LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2004

ST 6600/STA 600 – DESIGN AND ANALYSIS OF EXPERIMENTS

02.04.2004                                                                                                           Max:100 marks

1.00 – 4.00

 

SECTION – A

 

Answer ALL the questions                                                                          (10 ´ 2 = 20 marks)

 

1. Define orthogonal contrasts with an example.
2. State Cochran’s theorem
3. Briefly explain the term ‘Local control’.
4. Give the missing value formula for the RBD with one missing observation.
5. Explain orthogonal Latin Square Design.
6. Give any two differences between RBD and LSD.
7. State any two advantages of factorial design.
8. Define a symmetric BIBD.
9. Explain Experimental unit and Treatments.
10. Define Affine Resolvable Design.

 

SECTION – B

 

Answer any FIVE questions                                                                        (5 ´ 8 = 40 marks)

 

11. Explain the difference between ‘Randomization’ and ‘Replication’ with a suitable example.
12. In CRD, show that , with usual notations.
13. Develop in detail the analysis of variance of Randomised block design.
14. Explain the concept of ANOVA. When do you perform critical difference?
15. Complete the following table

Source of Variance	d.f.	Sum of Squares	Mean Sum of Squares	F-ratio
Columns	5	–	–	–
Rows	–	4.20	–	–
Treatments	–	–	2.43	–
Error	–	–	0.65
Total	–	39.65	–

The columns as representing schools, the row as classes, the treatments as methods of

teaching Spelling and the observations as grades based on 100 points.  Test the hypothesis

that the treatment effects are equal to zero, showing all steps in the general procedure.

16. Distinguish between ‘complete confounding’ and ‘partial confounding’
17. Explain YATE’S method of computing the sum of squares due to main effects and interaction effects in the case of 2² factorial design.
18. State and prove the parametric conditions of a BIBD.

 

SECTION – C

 

Answer any TWO questions                                                                       (2 ´ 20 = 40 marks)

 

19. a) Estimate a single missing observation in LSD.
20. b) Develop the analysis of variance in the case of LSD. when one observation is missing

in the design.                                                                                                           (8+12)

 

20. a) Derive the analysis of two-way classification with m-observations per cell by stating

all the effects, ANOVA  and conclusion.                                                                   (12)

1. b) Consider the results given in the following table for an experiment involving six

treatments in four randomised blocks. The treatments are indicated by numbers within

parentheses.

 

Yield for a randomised block experiment treatment and yield.

Blocks
1	(1) 24.7	(3) 27.7	(2) 20.6	(4) 16.2	(5) 16.2	(6) 24.9
2	(3) 22.7	(2) 28.8	(1) 27.3	(4) 15.0	(6) 22.5	(5) 17.0
3	(6) 26.3	(4) 19.6	(1) 38.5	(3) 36.8	(2) 39.5	(5) 15.4
4	(5) 17.7	(2) 31.0	(1) 28.5	(4) 14.1	(3) 34.9	(6) 22.6

Test whether the treatments differ significantly at 5% level of significance.             (8)

 

21. Explain in detail the analysis of 3² factorial design by stating all the effects, ANOVA and Inference.                                                                                                                  (20)

 

22. a) Construct a BIBD with the following parameters

v = 5, b= 20, r = 8, k = 2, l = 2                                                                                 (10)

1. b) For a BIBD, show that i) bk = rv  and       ii) l (v – 1) = r (k – 1)                            (10)

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

AC 22

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2007

ST 6600 DESIGN AND ANALYSIS OF EXPERIMENTS

 

 

 

Date & Time : 16.04.2007/9.00-12.00      Dept. No.                                                      Max. : 100 Marks

 

 

SECTION A

 

Answer ALL questions. Each carries TWO marks.                                                 10 X 2 = 20

 

1. Give an example of a Contrast.
2. Write the number of error degrees of freedom in a Latin Square Desgin of order 4.
3. When do you recommend RBD instead of CRD ?
4. Give the model representing one way classified data.
5. Write all possible treatment combinations in a design.
6. What is confounding ?
7. Give a consistent set of values for the parameters involved in a BIBD.
8. Write the contrast defining highest order interaction in design.
9. What is a generalized effect ?
10. What is an Incidence matrix ?

SECTION B

 

Answer any FIVE. Each carries EIGHT marks.                                                        5 X 8 = 40

 

1. Estimate the block effects in two way statistical model.
2. Show that the mean of available values can be taken as the missing value when a single observation is missing in CRD.
3. Explain the preparation of a Randomised Block design with 4 blocks and 3 treatments.
4. Explain how various sums of squares are computed in design.
5. Explain Yates method of computing various sums of squares in design.
6. Show that (under usual notations).
7. Illustrate with an example of your choice how partial confounding is executed in  designs.
8. Obtain the factorial effect of the highest order interaction in three different ways known to you in the case 2³ design.

SECTION C

 

Answer any TWO. Each carries TWENTY MARKS marks.                                2 X 20 = 40

 

1. Explain the analysis of RBD in detail.

20. With the help of a suitable statistical model illustrate how block differences are

made to  contain a confounded treatment effect.

1. (a) Explain how confounding is done in designs

(b) Show that is always non-singular where is the incidence matrix of a                 BIBD.

22. Explain the analysis of BIBD .

 

 

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