Sampling is widely used in the modern world. The statistical offices of many nations have sample surveys conducted on topics of interest such as unemployment, size of labor force etc.. Furthermore, sample surveys are often conducted by company on topics of the behavior of consumers. Sampling design determines the precision of the estimates. Thus, the way a sample is drawn is as important as the mathematical form of the estimator. Sample design consists of both a sample selection plan and an estimation procedure. In this course, we shall first define population, sampling units (primary, secondary, etc.); then introduce many sampling schemes, such as simple random sampling (with or without replacement), stratified sampling (optimum allocation of sampling units to various strata), multistage sampling (e.g. two-stage stratified cluster sampling), systematic sampling, double sampling, and sampling with unequal probabilities (with or without replacement). We shall also introduce ratio estimator, regression estimator, and poststratification estimators. Finally, we shall derive the variances of the proposed estimators and the estimators of their variances. For estimating the variance of the estimators, the topics of Jackknife method and bootstrap method are also included in this course.

The course aims to equip the students with sampling techniques, including methods of sampling, derivation of expected values, variances, and the estimated variances of the estimators. It is expected that the students have sufficient knowledge to design survey and analyze survey data. This course will cover the following topics: 1. the simple random sampling (with/without replacement) 2. the stratified random sampling (the optimum allocation) 3. the poststratified estimator 4. the ratio estimator 5. cluster sampling (one-stage and two-stage, systematic sampling) 6. sampling with unequal probability (probability proportional to size (PPS) with/without replacement) 7. Horvitz–Thompson estimator.

1. Sampling Methods for Applied Research by Peter Tryfors, John Wiley and Sons, Inc.