SOR2250 - Sampling Chapter 2 PDF

SOR2250 – Sampling I Dr Fiona Sammut CHAPTER 2 SIMPLE RANDOM SAMPLING 2.1 WHAT IS SIMPLE RANDOM SAMPLING (SRS)? Though other sampling techniques may be more ideal to work with when a sample is to be selec...

SOR2250 – Sampling I Dr Fiona Sammut CHAPTER 2 SIMPLE RANDOM SAMPLING 2.1 WHAT IS SIMPLE RANDOM SAMPLING (SRS)? Though other sampling techniques may be more ideal to work with when a sample is to be selected from a population about which we have some suitable information, simple random sampling still provides an important theoretical point of departure. In simple random sampling, sampling of n units from a population of N units may be carried out by using either sampling with replacement or without replacement. In what follows, if not stated otherwise, we will focus on sampling without replacement. Simple random sampling is a sampling design in which n distinct units are selected from the N units of a population in such a way that every sample of size n has the same probability of being selected from a population as per any other possible sample. Each element will thus also have the same probability of being selected from a finite population of size N. This 1 1 probability of selection is N or N , as mentioned in Section 1.4. Pn Cn Furthermore, a sample of n units is said to be chosen from a finite population by simple random sampling if the units in the sample are chosen independently of each other (the choice of a unit is not influenced by the choice of another unit). 1 SOR2250 – Sampling I Dr Fiona Sammut The actual process of selection is carried out in stages: Once a sampling frame is defined, proper simple random sampling requires that we have a list of all N units in the population, so that we can assign a number from 1 to N to each of these units. A random number generator, or equivalently1, adapted to give uniformly distributed integers in the range of values {1, 2,…, N } , is used to select n random numbers from the whole set of values. The randomly chosen numbers are decoded and the corresponding units in the population will form our sample. The use of sampling frames makes it easy to draw random samples with the aid of computers. Computer generation is simply much more convenient, since all computers are equipped with suitable programs capable of generating pseudo-numbers with seeds selected by the user. Suppose that a sample of size 20 is to be selected from a population of size 100 using simple random sampling. In R/RStudio, sampling using simple random sampling with and without replacement may be carried out using the command sample as follows: 1 Amongst others, selecting manually and blindfoldedly n numbers from an urn containing the first N integers provides an alternative way of selecting a simple random sample. 2 SOR2250 – Sampling I Dr Fiona Sammut set.seed(2017) x