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Source document. This page reproduces the syllabus this course was written to, as published — its semesters, credits and paper numbers are that document’s, not this site’s. The course itself is studied on its own, in any order.

Course Information

TitleSampling Techniques
Theory Credits3 (3 hrs/week)
Practical Credits1 (2 hrs/week)

Course Outcomes

  1. Review population concepts, methods of data collection and types of errors.
  2. Get introduced to various statistical sampling schemes — simple, stratified, systematic.
  3. Understand how to conduct sample surveys and select appropriate sampling techniques.
  4. Compare various sampling techniques on precision and efficiency.
  5. Use appropriate sampling experimental schemes to analyse data.

Theory — Five Units

Unit 1: Sample Survey Concepts

Brief review of parameter and statistic, sampling distribution. Principal steps and principles in a sample survey, sampling and non-sampling errors, advantages of sampling over census, limitations, types of sampling — concept of subjective, probability and mixed sampling.

Open Unit 1 →

Unit 2: Simple Random Sampling (with and without replacement)

Notations and terminology, various probabilities of selection. Random numbers tables and their uses. Methods of selecting a simple random sample — lottery method, method based on random numbers. Estimates of population total, mean and their variances and standard errors; determination of sample size; simple random sampling of attributes.

Open Unit 2 →

Unit 3: Stratified Random Sampling

Stratified random sampling, advantages and disadvantages. Estimation of population mean and its variance. Stratified random sampling with proportional and optimum allocations. Comparison between proportional and optimum allocations with SRSWOR.

Open Unit 3 →

Unit 4: Systematic Sampling

Systematic sampling — definition when \(N = nk\); merits and demerits; estimate of mean and its variance. Comparison of systematic sampling with stratified and SRSWOR. Comparison of variance of SRS, StRS and Sys for a linear trend. Concept of Cluster Sampling, Multistage Sampling and Quota Sampling.

Open Unit 4 →

Unit 5: National Statistics Office

National Statistical Organization — vision and mission; National Statistics Office (NSSO and CSO), roles and responsibilities, important activities, publications. National Statistical Commission — need, constitution, role, functions and important acts.

Open Unit 5 →

Practical — List of Experiments (7)

  1. Show the sample mean is an unbiased estimator of population mean in SRSWOR and find its variance.
  2. Show the sample mean square is an unbiased estimator of population mean square in SRSWOR.
  3. Show the sample mean is an unbiased estimator of population mean in SRSWR and find its variance.
  4. Compare means and variances between SRSWR and SRSWOR.
  5. Allocate sample sizes to strata using proportional and optimum allocations.
  6. Compare precision in proportional and optimum allocations with SRSWOR and compute the gain in efficiency.
  7. Systematic sampling with \(N = nk\) and comparing its precision with stratified and SRSWOR.

Open practical course material →

Text Books

  1. S. C. Gupta & V. K. Kapoor — Fundamentals of Mathematical Statistics, Sultan Chand & Sons.
  2. K. Rohatgi & Ehsanes Saleh — An Introduction to Probability and Statistics, John Wiley & Sons.

References

  1. O. P. Gupta — Mathematical Statistics, Kedarnath Ramnath & Co.
  2. P. N. Arora & S. Arora — Quantitative Aptitude Statistics — Vol II, S. Chand & Company Ltd.

Suggested Co-Curricular Activities

  1. Training of students by related industrial experts.
  2. Assignments including technical assignments, if any.
  3. Seminars, group discussions, quiz, debates etc. on related topics.
  4. Preparation of audio and videos on tools of diagrammatic and graphical representations.
  5. Collection of material / figures / photos of related topics.
  6. Invited lectures and presentations of stalwarts on those topics.
  7. Visits / field trips of firms, research organizations etc.
UnitTopicApprox. Weightage
1Sample Survey Concepts15 %
2Simple Random Sampling25 %
3Stratified Random Sampling25 %
4Systematic, Cluster, Multistage20 %
5NSO & NSC15 %

Quick Reference — Key Formulas

SchemeVar(\(\bar y\))
SRSWR\(\sigma^2/n\)
SRSWOR\((N - n)/(Nn) \cdot S^2\)
Stratified, proportional\((1 - f)/n \cdot \sum W_h S_h^2\)
Stratified, optimum\((\sum W_h S_h)^2/n - (\sum W_h S_h^2)/N\)
Systematic, linear trend\(b^2(k^2 - 1)/12\)