AC 52

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

FOURTH SEMESTER – APRIL 2007

ST 4805 – APPLIED EXPERIMENTAL DESIGN

 

 

 

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

 

 

SECTION – A

Answer all the questions                                                          (10 x 2  = 20 marks)

 

1. Give any two industrial applications of Experimental Designs.
2. Obtain the relative efficiency of RBD over CRD.
3. State the regression model for 2² factorial design.
4. Define a simple Lattice design, with an example.
5. Define the FINITE FIELD with an example.
6. Briefly explain any one of the principles of experimental designs.
7. What is meant by Whole-plot treatments?
8. State the parametric conditions of a BIBD.
9. Give any two advantages of Split-plot design.
10. When do we go for RLSD ?

 

SECTION-B

 

Answer any Five questions                                                         (5 x 8  = 40 marks)

 

11. Discuss Fixed, Mixed and Random effect models with suitable illustrations.
12. Describe, the analysis of variance for a 2⁵ factorial design, stating all the

hypothesis, ANOVA and conclusions

13. Discuss half fractional factorial design with suitable illustration.
14. Construct a Lattice Square Design using  nine treatments.
15. Distinguish between RBD and BIBD with suitable illustration.
16. Show that all the treatment contrasts are mutually orthogonal in the case of 2³ factorial design.
17. Describe briefly the method of Steepest accent?
18. Explain the Analysis of Repeated Latin Square Design.

 

SECTION-C

 

Answer any Two questions                                                        (2 x 20  = 40 marks)

 

19. a)Explain the term Complete Confounding with suitable illustration.

b)Describe in detail confounding in more than two blocks in which two independent and one generalized

interactions are confounded.                                                                                               (6+14-Marks)

 

 

20. a) Distinguish between the Analysis of RBD and the analysis of RBD when one observation is missing.
21. b) Derive the missing formula when two observations are missing in the case of RBD.

(10+10-Marks)

21. a) When do we go for BIBD? Construct a BIBD when the number of treatment v = 5.
22. b) Develop the analysis of variance for a BIBD, stating all the  hypothesis, ANOVA and conclusions.

(3+5+12-Marks)

22 Write shorts on the following

1. MOLS
2. Galois Field
3. Biological applications of experimental designs
4. Homogenous Equations                                                                   (5+5+5+5-Marks)

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

NO 50

FOURTH SEMESTER – APRIL 2008

ST 4805 – APPLIED EXPRIMENTAL DESIGN

 

 

 

Date : 16-04-08                  Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION – A

Answer all the questions                                                          (10 x 2  = 20 marks)

 

1. Briefly explain the term “Randomization”
2. Define mutually orthogonal contrast with an example.
3. Give sum of squares for 3 factors interaction for 3³ Factorial Design.
4. If G(F) = pⁿ where p = 5 and n = 1, list the elements of the finite field.
5. When do we go for confounding Design?.
6. What is meant by resolvable BIBD? Give an example.
7. Give any two advantages of fractional factorial design
8. Define a simple Lattice Square.
9. State any two parametric conditions of a BIBD.
10. What is meant by optimal surfaces?

 

SECTION-B

 

Answer any Five questions                                                         (5 x 8  = 40 marks)

11. Describe, the analysis of variance for a 3³ factorial design, stating all the

hypothesis, ANOVA and conclusions

 

12. Distinguish between FIXED EFFECT MODEL and RANDOM EFFECT MODEL with suitable

illustrations.

 

13. Construct a mutual mutually orthogonal Latin Square when the number of treatments v = 5.

 

14. When do go for a PBIBD? Explain briefly with an illustration.

 

15. Discuss in detail the various RESOLUTION DESIGNS.

 

16. Explain the term repeated Latin Square Design and hence construct 5 X 5 repeated Latin Square

Design.

 

17. Distinguish between ANOVA and ANOCOVA.

 

18. Explain the term SPLIT – PLOT and STRIP = PLOT with an example.

 

 

 

 

 

 

SECTION-C

 

Answer any Two questions                                                        (2 x 20  = 40 marks)

 

 

 

19. a) Distinguish between confounding and fractional replication.

