday)
  Last day of classes: November 30 (Friday)
  Final Exam: December 4 (Tuesday) 6:00 - 7:50 P.M.
   

Dr. Sen
Fall ‘12

STA 6205 - Design of Experiments
Assignment # 1

Total 40 points Due on 08/30/12
1. Do the following problems from your text, Montgomery

# 2-14, 2-26, 2-32 , 2-36, 2.38.


2. The following data were from a study of red-blood cell counts before and after surgery. The
counts were taken on 23 patients, all of whom were of the same sex and who had the same blood
type. Assume that the blood type follow an approximate normal distribution.

Count                                                            Count
____________________________________ __________________________________
Patient           Pre-op           Post-op            Patient             Pre-op                  Post-op
_____________________________________ ___________________________________
1                  14                    0                        13                   5                           6
2                  13                   26                       14                   4                           0
3                   4                     2                        15                  15                          3
4                   5                     4                        16                    4                          2
5                   3                     1                        17                    0                          3
6                 18                     8                        18                    7                          0
7                  6                      0                        19                    2                          0
8                 11                     3                        20                    8                          13
9                 33                    23                       21                    4                           24
10               11                     2                        22                    4                            6
11                3                      2                        23                    5                            0
12                3                      2

(a) Make a scatter diagram of the two sets of count. Is there an apparent relationship between the
two sets of counts?

(b) Suppose we would like to estimate the mean count difference for the pre-op and post-op
patients for the same sex and same blood type using the given data. Construct a 95% confidence
interval for the difference of mean count for this group of patients.


 

Dr. Sen
Fall '12
STA 6205 - Design of Experiments
Assignment # 2
Total 40 points Due on 09/06/12
1. handout

2. #3.1, and 3.3 from the text.

3. Prove that .....handout


 

Dr. Sen
Fall '12
STA 6205 - Design of Experiments
Assignment # 3
Total 30 points Due on 09/13/12

Submit only the relevant computer output. You may consider the following:

a) ANOVA table

b) residual plots (if asked) with comments

c) multiple comparisons for the means (The one method that you use).


1. Do # 3-18 from the text. No need for part (e). Now answer the following questions based on the same data.

(d) Construct a set of orthogonal contrasts, assuming that the four coating types may be replaced by only two types. Carry out the tests for the contrasts. Use significant level = .01.

(e) Write the linear model you are using for the problem. Estimate all the model parameters using your data.

Note: You may expect to see questions like these in tests.

2. Problem 3-25 from the text.


 

Dr. Sen
Fall '12
STA 6205 - Design of Experiments
Assignment # 4
Total 30 points Due on 09/20/12
Do problems 3-26, 3-27, 3.39 from the text.


For each problem, state clearly

a) Statement of the hypotheses

b) ANOVA table (if possible) or appropriate test statistics

c) p-value of the test and your decision

d) residual plots (if asked) with comments

e) multiple comparisons for the means.


 

Dr. Sen
Fall '12
STA 6205 - Design of Experiments
Assignment # 5
Total 50 points Due on 09/27/12

1. Three fertilizers are tried on 27 plots of land in a random fashion such that each fertilizer is applied to nine plots. The total yield for each fertilizer type is given by

_______________________________
                             Type
_______________________________
                1               2              3
T.j         240           320           180
_______________________________

Sum of squares for treatments = 1096.30, SSE = 1440

a. Set up the ANOVA table for the analysis

b. Set up one set of orthogonal contrasts that might be used on these data.

c. For your first contrast, determine the sum of squares due to the contrast.

d. For your second contrast, find its standard error.

e. If one wished to compare types 1 and 2 and also the average of 1 and 3 versus 2, which method would you recommend and why? Do the comparison.

2. Do problem # 4-14 from the text.

Midterm October 9


 
Dr. Sen
Fall '12
STA 6205 - Design of Experiments
Assignment # 6
Total 30 points Due on 10/18/12
1. Do problems # 5-8 and 5-17 from the text.

2. Three technicians in a chemical plant are given the task of investigating the chemical yield of a raw material by applying one of the five experimental treatments. Three repeat tests are to be made with each of the five treatments. Design an experiment appropriate for this study. Is there a blocking factor in the design? If so, what is it? Write the design explicitly and identify each factor.


 

Dr. Sen
Fall '12
STA 6205 - Design of Experiments
Assignment # 7
Total 30 points Due on 10/25/12
Do problems 6-1, 6-2 and 6-3 from the text.

You may get your analysis done in SAS. But do some calculations by hand so that you will be able to do it in tests, if necessary. For any significant effects in 6-1, test further between the levels of the significant factors.


 

Dr. Sen
Fall '12
STA 6205 - Design of Experiments
Assignment # 8
Total 30 points Due on 11/01/12
Do problems 6-28 and 6-29 from the text.


You can do contour plots, surface plots, or the cubes. Use any tool you need to make a point.


 

Dr. Sen
Fall '12
STA 6205 - Design of Experiments
Assignment # 9
Total 30 points Due on 11/08/12

Do problems 7-5, 7-6, and 7-22 from the text.

You may get your analysis done in SAS, but should practice some of the calculations by hand so that you are able to derive these results in the final exam, if asked.


 

Dr. Sen
Fall '12
STA 6205 - Design of Experiments
Assignment # 10
Total 30 points Due on 11/15/12

1. Do problems # 13-1 and 13- 20 from the text.


2. In a chemical plant, five experimental treatments are to be used on a basic raw material in an effort to increase the chemical yield. Since batches of raw material may differ, five batches are chosen at random. The order of the experiments may affect yield as well as may the operator who performs the experiment. Considering order and operators as further restrictions on randomization, set up a suitable design for this experiment that will be least expensive to run. Write the ANOVA table with DF and outline its analysis.

Project due on 11/27/12

Final Exam December 4, 6:00 P.M. - 7:50 P.M.


 

Link: Pali Sen's Home Page