ASRB NET - Agricultural Statistics (and Computer Application / Bioinformatics) · India · Agricultural Scientists Recruitment Board (ICAR)
Original practice questions written to the published syllabus · not past papersFinding the best dose or combination: first- and second-order response surfaces, central composite and Box-Behnken designs, rotatability, fertiliser response optimisation, mixture designs for blends and feed formulations, and the alphabetic optimality criteria.
In the exams: Not an explicit unit in AICE-JRF Ag Stat; standard MSc/PhD course in agricultural statistics programmes; ASRB NET Ag Stat (reported)
ASRB NET / ARS Agricultural Statistics (reported)
Second-order designs (CCD, Box-Behnken), rotatability, canonical analysis, fertiliser response and optimum dose, mixture designs and optimality criteria.
How our questions for ASRB NET spread across the units of Response Surface, Mixture & Optimal Designs. Difficulty: 21 easy, 50 medium, 21 hard.
| First-order and second-order response surface models | 11 | |
| Central composite and Box-Behnken designs | 11 | |
| Rotatability and orthogonal blocking | 11 | |
| Canonical analysis and the method of steepest ascent | 11 | |
| Fertiliser response functions and economic optimum dose | 11 | |
| Mixture experiments: simplex lattice and simplex centroid designs | 11 | |
| Optimality criteria: A-, D-, E- and G-optimality | 10 | |
| Taguchi and robust parameter designs (introduction) | 9 | |
| Computer-generated optimal designs | 7 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A 2^2 factorial has mean 40.0 at its four corners; 5 centre points have mean 44.0 and SD 1.5. What is the t statistic for curvature?
B. 3.98
SE = s sqrt(1/4 + 1/5) = 1.006; t = 4.0/1.006 = 3.98 on 4 df.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology; Cornell, Experiments with Mixtures
The eigenvalues of B are -3.0 and +1.2. What does this indicate?
C. A saddle point
Mixed signs mean the response rises in one direction and falls in another.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology; Cornell, Experiments with Mixtures
For y = 2000 + 30x - 0.1x^2, at what rate is yield maximum?
C. 150
x_max = b/(2c) = 30/0.2 = 150 kg/ha.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology; Cornell, Experiments with Mixtures
What does E-optimality maximise?
B. The smallest eigenvalue of X'X
It minimises the variance of the worst-estimated linear combination of parameters.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology; Cornell, Experiments with Mixtures
Which criterion suits an experiment whose purpose is prediction over the whole region?
D. I-optimality
I-optimality minimises average prediction variance over the region.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology; Cornell, Experiments with Mixtures
What should be checked before running a computer-generated design?
B. Prediction variance, term correlations and lack-of-fit df
Optimality on one criterion does not guarantee good practical properties.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology; Cornell, Experiments with Mixtures
A potting medium has soil at least 30%, compost 10-50% and sand at most 40%. What kind of region results?
B. An irregular polygon inside the simplex
Bounds cut the simplex into a polytope, calling for vertex-based or optimal designs.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology; Cornell, Experiments with Mixtures
Which agricultural problem reflects robust-design thinking?
C. Practices whose yield varies little with weather
Weather is a noise factor; practices insensitive to it are robust.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology; Cornell, Experiments with Mixtures
In coded units, what are the factorial levels of a 2^k design?
A. -1 and +1
Coding centres the region at zero with half-range one.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology; Cornell, Experiments with Mixtures
What shape is the experimental region for three mixture components?
C. A triangle
Proportions summing to one form a two-dimensional simplex, which is a triangle.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology; Cornell, Experiments with Mixtures
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