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ICAR AICE-JRF/SRF Sampling Theory II: Unequal Probability, Cluster, Multistage & Repeated Sampling: practice questions

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 papers
10worked here, free
93written to this exam in this subject
12syllabus units

What this subject covers

The designs real agricultural surveys use: PPS sampling with and without replacement and its estimators, cluster and multistage sampling, double sampling, sampling on successive occasions, randomised response, non-response and imputation.

In the exams: AICE-JRF Ag Stat Unit 5 (heavy: each technique named); UPSC ISS Statistics III (heavy); ASRB NET Ag Stat (heavy)

What ICAR AICE-JRF/SRF asks from it

ICAR AICE-JRF/SRF Agricultural Statistics (Unit 5)

PPS with and without replacement, inclusion probabilities, cluster and multistage sampling, double sampling, successive occasions, non-sampling errors, randomised response and imputation.

Where the 93 questions fall

How our questions for ICAR AICE-JRF/SRF spread across the units of Sampling Theory II: Unequal Probability, Cluster, Multistage & Repeated Sampling. Difficulty: 20 easy, 51 medium, 22 hard.

Sampling without replacement with unequal probabilities: Horvitz-Thompson estimator10
PPS sampling with replacement: Hansen-Hurwitz estimator9
Des Raj and Murthy's estimators; Midzuno-Sen and Rao-Hartley-Cochran schemes8
Cluster sampling with equal and unequal clusters8
Two-stage and multistage sampling8
Randomised response techniques8
Imputation methods8
Variance estimation in complex surveys: linearisation, jackknife and bootstrap8
Sampling on successive occasions and rotation designs7
Non-response: Hansen-Hurwitz call-backs and weighting adjustments7
Double (two-phase) sampling for stratification and for ratio and regression6
Inverse and adaptive sampling (introduction)6

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Sampling without replacement with unequal probabilities: Horvitz-Thompson estimator · medium

What condition makes the Sen-Yates-Grundy variance estimator non-negative?

  1. pi_ij >= pi_i for all pairs of units in the sample
  2. pi_i = n/N for all units
  3. pi_ij = 0 for all pairs
  4. pi_i pi_j >= pi_ij for all pairs
Answer and working

D. pi_i pi_j >= pi_ij for all pairs

Each term then has a non-negative coefficient.

Further reading: Cochran, Sampling Techniques; Sukhatme et al., Sampling Theory of Surveys with Applications

2 · Des Raj and Murthy's estimators; Midzuno-Sen and Rao-Hartley-Cochran schemes · medium

In the Midzuno-Sen scheme, how are units selected?

  1. All by systematic sampling
  2. First PPS, rest by SRS
  3. All by PPS with replacement
  4. First by SRS, rest PPS
Answer and working

B. First PPS, rest by SRS

This makes the ratio estimator unbiased.

Further reading: Cochran, Sampling Techniques; Sukhatme et al., Sampling Theory of Surveys with Applications

3 · Cluster sampling with equal and unequal clusters · easy

Clusters of 10 units have intracluster correlation 0.1. What is the design effect?

  1. 2.0
  2. 1.9
  3. 0.9
  4. 1.1
Answer and working

B. 1.9

1 + (M - 1) rho = 1 + 9 x 0.1 = 1.9.

Further reading: Cochran, Sampling Techniques; Sukhatme et al., Sampling Theory of Surveys with Applications

4 · Cluster sampling with equal and unequal clusters · medium

Which estimator of the mean per unit suits unequal clusters best?

  1. Median cluster total
  2. Ratio estimator
  3. Largest cluster mean in the whole sample of clusters
  4. Mean of cluster totals
Answer and working

B. Ratio estimator

The ratio of sampled cluster totals to sampled sizes stabilises estimates when totals vary with size.

Further reading: Cochran, Sampling Techniques; Sukhatme et al., Sampling Theory of Surveys with Applications

5 · Double (two-phase) sampling for stratification and for ratio and regression · medium

What is the double-sampling regression estimator?

  1. y-bar x-bar'/x-bar^2
  2. y-bar + b(x-bar' - x-bar)
  3. y-bar - b(x-bar' - x-bar)
  4. x-bar' + b y-bar
Answer and working

B. y-bar + b(x-bar' - x-bar)

x-bar' is the first-phase mean.

Further reading: Cochran, Sampling Techniques; Sukhatme et al., Sampling Theory of Surveys with Applications

6 · Sampling on successive occasions and rotation designs · medium

What is rotation group bias?

  1. Bias of the ratio estimator in small samples
  2. Variance from clusters
  3. Responses changing with time in sample
  4. Bias from PPS selection
Answer and working

C. Responses changing with time in sample

A non-sampling error of rotation designs.

Further reading: Cochran, Sampling Techniques; Sukhatme et al., Sampling Theory of Surveys with Applications

7 · Non-response: Hansen-Hurwitz call-backs and weighting adjustments · medium

500 mailed; 300 respond with mean 40; 50 of 200 non-respondents interviewed with mean 30. What is the Hansen-Hurwitz estimate?

  1. 36
  2. 38
  3. 35
  4. 40
Answer and working

A. 36

(300 x 40 + 200 x 30)/500 = 36.

Further reading: Cochran, Sampling Techniques; Sukhatme et al., Sampling Theory of Surveys with Applications

8 · Non-response: Hansen-Hurwitz call-backs and weighting adjustments · hard

Which model estimates each unit's response probability for weighting?

  1. A Latin square model
  2. A response-propensity model
  3. A path model
  4. A Hardy-Weinberg model
Answer and working

B. A response-propensity model

Usually logistic regression on frame variables.

Further reading: Cochran, Sampling Techniques; Sukhatme et al., Sampling Theory of Surveys with Applications

9 · Inverse and adaptive sampling (introduction) · easy

What is fixed in advance in inverse sampling?

  1. Number of strata
  2. Total sample size
  3. Cluster size
  4. Number of units with the attribute
Answer and working

D. Number of units with the attribute

Sampling stops when m such units are found.

Further reading: Cochran, Sampling Techniques; Sukhatme et al., Sampling Theory of Surveys with Applications

10 · Inverse and adaptive sampling (introduction) · hard

Why are ordinary estimators biased in adaptive cluster sampling?

  1. Units are drawn with equal probability
  2. The initial sample is not random
  3. Inclusion depends on observed values
  4. Neighbours are never added
Answer and working

C. Inclusion depends on observed values

Modified HT/HH estimators based on networks are unbiased.

Further reading: Cochran, Sampling Techniques; Sukhatme et al., Sampling Theory of Surveys with Applications

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Sampling Theory II: Unequal Probability, Cluster, Multistage & Repeated SamplingThe full study manual, free ICAR AICE-JRF/SRFFormat, sections and how it has changed

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