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 papersFisher's three principles and how they shape a field or animal trial: uniformity trials, plot size and shape, the CRD, RCBD and Latin square with their analysis and efficiency, missing plots, transformations, multiple comparisons and analysis of covariance.
In the exams: AICE-JRF Ag Stat Unit 4 (heavy); AIEEA-PG Group 07 (CRD, RBD named); AICE-JRF Agronomy Unit 6 (heavy); ASRB NET Ag Stat (heavy); UPSC ISS Statistics III (present)
ICAR AICE-JRF/SRF Agricultural Statistics (Unit 4)
Uniformity trials, CRD, RCBD and Latin square, multiple comparison procedures, missing plot techniques, analysis of covariance and variance-stabilising transformations, at master's level: formulas for missing values and bias, relative efficiencies, assumptions and their tests.
ICAR AICE-JRF/SRF Agronomy (Unit 6) and other crop subjects
Standard error, CV, tests of significance, data transformation and missing plot techniques, the basic designs and their efficiency as used in agronomic trials.
How our questions for ICAR AICE-JRF/SRF spread across the units of Principles of Experimental Design & Basic Designs. Difficulty: 27 easy, 46 medium, 23 hard.
| Assumptions of ANOVA and variance-stabilising transformations | 11 | |
| Completely randomised design | 10 | |
| Size and shape of plots and blocks; Smith's variance law | 9 | |
| Randomised complete block design | 9 | |
| Multiple comparison procedures: LSD, Tukey, Duncan, Dunnett and Scheffe | 9 | |
| Principles: replication, randomisation and local control | 8 | |
| Missing plot techniques | 8 | |
| Analysis of covariance | 8 | |
| Latin square design and Graeco-Latin squares | 7 | |
| Relative efficiency of designs | 6 | |
| Sample size and number of replications | 6 | |
| Uniformity trials, fertility contour maps and soil heterogeneity | 5 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A fertility contour map drawn from a uniformity trial shows roughly parallel contour lines running east to west. What does this indicate and what layout follows?
C. A north-south gradient; blocks should be long strips running east-west
Contour lines join points of equal yield, so parallel east-west lines mean yield changes from north to south. Blocks should be laid across the gradient, i.e. along the contours (east-west), so each block is uniform. Patchy fertility would show closed contours.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
In a CRD with 20 observations the grand total is 224. What is the correction factor?
C. 2508.8
CF = G^2 / N = 224^2 / 20 = 50176 / 20 = 2508.8. 11.2 is the grand mean; dividing by N - 1 or by the number of treatments is wrong.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
An RCBD has 5 treatments in 4 blocks with block totals 92, 98, 104, 106 (grand total 400). What is the block sum of squares?
B. 24.0
CF = 400^2 / 20 = 8000.0. Block SS = (sum of B^2)/t - CF = 40120/5 - 8000.0 = 24.0. Dividing by the number of blocks (4) instead of the number of plots per block (5) gives 2030.0; 8.0 is the block mean square.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
In an RCBD, a nitrogen treatment raises yield by about 20% in every block, and the blocks differ greatly in yield level. Which assumption of the standard analysis is most at risk?
B. Additivity of treatment and block effects
A constant percentage effect means the absolute effect is larger in high-yielding blocks, so treatment and block effects multiply rather than add; a log transformation can restore additivity. Independence comes from randomisation, and block sizes are equal by design.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
Two plots are missing in different blocks and treatments of an RCBD. How are their values usually found by hand?
A. By iteration or simultaneous equations, losing 2 error df
Each estimate depends on the other, so guess one, estimate the other with the single-value formula, re-estimate the first and repeat until stable (or solve the two equations together). One error df is lost per missing value.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
Following Gomez and Gomez, germination percentages that all lie between 35% and 65% should be:
C. Analysed without transformation
Binomial variance changes little in the 30-70% range, so no transformation is needed. Square root is suggested when data lie wholly within 0-30% or 70-100%, and arcsine when they span a wider range.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
In a covariance analysis the error sums of squares and products are Eyy = 100, Exy = 30 and Exx = 60. What is the adjusted error sum of squares of Y?
C. 85.0
Adjusted Eyy = Eyy - Exy^2 / Exx = 100 - 900/60 = 85.0. Forgetting to square Exy gives 99.5; dividing by Eyy gives 91.0.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
An RCBD with 5 treatments and 4 blocks is analysed by covariance with one covariate. How many error degrees of freedom does the adjusted analysis have?
B. 11
Unadjusted error df = (4 - 1)(5 - 1) = 12; one is used to estimate the regression coefficient, leaving 11. 15 would be the CRD error df on 20 units.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
Which is an assumption of the analysis of covariance?
C. The regression of Y on X has the same slope in every treatment
ANCOVA assumes a linear relation with a common slope across treatments, a covariate unaffected by treatments and measured with little error. A perfect correlation is not required, and measuring after treatment risks treatment influence.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
Which assumption of ANOVA is protected mainly by randomisation?
C. Independence of the errors
Random allocation breaks any systematic link between neighbouring plots and treatments, so errors can be treated as independent. Normality, additivity and equal variances depend on the nature of the data and may need transformations.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
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