Simple random samples

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 ... 

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... 

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. 

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. 

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. 

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. 

As study populations are often very large, however, it is not possible to administer the drug to every member of the population, so a sample from the study population is chosen and the effects of the drug in that sample are determined in a clinical study. In clinical trials, samples are typically considered or assumed to be simple random samples from the study population. A simple random sample is a sample in which each observational unit (for example, study participant) has the same probability of selection from the population. In other fields in which Statistics are used (most notably population surveys) samples need not be selected in this manner. 

Assuming that these observations represent a simple random sample from the population of... 

Each group represents a simple random sample from each of k populations and the observations ate statistically independent. 

Each group represents a simple random sample from relevant populations observations are independent outcome is approximately normally distributed the variance is equal across the populations Placebo vs. low placebo vs. medium placebo vs. high low vs. medium low vs. high medium vs. high To control the overall Type I error... 

D. B. Rubin and N. Schenker, Multiple imputation for interval estimation from simple random samples with ignorable nonresponse. J Am Stat Assoc 81 366-374 (1986). 

Systematic sampling involves taking the position of the first sample at random and then taking further samples at fixed distances/directions from this. For example, samples may be taken at intervals of 5 m. This type of sampling has the potential to provide more accurate results than simple random sampling. However, if the soil contains a periodic (systematic) variation which coincides with this type of sampling, biased samples can result. An initial pilot study of the site can help prevent this. 

There are three advantages of stratified random sampling for large target populations, when properly done, relative to simple random sampling. The overall variance for the estimates should be significantly lower. Theoretically, there is an inverse square relationship between the number of strata and the variance, although practically the results are usually less dramatic ( 7, pp. 133-5). 

Random Sample—Selection of units chosen from a larger population of such units so that the probability of inclusion of any given unit in the sample is defined. In a simple random sample, each unit has an equal chance of being included. Random samples are usually chosen with the aid of tables of random numbers found in many statistical texts. Reference-Listed Drug [21 CFR 314.3] — Listed drug identified by the FDA as the drug product on which an applicant relies in seeking approval of its abbreviated application. 

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