# Chapter 2: Basic Sampling Techniques

In Chapter 2 of the textbook **Practical Methods for Design and Analysis of Complex Surveys**, Simple random sampling, systematic sampling and sampling with probability proportional to size are introduced as the basic sampling techniques. The estimation of three different population parameters (population total, ratio and median) is examined. A small fixed population – the Province’91 population - is used throughout to illustrate the estimation methods, where the main focus is on the derivation of appropriate sampling weights under each sampling technique. Special efforts are made in comparing the relative performances of the estimators (in terms of their standard errors) and the available information on the structure of the population is increasingly utilized. The use of such auxiliary information is considered for two purposes: the sampling design and the estimation of parameters for a given sampling design.

In **Training Key 28**, SRSWOR sampling is demonstrated by first reproducing the results of Example 2.1. Then, the SRSWOR estimation procedure is extended to samples with different sample sizes. Finally, the performance of SRSWOR estimators is examined by using Monte Carlo simulation methods.

In **Training Key 45**, intra-class correlation is demonstrated under systematic sampling. First, the results of Example 2.4 are reproduced. Then, intra-class correlation is examined for systematic sampling under varying sorting orders of the population.

In **Training Key 54**, PPS sampling is demonstrated by first reproducing the results of Example 2.6. Then, PPS sampling is examined in more detail by incorporating different types of auxiliary data into the estimation procedure.

NOTE: Instructions for the use of Training Keys are given in the Instructions section.