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)
- Define orthogonal contrasts with an example.
- State Cochran’s theorem
- Briefly explain the term ‘Local control’.
- Give the missing value formula for the RBD with one missing observation.
- Explain orthogonal Latin Square Design.
- Give any two differences between RBD and LSD.
- State any two advantages of factorial design.
- Define a symmetric BIBD.
- Explain Experimental unit and Treatments.
- Define Affine Resolvable Design.
SECTION – B
Answer any FIVE questions (5 ´ 8 = 40 marks)
- Explain the difference between ‘Randomization’ and ‘Replication’ with a suitable example.
- In CRD, show that , with usual notations.
- Develop in detail the analysis of variance of Randomised block design.
- Explain the concept of ANOVA. When do you perform critical difference?
- 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.
- Distinguish between ‘complete confounding’ and ‘partial confounding’
- Explain YATE’S method of computing the sum of squares due to main effects and interaction effects in the case of 22 factorial design.
- State and prove the parametric conditions of a BIBD.
SECTION – C
Answer any TWO questions (2 ´ 20 = 40 marks)
- a) Estimate a single missing observation in LSD.
- b) Develop the analysis of variance in the case of LSD. when one observation is missing
in the design. (8+12)
- a) Derive the analysis of two-way classification with m-observations per cell by stating
all the effects, ANOVA and conclusion. (12)
- 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)
- Explain in detail the analysis of 32 factorial design by stating all the effects, ANOVA and Inference. (20)
- a) Construct a BIBD with the following parameters
v = 5, b= 20, r = 8, k = 2, l = 2 (10)
- b) For a BIBD, show that i) bk = rv and ii) l (v – 1) = r (k – 1) (10)
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