LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
M.Sc., DEGREE EXAMINATION – STATISTICS
FOURTH SEMESTER – APRIL 2004
ST 4800/S 1015 – DESIGN OF EXPERIMENTS
01.04.2004 Max:100 marks
1.00 – 4.00
SECTION – A
Answer ALL the questions (10 ´ 2 = 20 marks)
- Define mutually orthogonal contrasts with an example.
- Briefly explain the term “Replication”.
- Define D – optimalilty.
- State the MINIMAL FUNCTION for 32 factorial design.
- Give sum of squares for 3 factors interaction for 33 factorial design.
- Define a ‘SIMPLE LATTICE SQUARE’.
- State any two applications of ‘FINITE FIELD’ in experimental design.
- Distinguish between an RBD and BIBD.
- Give an example for ‘SYMMETRIC BIBD’ which is NOT ‘RESOLVABLE’.
- Briefly explain the term CRITICAL DIFFERENCE.
SECTION – B
Answer any FIVE questions (5 ´ 8 = 40 marks)
- Develop the Analysis of variance for a 32 Factorial design.
- Distinguish between ‘COMPLETE’ and ‘PARTIAL’ Confounding in LSD.
- Develop the Analysis of variance for a 24 Factorial Design, when the highest order interaction is confounded.
- State clearly the model used in YOUDEN SQUARE and describe the analysis of variance.
- Construct a BIBD with V = 3 b = 6 r = 4 k = 2 and = 2.
- Explain the term Repeated Latin Square design with suitable illustration.
- Distinguish between ‘FIXED EFFECT MODEL’ and ‘RANDOM EFFECT MODEL’ with an example.
- State and prove all the parametric conditions of a BIBD.
SECTION – C
Answer any TWO questions (2 ´ 20 = 40 marks)
- a) Briefly explain the term MUTUALLY ORTHOGONAL LATIN SQUARES
(M.O.L.S) (5)
- b) Construct M.O.L.S. when the number of treatments V = 7. (7)
- c) Hence construct a SERIES OF BIBDS using the above MOLS, when the block size
k = 4, k = 5 and k = 6. (8)
- a) Distinguish between ‘Confounding’ and ‘FRACTIONAL REPLICATION’. (8)
- b) Develop the analysis of variance for a 24 FRACTIONAL FACTORIAL design stating all the hypothesis, effects and conclusions. (12)
- a) Discuss in detail confounding in ‘MORE THAN TWO BLOCKS’ using finite field.
(10)
- b) Develop the analysis of variance for a BIBD. (10)
- Write shot notes on the following:
- SPLIT – PLOT design
- PBIBD
- RESPONSE SURFACE DESIGN
- CONCOMITANT VARIABLE. (4 ´ 5 = 20 marks)