ASRB Agricultural Research Service (ARS) - Agricultural Statistics scientist · 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)
How our questions for ASRB Agricultural Research Service spread across the units of Response Surface, Mixture & Optimal Designs. Difficulty: 15 easy, 45 medium, 19 hard.
| Central composite and Box-Behnken designs | 11 | |
| Canonical analysis and the method of steepest ascent | 11 | |
| Mixture experiments: simplex lattice and simplex centroid designs | 11 | |
| First-order and second-order response surface models | 10 | |
| Rotatability and orthogonal blocking | 10 | |
| Optimality criteria: A-, D-, E- and G-optimality | 9 | |
| Taguchi and robust parameter designs (introduction) | 9 | |
| Computer-generated optimal designs | 7 | |
| Fertiliser response functions and economic optimum dose | 1 |
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
What does rotatability mean?
D. Prediction variance depends only on distance from the centre
Equal prediction precision in all directions at the same distance is rotatability.
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
Why is a rounded fertiliser recommendation near the economic optimum usually acceptable?
D. The profit curve is flat near its maximum
Small departures from the optimum cost little profit, and the estimate is uncertain anyway.
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
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
Ten here, 79 in the app. The Laisha app has every practice question we have written to ASRB Agricultural Research Service in this subject, marked as you go, with timed papers, a jump-to-unanswered list and a certificate when you pass at 70 per cent.
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