ASRB NET - Agricultural Statistics (and Computer Application / Bioinformatics) · India · Agricultural Scientists Recruitment Board (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)
ASRB NET / ARS Agricultural Statistics
The same Unit 4 content with applied judgment: which design for which field, which comparison procedure for which question, how to read an ANOVA.
How our questions for ASRB NET spread across the units of Principles of Experimental Design & Basic Designs. Difficulty: 2 easy, 39 medium, 24 hard.
| Assumptions of ANOVA and variance-stabilising transformations | 8 | |
| Multiple comparison procedures: LSD, Tukey, Duncan, Dunnett and Scheffe | 8 | |
| Size and shape of plots and blocks; Smith's variance law | 7 | |
| Latin square design and Graeco-Latin squares | 7 | |
| Missing plot techniques | 7 | |
| Analysis of covariance | 7 | |
| Relative efficiency of designs | 6 | |
| Uniformity trials, fertility contour maps and soil heterogeneity | 4 | |
| Principles: replication, randomisation and local control | 3 | |
| Randomised complete block design | 3 | |
| Sample size and number of replications | 3 | |
| Completely randomised design | 2 |
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 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
An RCBD with 4 blocks and 5 treatments has block mean square 8.000 and error mean square 3.1667. Ignoring the degrees-of-freedom adjustment, what is its efficiency relative to a CRD?
C. 124.1%
RE = [(r - 1)Eb + r(t - 1)Ee] / [(rt - 1)Ee] = [3 x 8.000 + 16 x 3.1667] / [19 x 3.1667] = 74.667 / 60.167 = 1.241, i.e. 124.1%. The simple ratio Eb/Ee overstates it (252.6%); 132.1% swaps r and t.
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
Insect counts range from 5 to 2000 across treatments and the standard deviations are roughly proportional to the means. Which transformation is indicated?
A. Logarithm, as log(x + 1) if zeros occur
When SD is proportional to the mean (constant CV), the log transformation equalises variances and turns multiplicative effects into additive ones. Square root suits Poisson-like data where variance, not SD, is proportional to the mean; arcsine is for proportions.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
Why is Bartlett's test not always preferred for checking equal variances in agricultural data?
A. It is sensitive to non-normality, so Levene's test is often used instead
Bartlett's test can signal unequal variances when the real problem is non-normal (e.g. heavy-tailed) data; Levene's test, based on absolute deviations, is more robust. Bartlett's test handles any number of groups and tests variances, not additivity.
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
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