 

1. b) Develop, the analysis of variance for a 2⁴ fractional factorial design, stating all the

hypothesis, ANOVA and conclusions

 

(10+10-Marks)

 

20. a) Construct a PBIBD with 2 associate classes, stating all the parametric conditions.

 

1. b) Discuss in detail the Linear and Quadratic Response Surface Designs stating the model analysis

and conclusions.

 

(10+10-Marks)

 

21. a) Discuss in detail confounding in MORE THAN TWO BLOCKS using finite field.
22. b) Construct BIBDs with v = 5 with k = 2,  k = 3 and k = 4.

(10+10-Marks)

 

22 Write shorts on the following

1. Local control
3. Partial confounding
4. Orthogonal Design.                                       (5+5+5+5-Marks)

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

AF 01

FOURTH SEMESTER – April 2009

ST 4805 – APPLIED EXPRIMENTAL DESIGN

 

 

 

Date & Time: 18/04/2009 / 9:00 – 12:00       Dept. No.                                                       Max. : 100 Marks

 

 

 

SECTION – A

Answer all the questions                                                          (10 x 2 = 20 marks)

 

1. What is meant by non statistical principle of experimental design?
2. Briefly explain the term Random effect model with an example .
3. When do we go in for factorial design ?
4. State the minimal function for 5² factorial design.
5. Define the “term irreducible polynomial”.
6. State the formula for a missing value in a LSD ?
7. Define the term Aliases with an example .
8. Distinguish between RLSD and LSD.
9. Give any two advantages of BIBD.

10.Write the homogeneous equation for the highest order interaction in the case of 2⁴

       factorial design.

 

SECTION-B

 

Answer any Five questions                                                         (5 x 8  = 40 marks)

 

11. Explain the term “Effiency of LSD relative to RBD” with suitable illustration
12. Define linear contrast show that in 2⁵ designs the main effects and interaction

effects are mutually orthogonal.

13. Describe, the analysis of variance for a 3³ factorial design, stating all the

hypothesis, ANOVA and conclusions.

14.Develop the analysis of variance for a 2⁴ fractional design in which the highest

order interaction is confounded in all the replications

15. If G (F) = pⁿ when p = 11 and n = 1 list the elements of the finite field

and explain all the operations with suitable example.

16. State clearly the model used in the case of Youden Square and construct a real life

example.

17. Derive the minimal function for 2³ experiment and hence list the power cycle.
18. State and prove all the parametric conditions of a BIBD.

 

 

 

 

 

 

SECTION-C

 

Answer any Two questions                                                        (2 x 20 = 40 marks)

 

19.a) Discuss in detail the applications of the finite field with suitable illustrations.

1. b) Define the term key BLOCK in the case of 2⁵ factorial design of size 2³ in

which 2 independent interactions and 1 generalized interaction are Confounded

Discuss in detail using the required linear equations for the confounded effects.

(8 +12-Marks)

20.a) When do we go for Split plot design? Explain with an example.

 

1. b) Develop the Analysis of variance for the Split-plot design stating all the

hypothesis ANOVA and Inferences.                                            (8 +12-Marks)

 

21 a) Distinguish between Lattice Square and Lattin square designs.

1. b) Explain the m-ple Lattice Square design and hence construct lattice square design

when the block size k=5.                   (8+12-Marks)

 

22 Write shorts on the following

1. Critical difference
2. PBIBD
3. Response surface design
4. Primitive root (5+5+5+5-Marks)

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

FOURTH SEMESTER – APRIL 2011

ST 4809 / 4805 – APPLIED EXPERIMENTAL DESIGN

 

 

 

Date : 5/4/2011                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION – A

 

Answer all the questions                                                                                         (10 x 2  = 20 marks)

 

1. State the linear model used in 2³ factorial design
2. Briefly explain the term Blocking.
3. When do we go for repeated L.S.D ?
4. State Fermat’s theorem.
5. Define the term linear contrast with an example.
6. State the missing formula for RBD.
7. Define a resolvable BIBD with an example .
8. Distinguish between RBD and BIBD.
9. Give any two advantages of factorial design.
10. State any two applications of response surface design.

