ICAR AIEEA-PG - Group 07 Statistical Sciences (Master's admission and PG scholarship) · 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 AIEEA-PG Group 07 Statistical Sciences
Basic principles of experimental design, the analysis of variance, CRD and RBD: degrees of freedom, sums of squares, F, standard errors and critical differences on small data sets.
How our questions for ICAR AIEEA-PG spread across the units of Principles of Experimental Design & Basic Designs. Difficulty: 25 easy, 13 medium, 0 hard.
| Completely randomised design | 8 | |
| Randomised complete block design | 6 | |
| Principles: replication, randomisation and local control | 5 | |
| Sample size and number of replications | 4 | |
| Assumptions of ANOVA and variance-stabilising transformations | 3 | |
| Uniformity trials, fertility contour maps and soil heterogeneity | 2 | |
| Size and shape of plots and blocks; Smith's variance law | 2 | |
| Latin square design and Graeco-Latin squares | 2 | |
| Missing plot techniques | 2 | |
| Multiple comparison procedures: LSD, Tukey, Duncan, Dunnett and Scheffe | 2 | |
| Relative efficiency of designs | 1 | |
| Analysis of covariance | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
As plot size increases in a uniformity trial, the coefficient of variation of plot yields:
C. Decreases, but at a diminishing rate
Larger plots average over more soil so the CV falls, but neighbouring soil is correlated, so each extra unit of area buys less reduction. Only with uncorrelated units (b = 1) would variance per unit fall in proportion to size.
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
For which experiment is a completely randomised design most appropriate?
A. A laboratory test of fungicides on agar plates kept in one incubator
The CRD puts all unit-to-unit variation into error, so it suits homogeneous material such as plates in one incubator. A slope, varied animals or two soil types call for blocking (or a covariate for initial weight).
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
How are treatments randomised in an RCBD?
D. Separately and independently within each block
Each block is a complete replicate, and a fresh randomisation in each block keeps treatment and position independent. Once-over randomisation is a CRD; row-and-column balance is a Latin square; repeating one order in every block is a systematic layout.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
How many error degrees of freedom does a 6 x 6 Latin square have?
D. 20
Error df = (t - 1)(t - 2) = 5 x 4 = 20. 25 would be (t - 1)^2, which is the RCBD formula with t blocks; 30 = t(t - 1); 15 subtracts the treatment df twice.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
An RCBD with 6 treatments and 4 blocks has one missing plot estimated by the missing-plot formula. How many error degrees of freedom remain?
D. 14
Normal error df = (4 - 1)(6 - 1) = 15; one df is lost for the estimated value, leaving 14. 23 is the total df of the complete experiment.
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
Which procedure is designed specifically to compare each treatment with a single control?
C. Dunnett's test
Dunnett's critical values allow for t - 1 comparisons against the same control and are more powerful for that question than procedures built for all pairs (Tukey, Duncan) or all contrasts (Scheffé).
Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Cochran and Cox, Experimental Designs
If the difference to be detected is halved while everything else stays the same, the required number of replications:
D. Becomes four times as large
r is proportional to 1/d^2, so halving d multiplies r by 4. Equivalently, the SE of a difference falls only with the square root of r.
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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