Loyola College B.Sc. Statistics April 2006 Design & Analysis Of Experiments Question Paper PDF Download

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2006

                                       ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

(Also equivalent to STA 600)

 

 

Date & Time : 19-04-2006/FORENOON     Dept. No.                                                       Max. : 100 Marks

 

 

Part – A

Answer all the questions.                                                                      10 ´ 2 = 20

 

  1. Define mixed effect model.
  2. Define orthogonal contrast.
  3. What is an experimental unit?
  4. Define uniformity trial.
  5. What do you mean by randomized block design?
  6. Write any two advantages of completely randomized design.
  7. Under what conditions can LSD be used?
  8. When a BIBD is called symmetric?
  9. Define resolvable design.
  10. What is the need for factorial experiments?

Part – B

 

Answer any five questions.                                                                     5 ´ 8 = 40

 

  1. Explain the basic principles in the design of experiments.
  2. Compute the least square estimates of randomized block design
  3. A randomized block experiment has been carried out in 4 blocks with 5 treatments A, B, C, D and E. The reading for treatment B in block 2 is missing. Explain the procedure of obtaing the estimate of one missing observation in the above design.
  4. Complete the following table for the analysis of variance and give your conclusion.
Source of variance Sum of square D. F M.S.S Variance Ratio
R

C

T

Error

46.67

—–

—–

—–

4

—–

—–

—–

—–

—–

49.152

2.336

—–

1.500

—–

Total —– —–

 

  1. How do you compute effects of totals using Yate’s method for 32?
  2. Derive main effects and interaction effects for 22 factorial experiments.
  3. From the following table, find out the confounded treatment combinations
 

Block

Replication I Replication II Replication III Replication IV
1 2 3 4 5 6 7 8
abc

a

b

c

 

ab

ac

bc

(1)

abc

ab

c

(1)

ac

bc

a

b

 

abc

bc

a

(1)

ab

ac

b

c

 

Abc

Ac

B

(1)

ab

bc

a

c

 

 

  1. Prove that l (v – 1) = r (k-1) for a BIBD.

 

Part – C

 

Answer any two questions.                                                                   2 ´ 20 = 40

 

  1. Explain the analysis of variance table for a one-way layout dealing with homogeneity of data relative to k groups in detail.
  2. Give the complete statistical analysis of Latin square design
  3. Analyze the following 23 completely confounded factorial design.
Block 1 Block 2
Replicate 1 ‘1’ 101 (nk)291 (np)373 (kp)391 (nkp)450 (n)106 (k)265 (p)312
Block 3 Block 4
Replicate 2 ‘1’ 106 (nk)306 (np)338 (kp)407 (nkp)449 (n)189 (k)272 (p)324
Block 5 Block 6
Replicate 3 ‘1’ 187 (nk)334 (np)324 (kp)423 (nkp)417 (n)128 (k)279 (p)323
Block 7 Block 8
Replicate 4 ‘1’ 131 (nk)272 (np)361 (kp)245 (nkp)437 (n)103 (k)302 (p)324

 

  1. a). State and prove Fisher’s inequality in BIBD.

b). Obtain the analysis of a BIBD using intra block information.            (10 +10)

 

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Loyola College B.Sc. Statistics April 2008 Design & Analysis Of Experiments Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 28

 

SIXTH SEMESTER – APRIL 2008

ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

 

 

 

Date : 16/04/2008             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION – A

Answer ALL the questions:                                                              (10 x 2 = 20)

  1. Define linear contrasts and given an example.
  2. State the assumptions in an analysis of variance.
  3. Write the model representing two-way classified data.
  4. Give a layout for 4 x 4 LSD.
  5. Write all possible treatment combinations in a 23 design.
  6. What do you understand by a missing plot in a design of experiment?
  7. State the advantages of factorial experiments over single factor experiments.
  8. What is confounding?
  9. Define BIBD.
  10. State the parametric relations for the existence of a BIBD.