 

SECTION-B

 

Answer any Five questions                                                                                     (5 x 8  = 40 marks)

 

11. Distinguish between CRD and RBD and derive the efficiency of RBD over CRD.
12. Describe the analysis of variance for a GRAECO-LATIN SQUARE, stating all the

Hypothesis,  ANOVA and conclusions.

13. Define mutually orthogonal contrast and show that in 2³ design the

main effects and interaction effects are mutually orthogonal.

 

14. Discuss in detail the need for a Nested design with suitable illustration.
15. Describe, the analysis of variance for a 3³ factorial design, stating all the

hypothesis, ANOVA and conclusions.

16. Develop the analysis of variance for a 2⁴ completely confounded factorial design.
17. State clearly the model used in the case of Youden Square and construct a real life

example.

18. Describe in detail the LINEAR and QUADRATIC response surface Designs.

 

 

 

 

 

 

 

 

 

 

SECTION-C

 

Answer any Two questions                                                                                         (2 x 20  = 40 marks)

 

 

 

19. Discuss in detail the real life scenario of application of experimental designs in
20. i) Agriculture ii) Industry  iii) Health sciences. (  6+7+7 marks)

 

 

20.a) Define the term key BLOCK in the case of  2⁵ factorial design of size 2³ in

which 2 independent interactions and 1 generalized interaction are Confounded

Discuss in detail using the required linear equations for the confounded effects.

 

1. b) State and prove any one of the parametric conditions of a BIBD

(15 +5-Marks)

 

21 a) When do we go for PBIBD?

1. b) Construct a PBIBD with 2 associate classes stating all the parametric conditions
2. c) Explain the m-ple Lattice Square design and hence construct lattice square design

when the block size k=3.                   (2+8+10-Marks)

 

22 Write short notes on the following

1. Replication
2. MOLS
3. Partial Confounding
4. Split plot (5+5+5+5-Marks)

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

FOURTH SEMESTER – APRIL 2012

ST 4809 / 4805 – APPLIED EXPERIMENTAL DESIGN

 

 

Date : 16-04-2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer all the questions:                                                                                            (10 x 2  = 20 marks)

 

1. Define fixed effect model with an example.

2. List the principles of experimental design.

1. Define orthogonal contrasts with suitable illustration.
2. State the model used in LSD.
3. State the power cycle  for 3² factorial design.
4. Briefly explain the term sub-plot treatments.
5. Define the term Simple Lattice with an example .
6. State the parametric conditions of a BIBD.
7. Give any two advantages of confounding.
8. What is meant by surfaces ?

 

SECTION-B

 

Answer any Five questions:                                                                                            (5 x 8  = 40 marks)

 

11. Explain how you would analyse a randomized block design.
12. Describe, the analysis of variance for a 2⁵ factorial design, stating all the

hypothesis, ANOVA and conclusions

13. Discuss in detail fractional(half) factorial design with suitable illustration.
14. Describe the analysis of completely confounded 2⁴ factorial design in which the highest order

interaction is confounded stating all the  hypothesis, Anova and conclusions.

15. Discus in detail the importance and the analysis of a SPLIT-Plot design.
16. Construct a Youden Square, when the number of treatments is equal to seven.
17. Distinguish between RBD and BIBD with suitable illustration.
18. Explain the term key block with an example.

 

 

 

 

SECTION-C

 

Answer any Two questions:                                                                                         (2 x 20  = 40 marks)

 

19.a) Describe, the analysis of  variance for a 3² factorial design, stating all the

hypothesis, anova and conclusions.

b)Construct Mutually orthogonal Latin squares (MOLS), when the number of treatments is equal to

five.                                                                                                                                 (10+10 Marks)

 

20. a) Explain the the method of Steepest ascent, with neat diagram.
21. b) Discuss the first order and second order response surface designs.(8+12 Marks)

 

21. a) Construct a PBIBD with 3 associate classes stating all the parametric conditions
22. b) Explain the Group divisible design. (12+8-Marks)

 

22 Write shorts on the following

1. Incomplete block design
2. Replication
3. Industrial applications of experimental designs
4. FERMAT’S theorem. (5+5+5+5-Marks)

 

 

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