ASRB Agricultural Research Service (ARS) - Agricultural Statistics scientist · India · Agricultural Scientists Recruitment Board (ICAR)
Original practice questions written to the published syllabus · not past papersMethods that hold without a normal model: the empirical distribution, goodness-of-fit, sign and rank tests for one, two and many samples, rank correlation, and tests used for scored or ranked agricultural data such as disease ratings and sensory panels.
In the exams: AICE-JRF Ag Stat Unit 2 (heavy: run, sign, rank, Wilcoxon, Kruskal-Wallis, Mann-Whitney, Cochran, Friedman named); GATE ST 'Non-parametric Statistics' (heavy); UPSC ISS Statistics II (present)
How our questions for ASRB Agricultural Research Service spread across the units of Nonparametric & Rank-Based Methods. Difficulty: 7 easy, 19 medium, 1 hard.
| Analysing ordinal scores: disease ratings and sensory panels | 7 | |
| Sign test and Wilcoxon signed-rank test | 3 | |
| Friedman's test for randomised blocks | 3 | |
| Cochran's Q test | 3 | |
| Goodness of fit: chi-square and Kolmogorov-Smirnov tests | 2 | |
| Run test for randomness | 2 | |
| Mann-Whitney U test and two-sample Kolmogorov-Smirnov test | 2 | |
| Kruskal-Wallis test | 2 | |
| Empirical distribution function and its properties | 1 | |
| Spearman's and Kendall's rank correlations | 1 | |
| Asymptotic relative efficiency | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
In a chi-square goodness-of-fit test of insect counts, several classes have expected frequencies below 5. What is the usual remedy?
B. Pool adjacent classes, then count df after pooling
Small expected counts make the χ² approximation unreliable; adjacent classes are pooled and the df counted on the pooled classes. Dropping classes discards data and biases the test.
Further reading: Gibbons and Chakraborti, Nonparametric Statistical Inference; Conover, Practical Nonparametric Statistics; Hollander, Wolfe and Chicken, Nonparametric Statistical Methods
A row of 20 plants (10 diseased, 10 healthy) shows only 6 runs. What is the normal-approximation Z and the interpretation?
D. Z = −2.30: too few runs, indicating clustering of disease
E(R) = 11, Var(R) = 4.737, Z = (6 − 11)/2.176 = −2.30, beyond −1.96: diseased plants occur in clumps, as with plant-to-plant spread. Dividing by the variance instead of the SD understates |Z|.
Further reading: Gibbons and Chakraborti, Nonparametric Statistical Inference; Conover, Practical Nonparametric Statistics; Hollander, Wolfe and Chicken, Nonparametric Statistical Methods
Six treated and six untreated plants are scored for disease; the Mann-Whitney U for the treated group is 4. What is the normal-approximation Z, ignoring ties and continuity correction?
C. −2.24
E(U) = 36/2 = 18, Var(U) = 36 × 13/12 = 39, Z = (4 − 18)/√39 = −2.24. Using 36/4 as the variance gives −4.67.
Further reading: Gibbons and Chakraborti, Nonparametric Statistical Inference; Conover, Practical Nonparametric Statistics; Hollander, Wolfe and Chicken, Nonparametric Statistical Methods
A breeder wants to know whether variety rankings for yield are consistent between two environments. Which summary is most appropriate?
B. Spearman's or Kendall's rank correlation
Consistency of ranking (a rank-based view of crossover genotype-by-environment interaction) is measured by rank correlation. A paired t-test compares mean levels, not rankings.
Further reading: Gibbons and Chakraborti, Nonparametric Statistical Inference; Conover, Practical Nonparametric Statistics; Hollander, Wolfe and Chicken, Nonparametric Statistical Methods
Ten panellists each rank four mango samples for sweetness. Which statistic summarises their agreement?
D. Kendall's coefficient of concordance W
W = χ²_F/[b(k − 1)] measures concordance among b judges ranking k items. Spearman's ρ compares two rankings only.
Further reading: Gibbons and Chakraborti, Nonparametric Statistical Inference; Conover, Practical Nonparametric Statistics; Hollander, Wolfe and Chicken, Nonparametric Statistical Methods
Farmers in a participatory trial each rank the same five varieties. Which test compares the varieties?
D. Friedman's test, with farmers as blocks
Each farmer ranks all varieties, so farmers are blocks and Friedman's test applies; Kendall's W measures agreement among farmers. Kruskal-Wallis assumes independent groups.
Further reading: Gibbons and Chakraborti, Nonparametric Statistical Inference; Conover, Practical Nonparametric Statistics; Hollander, Wolfe and Chicken, Nonparametric Statistical Methods
A blocked trial has many treatments but only three blocks. Which rank test weights blocks by their range of responses and is often more powerful than Friedman's test here?
D. Quade's test
Quade's test ranks the blocks by their ranges and weights within-block ranks accordingly; with few blocks and many treatments it tends to beat Friedman. Page's test targets ordered alternatives.
Further reading: Gibbons and Chakraborti, Nonparametric Statistical Inference; Conover, Practical Nonparametric Statistics; Hollander, Wolfe and Chicken, Nonparametric Statistical Methods
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