 

SECTION – B

Answer any FIVE questions:                                                           (5 x 8 = 40)

  1. Discuss the classification of linear models with suitable examples.
  2. Describe two-way classification in analysis of variance.
  3. Give the advantages and disadvantages of randomized block design.
  4. Explain how a missing value is estimated in Latin square design.
  5. Distinguish between complete and partial confounding with illustrations.
  6. Explain confounding in 23 factorial experiment.
  7. Starting with a suitable linear model, obtain intra block analysis of BIBD.
  8. Obtain the efficiency of RBD over CRD.

 

SECTION – C

Answer any  TWO questions:                                                           (2 x 20 = 40)

  1. a) What is random effects model? Give the complete analysis of random effects model.
  2. b) Explain the basic principles of design of experiments. (10+10)
  1. a) Carry out the complete analysis of a CRD.
  1. b) How is the efficiency of a design is measured. Derive the expression to measure the efficiency of a LSD over a RBD. (8+12)
  1. a) Discuss the analysis of a 32 factorial design.
  1. b) Explain the purpose and principle of confounding in factorial experiments. (12+8)
  1. a) With usual parameters a, b, r, k, λ establish the three parametric relation of BIBD.
  1. b) Bring out the significance of recovery of inter-block information in BIBD.

 

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Loyola College B.Sc. Statistics April 2009 Design & Analysis Of Experiments Question Paper PDF Download

YB 28

    LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – April 2009

ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

 

 

 

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

 

 

PART – A

 

Answer ALL the questions.                                                                               (10 X 2 = 20 marks)

 

  1. Give a contrast orthogonal to the contrast
  2. What is a mixed effect model?
  3. Mention the principle of experimental design which is not taken care by CRD if fertility gradient is present in one direction
  4. Give the skeleton ANOVA table for two-way classification with interaction
  5. What should be the number of treatments if the error degrees of freedom associated with a Randomised Block Design with 5 blocks is 12?
  6. What are Latin Squares ? Give an example of a latin square.
  7. Write all possible treatment combinations in a design.
  8. When do you recommend confounding ?
  9. Write the factorial effect corresponding to in design
  10. If the interactions BCD and ABE are confounded in a replication consisting of four blocks of 8 plots in factorial design which effect also gets confounded automatically.

 

PART – B

 

Answer any FIVE Questions.                                                                            (5 X 8 = 40 marks)

     

  1. Explain in detail the principles of experimental design.
  2. Write a descriptive note which highlights the difference between fixed effect and random effect models.
  3. Develop ANOVA for one way classified data
  4. Derive the formula for estimating the missing value in a LSD when one observation is missing.
  5. Explain the preparation of layout of a 5 x 5 Latin square design.
  6. Explain the process of computing various factorial effects in the case of a design.
  7. Illustrate with an example the method of finding the contrast defining the interaction between a Quadratic Effect and Linear Effect in the case of a factorial design involving two factors with three levels each.
  8. It is decided to confound an effect in the case of a experimental design.
  • What will be your choice of the effect to be considered for confounding ? Justify your answer.
  • Explain the preparation of lay out for such a confounding in 4 replications.

 

PART – C

 

Answer any TWO Questions.                                                                            (2 x 20 =40 marks)

 

  1. Describe in detail the preparation of layout for a randomized block design and the  steps involved in its analysis.
  2. Describe fully the analysis of a factorial design
  3. Develop the complete analysis of Balanced Incomplete Block Design
  4. Write short notes on the following:
  • Efficiency of RBD over CRD b) Cochran’s theorem   c) Generalized Effect

(d) Partial Confounding

 

 

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Loyola College B.Sc. Statistics April 2011 Design & Analysis Of Experiments Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2011

ST 6603/ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

 

 

 

Date : 05-04-2011              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION – A

Answer ALL the questions                                                                                                 (10 X 2 = 20 Marks)

 

  1. State the assumptions used in a linear model.
  2. Distinguish between pair-wise and non-pair-wise contrasts.
  3. What do you mean by randomization in experimental designs?
  4. State the assumptions for ANOVA.
  5. What are the demerits of a completely randomized design?
  6. Give the layout of a 4 x 4 Latin Square Design.
  7. What is meant by a factorial experiment?
  8. What are the advantages of confounding?
  9. What is meant by incomplete block designs?
  10. When do we go for a BIBD?

