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Encyclopedia > Random sample

A sample is a subset chosen from a population for investigation. A random sample is one chosen by a method involving an unpredictable component, in the sense that the selection of any element of the population is independent of the selection of any other element. A probability sample is one in which each item has a known probability of being in the sample. An expert is someone widely recognized as a reliable source of knowledge, technique, or skill whose judgment is accorded authority and status by the public or their peers. ...

Whenever sampling is used there is a risk that the sample will not be sufficiently representative of the population from which it was drawnâ€”this is known as sampling error. In the case of random samples, mathematical theory is available to assess the risk associated with sampling error. Thus, estimates obtained from random samples can be accompanied by measures of the uncertainty associated with the estimate. This can take the form of a standard error, or if the sample is large enough for the Central limit theorem to take effect, confidence intervals may be calculated. In statistics, when analyzing collected data, the samples observed differ in such things as means and standard deviations from the population from which the sample is taken. ... Standard error can refer to: In statistics, an expression of the uncertainty in a value - see standard error (statistics). ... Central limit theorems are a set of weak-convergence results in probability theory. ... A confidence interval (CI) consists of two two random boundary points between which we have a certain specified level of confidence that population parameter lies. ...

## Types of random sample GA_googleFillSlot("encyclopedia_square");

• A simple random sample, also known as an epsem sample, is one in which every in the population of interest has an equal opportunity of being selected for the sample
• Stratified random sample, in which the population consists of a mixture of distinct subpopulations, each with its own mean and variance, and the sample is structured to make use of this fact. Great gains in efficiency are possible from stratification.
• A cluster sample, in which the sampling units are collected in groups. For example, a sample of telephone calls may be collected by first taking a collection of telephone lines and collecting all the calls on the sampled lines. The analysis of cluster samples must take into account the intra-cluster correlation which reflects the fact that units in the same cluster are likely to be more similar than two units picked at random.

In statistics, a simple random sample from a population is a sample chosen randomly, in which each member of the population has the same probability of being chosen. ... Stratified sampling is a method of sampling from a population in statistics. ... In statistics, mean has two related meanings: the average in ordinary English, which is more correctly called the arithmetic mean, to distinguish it from geometric mean or harmonic mean. ... In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are. ...

## Methods of producing random samples

• Tables of random numbers
• Mathematical algorithms for pseudorandom number generators
• Physical randomisation devices such as coins, playing cards or sophisticated devices such as ERNIE

A pseudorandom number generator (PRNG) is an algorithm that generates a sequence of numbers which are not truly random. ... Ernie, in a skit with Bert Ernie, in an Egyptian pyramid with Bert, meets an Egyptian statue counterpart to dance with. ...

## An example application

The CEO of a company which provides call centres is considering the introduction of new software that she hopes that will reduce average call handling times. She designs an experiment to find out the reduction in mean call handling time associated with the new software. At one of her call centres a sample of 50 call agents will use the new software and the remaining 150 staff will use the existing software. She knows that if she simply asks the centre manager to choose the staff to operate the new software he will likely choose the most intelligent and cooperative agents. The results of the trial will thus be subject to substantial bias in favour of the new software. To avoid this problem she allocates the agents randomly by putting the names of the agents in a column in a spreadsheet. She then creates a second column consisting of random numbers from the spreadsheet's random number generator. By sorting using the second column as the sort key she puts the staff names in random order and selects the first 50 names. These will be the staff using the new software. Chief Executive Officer (CEO) is the job of having the ultimate executive responsibility or authority within an organization or corporation. ... The first statistician to consider a methodology for the design of experiments was Sir Ronald A. Fisher. ... In probability and statistics, if a bias exists it means that the processes involved are not totally random, or one outcome is favoured over others. ... Sorting refers to a process of arranging items in some sequence and/or in different sets, and accordingly, it has two common, yet distinct meanings: ordering: aranging items of the same kind, class, nature, etc. ...

Results from FactBites:

 Sampling (statistics) - Wikipedia, the free encyclopedia (2031 words) Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference. The sampling frame must be representative of the population and this is a question outside the scope of statistical theory demanding the judgement of experts in the particular subject matter being studied. However, the importance of random sampling was not universally appreciated and in the USA the 1936 Literary Digest prediction of a Republican win in the presidential election went badly awry, due to severe bias.
 PA 765: Sampling (4807 words) Non-random sampling is widely used as a case selection method in qualitative research, or for quantitative studies of a preliminary and exploratory nature where random sampling is too costly, or where it is the only feasible alternative. Repeated systematic sample has the side benefit that the variability in the subsample means for a given variable is a measure of the variance of that estimate in the entire sample. Technically, cluster sampling is where all subjects at the lowest hierarchical level (ex., all students in a school) are sampled for each primary sampling unit (PSU's, which are the second-lowest hierarchical level, such as schools or Census blocks), whereas multistage sampling is where only a random sample of lowest hierarchical level subjects are selected.
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