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Programmes → I.M.Sc. in Mathematical Sciences and M.Sc. in Statistics-OR

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Theory of Sampling

Course Code: ST 354; ST 455  |  Credits: 4  |  Prerequisite: None

Syllabus Details

  • Simple Random Sampling: The role of sampling theory; simple random sampling for mean, proportions and percentages; estimation of sample size.
  • Stratified Sampling: Stratified sampling for mean and proportions; optimum allocation; relative precision of stratified random and simple random sampling; effect of deviations from the optimum allocation; effect of errors in the stratum sizes.
  • Systematic Sampling: Systematic sampling for linear and circular cases; variance of estimated mean; comparison of systematic sampling with simple random sampling and stratified sampling for population with linear trend.
  • Sampling with Varying Probabilities: Procedure of selecting a sample with varying probabilities; estimation of the population mean and variance of the estimated mean; sampling with varying probabilities and without replacement; ordered estimates; the Horvitz–Thompson estimator; some IPPS sampling without replacement procedures; Rao, Hartley and Cochran’s procedure.
  • Ratio Estimator: Bias and mean squared error of the ratio estimator and its approximation; ratio estimates in stratified sampling; comparison of the ratio estimate and the mean per unit.
  • Regression Estimator: Bias and mean squared error of the regression estimator; efficiency of the regression estimator; regression estimates in stratified sampling.

Course Learning Objective

  1. Explain and suggest where and when sample studies and surveys are needed, and the pros and cons of a complete enumeration study.
  2. Suggest what parameters of the population and what the population frame should be to experts from other fields in their research.
  3. Explain the various sampling schemes and designs (SRSWOR, SRSWR, stratified, systematic, cluster sampling, sampling with varying probabilities) and how estimators and sample sizes are to be determined.
  4. Explain sampling errors and non-sampling errors, and the need for exploring sampling designs and plans that minimize sampling errors.
  1. Cochran, W. C. Sampling Techniques. 3rd ed. Wiley Eastern, 1977
  2. Sukhatme, P. V., Sukhatme, B. V., Sukhatme, S. and Asok, C. Sampling Theory of Surveys with Applications. Indian Society of Agricultural Statistics, 1954
  3. Raj, Des. Sampling Theory. Tata McGraw-Hill, 1968
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