SECTION – B

Answer any FIVE questions                                                                                      (5 x 8 = 40 Marks)

 

  1. In what way are contrasts helpful in the analysis of experimental data?
  2. Give the statistical analysis of a two-way classification.
  3. Derive the expression to measure the efficiency of RBD over CRD
  4. What is Latin Square Design? Carry out the analysis of LSD.
  5. Explain the least square method of estimating one missing observation in a LSD.
  6. Explain in detail the analysis of 22 factorial experiment.
  7. Give the analysis of 32 factorial experiment.
  8. Develop the intra-black analysis of a BIBD.

SECTION – C

Answer any TWO questions                                                                                  (2 x 20 = 40 Marks)

 

  1. a) Discuss clearly between one-way and two-way classifications of analysis of

variance.

 

  1. b) Describe in detail analysis of variance in one-way classification with suitable

examples.

 

  1. a) What is missing plot technique?  Derive the formula for missing value when one

observation is missing in the case of LSD.

 

  1.   b) Discuss briefly the advantages and disadvantages of a Latin Square Design.

 

  1.   a) Distinguish between  Complete and Partial Confounding.

 

  1.     b) Give the Yates method of computing the factorial effects in a 23 factorial experiment.

 

  1. a) Explain a BIBD with suitable illustration.

 

  1. b) Develop the inter – block analysis of a BIBD stating the model, Hypothesis, ANOVA

and inference.

 

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Loyola College B.Sc. Statistics April 2012 Design & Analysis Of Experiments Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2012

ST 6603/ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

 

 

 

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

Time : 1:00 – 4:00

 

PART – A

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

 

  1. Define: Linear contrast and give an example of the same.
  2. Write down the mathematical model of a LSD.
  3. Mention how the principle of randomization is achieved in a completely randomized design.
  4. Give the skeleton ANOVA table for one-way classification.
  5. State the number of degrees of freedom associated with error in the analysis of  6 x 6 LSD.

 

  1. When do you recommend RBD?
  2. Write all possible treatment combinations in a design.
  3. Mention the difference between Partial and Total confounding.
  4. Write the factorial effect corresponding to in design.
  5. Write down all possible first order interactions in a 23 experiment.

 

PART – B

Answer any FIVE Questions:                                                                                   (5 x 8 = 40  marks)

 

  1. Write a descriptive note on Local Control.
  2. Obtain the Least Squares Estimators of the parameters of a RBD.
  3. Describe the linear model suitable for one way classified data and estimate the parameters in it.
  4. Derive the formula for estimating the missing value in a RBD when one observation is missing.
  5. Present the ANOVA table for a k x k LSD and explain the test for equality of treatment effect.
  6. Explain Yates method of computing  in the case of a design.
  7. Explain the terms: Quadratic Effect and Linear Effect in the case of a factorial design involving two factors with three levels each.
  8. State and prove Fisher’s inequality associated with BIBD.

 

 

(P.T.O)                       

 

 

 

 

 

PART – C

Answer any TWO Questions:                                                                                  (2 x 20 =40 marks)

 

  1. Describe in detail the preparation of layout for a Randomized Block Design and the steps involved in its analysis.
  2. Describe fully the analysis of a factorial design.
  3. Explain Balanced Incomplete Block Design and describe in detail the intra-block analysis for the same.
  4. (a) Explain the analysis of experimental design wherein the highest order interaction effect

is totally confounded.

(b) Explain : (i) Duncan’s Multiple Range Test          (ii) Cochran’s Theorem.

 

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Loyola College B.Sc. Statistics April 2015 Design & Analysis Of Experiments Question Paper PDF Download

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Loyola College B.Sc. Statistics April 2016 Design & Analysis Of Experiments Question Paper PDF Download

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Loyola College B.Sc. Statistics Nov 2016 Design & Analysis Of Experiments Question Paper PDF Download

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