Random Sampling
Source: Frerichs, R.R. Rapid Surveys (unpublished), © 2008.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 Formulas 2.1 and 2.3 in Chapter 2. Instead of estimating the two forms of average values in the population, they would be measuring directly. Of course, when measuring everyone in a population, the true value is known; thus there is no need for confidence intervals. After all the purpose of the confidence interval is to tell how certain the author is that a presented interval brackets the true value in the population. With everyone measured, the true value would be known, unless of course there were measurement or calculation errors. When the true value in a population is estimated with a sample of persons, things get more complicated. Rather then just the mean or proportion, we need to derive the standard error for the variable of interest, used to construct a confidence interval. This chapter will focus on simple random sampling or persons or households, done both with and without replacement, and present how to derive the standard error for equal interval variables, binomial variables, and ratios of two variables. The latter, as described earlier, is commonly used in rapid surveys and is termed a ratio estimator. What appears to be a proportion, may actually be a ratio estimator, with its own formula for the mean and standard
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 Formulas 2.1 and 2.3 in Chapter 2. Instead of estimating the two forms of average values in the population, they would be measuring directly. Of course, when measuring everyone in a population, the true value is known; thus there is no need for confidence intervals. After all the purpose of the confidence interval is to tell how certain the author is that a presented interval brackets the true value in the population. With everyone measured, the true value would be known, unless of course there were measurement or calculation errors. When the true value in a population is estimated with a sample of persons, things get more complicated. Rather then just the mean or proportion, we need to derive the standard error for the variable of interest, used to construct a confidence interval. This chapter will focus on simple random sampling or persons or households, done both with and without replacement, and present how to derive the standard error for equal interval variables, binomial variables, and ratios of two variables. The latter, as described earlier, is commonly used in rapid surveys and is termed a ratio estimator. What appears to be a proportion, may actually be a ratio estimator, with its own formula for the mean and standard