ICAR AICE-JRF/SRF - Agricultural Statistics, Computer Application, Bioinformatics (PhD admission and fellowship) · India · National Testing Agency for ICAR
Original practice questions written to the published syllabus · not past papersResearch-level design theory as practised at IASRI and Rothamsted: optimality of block and row-column designs, designs for correlated errors and neighbour effects, designs for bioassays and diallel crosses, supersaturated and computer-search designs, and designs for computer experiments.
In the exams: AICE-JRF Ag Stat Unit 4 (present at depth); ASRB ARS Ag Stat interview (reported); the research frontier for PhD scholars
ICAR AICE-JRF/SRF Agricultural Statistics (Unit 4)
General block design analysis and design construction, which this subject extends to optimality, row-column designs and orthogonal arrays.
How our questions for ICAR AICE-JRF/SRF spread across the units of Advanced Design of Experiments (PhD). Difficulty: 19 easy, 42 medium, 25 hard.
| Optimality theory of block designs: universal optimality | 10 | |
| Row-column designs and their analysis | 10 | |
| Designs for bioassays and parallel-line assays | 10 | |
| Supersaturated and screening designs | 10 | |
| Orthogonal arrays and their construction | 9 | |
| Designs for computer experiments: Latin hypercube sampling | 9 | |
| Designs with neighbour effects and correlated errors | 7 | |
| Designs for diallel crosses and for factorial treatments in blocks | 7 | |
| Computer-aided search for efficient designs | 7 | |
| Robustness of designs to missing observations | 7 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Whenever a BIBD exists for given v, b and k, it is:
A. Universally optimal
Its C-matrix is completely symmetric with maximum trace.
Further reading: Shah and Sinha, Theory of Optimal Designs; Dey, Theory of Block Designs; Hedayat, Sloane and Stufken, Orthogonal Arrays
Which criterion minimises the average variance of elementary contrasts?
C. A-optimality
A minimises the sum of reciprocal eigenvalues of C (average variance); D maximises their product; E the smallest.
Further reading: Shah and Sinha, Theory of Optimal Designs; Dey, Theory of Block Designs; Hedayat, Sloane and Stufken, Orthogonal Arrays
How many error df does a connected row-column design with p = 4 rows, q = 6 columns and v = 12 treatments have?
D. 4
pq - p - q - v + 2 = 24 - 4 - 6 - 12 + 2 = 4.
Further reading: Shah and Sinha, Theory of Optimal Designs; Dey, Theory of Block Designs; Hedayat, Sloane and Stufken, Orthogonal Arrays
In a latinized design, what extra condition holds?
A. Each entry once in each long field column
Latinization protects against trends along the full length of the field.
Further reading: Shah and Sinha, Theory of Optimal Designs; Dey, Theory of Block Designs; Hedayat, Sloane and Stufken, Orthogonal Arrays
What are border plots used for in circular neighbour-balanced designs?
D. Giving end plots their designed neighbours
Border plots repeat end treatments so every plot has the intended neighbours.
Further reading: Shah and Sinha, Theory of Optimal Designs; Dey, Theory of Block Designs; Hedayat, Sloane and Stufken, Orthogonal Arrays
In a slope-ratio assay, how is relative potency estimated?
B. Ratio of slopes on dose
Lines in dose share an intercept; potency is the slope ratio.
Further reading: Shah and Sinha, Theory of Optimal Designs; Dey, Theory of Block Designs; Hedayat, Sloane and Stufken, Orthogonal Arrays
For quantal-response assays, where should doses be placed?
B. Around 20% to 80% expected response
Information about the LD50 is greatest in the middle response range.
Further reading: Shah and Sinha, Theory of Optimal Designs; Dey, Theory of Block Designs; Hedayat, Sloane and Stufken, Orthogonal Arrays
Which criterion is commonly minimised in choosing supersaturated designs?
B. E(s^2)
E(s^2), the average squared inner product of column pairs (Booth and Cox), measures non-orthogonality.
Further reading: Shah and Sinha, Theory of Optimal Designs; Dey, Theory of Block Designs; Hedayat, Sloane and Stufken, Orthogonal Arrays
How many times does each level pair occur in two columns of OA(8, 7, 2, 2)?
A. 2
Each pair of columns has 2^2 = 4 level combinations, each occurring lambda = 8/4 = 2 times.
Further reading: Shah and Sinha, Theory of Optimal Designs; Dey, Theory of Block Designs; Hedayat, Sloane and Stufken, Orthogonal Arrays
Why are computer experiments not replicated?
C. The simulator is deterministic
Repeating a run gives the same output, so replication adds nothing.
Further reading: Shah and Sinha, Theory of Optimal Designs; Dey, Theory of Block Designs; Hedayat, Sloane and Stufken, Orthogonal Arrays
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