Lesson 3: Unequal Probability Sampling

Overview Section

This lesson starts with the rationale for using unequal probability sampling in section 3.1. We then discuss in section 3.2 the Hansen-Hurwitz estimator which may be used when the sampling is with replacement. In section 3.3, we introduce the Horvitz-Thompson estimator which can be used when the sampling is with or without replacement. In section 4, a small population example is used to illustrate some properties of these two estimators. Through this example, one can see that both estimators are unbiased.

 Lesson 3: Ch. 6.1, 6.2, 6.4 of Sampling by Steven Thompson, 3rd edition


Upon completion of this lesson, you should be able to:

  1. Identify the situations that unequal probability sampling is beneficial and explain why,
  2. Explain and perform unequal probability sampling,
  3. Compute the Hansen-Hurwitz estimator and its estimated variance,
  4. Compute the Horvitz-Thompson estimator and its estimated variance, and
  5. Demonstrate that Hansen-Hurwitz and Horvitz-Thompson these two estimators are unbiased through an artificial small population example.