Simple random sampling

Simple random sampling. Simple random sampling is performed directly on the whole population (area or section) under investigation. Any increment taken from the parent population has an equal chance of being selected. In practice, the problem is that the sample has to be taken in space or time after random number generation, not haphazardly. 

Three major random sampling techniques exist systematic sampling , simple random sampling , and stratified random sampling . (IPCS, 1992). All three techniques have a common purpose, namely that the samples are representative of the population or compartment to be sampled. 

For all practical purposes, source testing can be considered as simple random sampling (2). The source may be considered to be composed of such a large population of samples that the populahon N is infinite. From this population, n units are selected in such a manner that each unit of the population has an equal chance of being chosen. For the sample, determine the sample mean, y ... 

The aims of sampling are to establish whether eontaminants are present, their distribution and eoneentrations. Commonly-used sampling regimes inelude square grid, stratified random or simple random teehniques. Evenly-spaeed sampling points may be appropriate if the eontamination is visible otherwise judgement is required based on whether the land slopes or is flat. Samples are also taken near to the point of release. 

Simple random sampling involves taking increments from the bulk material in such a way that any portion of the bulk has an equal probability of being sampled. This type of sampling is often used when little information is available about the material that is being sampled. It is also commonly used when... 

The number of sampling iterations must be sufficient to give stable results for output distributions, especially for the tails. There are no simple rules, because the necessary number of runs depends on the number of variables entered as distributions, model complexity (mathematical structure), sampling technique (random or Latin hypercube), and the percentile of interest in the output distribution. There are formal methods to establish the number of iterations (Cullen and Frey 1999) however, the simulation iterations could simply be increased to a reasonable point of convergence. 

Simple random sampling should, therefore, generally be used either in conjunction with other sampling methods or in cases involving only small study populations [SPRINGER and McCLURE, 1988],... 

Stratified random sampling, which is a variation of simple random sampling, is used for media that are stratified with respect to their chemical and physical properties. Each stratum is identified and randomly sampled. The number of grab samples and the sampling point selection depend on the nature of contaminant distribution within each stratum. Stratified random sampling is used for the characterization of multiphase liquid wastes or process waste batches that undergo stratification over time and/or space. 

The underlying assumptions of the Student s t-test include simple random and systematic sampling and a normal distribution of the sample mean. The upper limit of the confidence interval for the mean concentration is compared to the action level to determine whether solid waste contains a contaminant of concern at a hazardous level. (The calculation is conducted according to Equation 10, Appendix 1.) A contaminant of concern is not considered to be present at a hazardous level, if the upper limit of the confidence interval is below the action level. Otherwise, the opposite conclusion is reached. Example 5.13 demonstrates the application of this test for deciding whether the waste is hazardous or not. 

Sample mean for simple random sampling and systematic random sampling ... 

Let us first look at the simple random sampling scheme. Suppose we want to evaluate the one-dimensional integral... 

In an unmodified Monte Carlo method, simple random sampling is used to select each member of the 777-tuple set. Each of the input parameters for a model is represented by a probability density function that defines both the range of values that the input parameters can have and the probability that the parameters are within any subinterval of that range. In order to carry out a Monte Carlo sampling analysis, each input is represented by a cumulative distribution function (CDF) in which there is a one-to-one correspondence between a probability and values. A random number generator is used to select probability in the range of 0-1. This probability is then used to select a corresponding parameter value. 

Figure 2.2 Simple random sampling. The sampling units are selected on a random basis. A drawback is that large parts of the sampling site may be left out completely the buried tanks could be missed altogether.

In the previous section we discussed the ramifications of the uncertainty in estimating means from small samples and described how the sample mean, x, follows a f-distribution. In this section, we discuss the ramifications of the uncertainty in estimating s2 from small samples. The variable s2 is called the sample variance, which is an estimate of the population variance, a2. For simple random samples of size n selected from a normal population, the quantity in Equation 3.10... 

The simplest way to obtain a subset of a dataset is by means of simple random sampling but this is most unlikely to provide a subset that encompasses all of the structural classes present within that dataset. Instead, classes that are heavily populated in the dataset, such as the very large sets of analogues that characterise many corporate databases, will be represented proportionally in the subset, while low-frequency classes, where only a few molecules have been synthesised or otherwise acquired, are unlikely to be represented. Thus, while random selection samples the molecules that are present within a dataset, the selection methods discussed in this chapter are intended to sample the classes of molecules that are present within that dataset. The first question to be addressed when considering the effectiveness of the various methods is thus whether they do, in fact, perform better than random only when an affirmative answer has been received to this question is it appropriate to consider which method (or class of methods) is the best ofthose that are available. 

The key is to apply the statistical principle of random sampling. We saw in Chapter 2 that the sampling of individual units at random minimized the sample-to-sample variation. Random samples may seem to be taken in an arbitrary and unorganized fashion. But, in fact, they are more representative, and consistently so, in repeated sampling situations (day in and day out) than samples obtained any other way. Actually, we all practice random sampling in simple situations, as we will illustrate below. The real trick is applying this principle to solids, liquids, and gases, where individual units are rarely available for selection. 

In statistical terms, if the whole population to be sampled is homogeneous, that is, can be described by a single set of parameters, simple random sampling is as efficient as stratified sampling. But, if the population consists of a set of appreciably different subpopulations and so cannot be described by a single set of parameters. 

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