STA 4202 Syllabus
Fall 2013 -- 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: 3:00 - 4:00 P.M. on Mondays, Tuesdays, Wednesdays, and Thursdays, other times by appointments 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 use SAS on Virtual Lab. 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.
45% of your grade will be based on the assignments (it is very important that you turn in your
assignments on time), 25% is on the midterm, and 30% is on the final exam, both are in class tests.
VLAB link

http://www.unf.edu/its/services/Virtual_Software.aspx


Important Dates:
Holidays: Sept 2(Monday), Nov. 11 (Monday), Nov. 28 - Dec. 1(Thur - Sat)
  Midterm: October 9 (Wednesday)
  Last day to withdraw: November 1, 2013 (Friday)
  Last day of classes: December 6 (Friday)
  Final Exam: December 9 (Monday) 1:00 - 2:50 P.M.
   

Dr. Sen
Fall ‘13

STA 4202 - Design of Experiments
Assignment # 1

Total 40 points Due on 09/04/13
1. Do the following problems from your text, Montgomery

# 2.1, 2.3, 2.8, 2.16, 2.28, 2.32.


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 '13
STA 4202 - Design of Experiments
Assignment # 2
Total 30 points Due on 09/11/13

1. Use SAS to do # 3.15, 3.16, and 3.17 from the text.


 

Dr. Sen
Fall '13
STA 4202 - Design of Experiments
Assignment # 3
Total 30 points Due on 09/18/13

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 not all of them).


1. Do # 3.24 from the text. Now answer the following questions based on the same data.

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

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

2. Problem 3.25 from the text.


 

Dr. Sen
Fall '13
STA 4202 - Design of Experiments
Assignment # 4
Total 40 points Due on 09/25/13
Do problems 3.20, 3.27, 3.54 (a - e) 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 plot (if asked) with comments

e) multiple comparisons for the means (only the one you use).

For #3.27 use Bartlett's test to determine if the assumption of equal variances is satisfied.


 

Dr. Sen
Fall '13
STA 4202 - Design of Experiments
Assignment # 5
Total 50 points Due on 10/02/13

1. Three fertilizers are tried on 27 plots of land in a random fashions 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 problems # 4.1, 4.3, 4.5, and 4.21.

Midterm October 9

 

 
Dr. Sen
Fall '13
STA 4202 - Design of Experiments
Assignment # 6
Total 30 points Due on 10/23/13

1. Do problems # 5.9 and 5.21 from the text. Write models for each problem identifying wach parameters.

2. For problem # 5.9 estimate model parameters.

You do not have to do #3 since you may find text does not ask question like this. But as a teacher I thought you may like to think about situation like this. Hence the question is not for credit.
3. 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 '06
STA 4202 - Design of Experiments
Assignment # 7
Total 30 points Due on 10/30/06
Do problems 6.8, 610 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 6-10, test further between the levels of the
significant factors.


 

Dr. Sen
Fall '13
STA 4202 - Design of Experiments
Assignment # 8
Total 30 points Due on 11/06/13
Do problems 6.15 and 6.16 from the text.


You can do Contour plots in SAS, but if you want to draw the cubes, use hand sketch.
Use any tool you need to make a point.


 

Dr. Sen
Fall '13
STA 4202 - Design of Experiments
Assignment # 9
Total 20 points Due on 11/13/13

Do problems 7.5, and 7.6 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 '13
STA 4202 - Design of Experiments
Assignment # 10
Total 30 points Due on 11/20/13

1. Do problems # 13.4, 13.5 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.
Also, 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.

Final Exam December 9, 1:00 P.M. - 2:50 P.M.
Link: Pali Sen's Home Page


 

Link: Pali Sen's Home Page