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Source: Frerichs, R.R. Rapid Surveys (unpublished), © 2008. NOT FOR COMMERCIAL DISTRIBUTION
3
Simple Random Sampling
3.1 INTRODUCTION
Everyone mentions simple random sampling, but few use this method for population-based surveys. Rapid surveys are no exception, since they too use a more complex sampling scheme. So why should we be concerned with simple random sampling? The main reason is to learn the theory of sampling. Simple random sampling is the basic selection process of sampling and is easiest to understand. If everyone in a population could be included in a survey, the analysis featured in this book would be very simple. The average value for equal interval and binomial variables, respectively, could easily be derived using*…show more content…*

Three of the nine addicts are now infected with the human immunodeficiency virus (HIV). To be derived are the proportion who are HIV infected (a binomial variable), the mean number of intravenous injections (IV) and shared IV injections during the past two weeks (both equal interval variables), and the proportion of total IV injections that were shared with other addicts. This latter proportion is a ratio of two variables and, as you will learn, is termed a ratio estimator. ----Figure 3-3 ----The total population of nine drug addicts is seen in Figure 3-3. Names of the nine male addicts are listed below each figure. The three who are infected with HIV are shown as cross-hatched figures. Each has intravenously injected a narcotic drug eight or more times during the past two weeks. The number of injections is shown in the white box at the midpoint of each addict. With one exception, some of the intravenous injections were shared with other addicts; the exact number is shown in Figure 3-3 as a white number in a black circle. Our intention is to sample three addicts from the population of nine, assuming that the entire population cannot be studied. To provide an unbiased view of the population, the sample mean 3-2 should on average equal the population mean, and the sample variance should on average equal the population

Three of the nine addicts are now infected with the human immunodeficiency virus (HIV). To be derived are the proportion who are HIV infected (a binomial variable), the mean number of intravenous injections (IV) and shared IV injections during the past two weeks (both equal interval variables), and the proportion of total IV injections that were shared with other addicts. This latter proportion is a ratio of two variables and, as you will learn, is termed a ratio estimator. ----Figure 3-3 ----The total population of nine drug addicts is seen in Figure 3-3. Names of the nine male addicts are listed below each figure. The three who are infected with HIV are shown as cross-hatched figures. Each has intravenously injected a narcotic drug eight or more times during the past two weeks. The number of injections is shown in the white box at the midpoint of each addict. With one exception, some of the intravenous injections were shared with other addicts; the exact number is shown in Figure 3-3 as a white number in a black circle. Our intention is to sample three addicts from the population of nine, assuming that the entire population cannot be studied. To provide an unbiased view of the population, the sample mean 3-2 should on average equal the population mean, and the sample variance should on average equal the population

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