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## Sampling

For practical and cost reasons, it is often impossible to collect information about the entire population of people or things in which social researchers are interested. In these cases, a sample of the total is selected for study.

Most statistical studies are based on samples and not on complete enumerations of all the relevant data. The main criteria when sampling are to ensure that a sample provides a faithful representation of the totality from which it is selected, and to know as precisely as possible the probability that a sample is reliable in this way. Randomization meets these criteria, because it protects against bias in the selection process and also provides a basis on which to apply statistical distribution theory that allows an estimate to be made of the probability that conclusions drawn from the sample are correct. A statistical sample is a miniature picture or cross-section of the entire group or aggregate from which the sample is taken. The entire group from which a sample is chosen is known as the population, universe or supply.

### Simple random sampling

The basic type of random sample is known as a simple random sample, one in which each person or item has an equal chance of being chosen. Often a population contains various distinct groups or strata that differ on the attribute that is being researched.

### Stratified random sampling

Stratified random sampling involves sampling of each stratum separately. This increases precision, or reduces time, effort and cost of allowing smaller sample sizes for a given level of precision. For example, poverty is known to be most common among the elderly, the unemployed and single parent families, so research on the effect of poverty might will sample separately each of these three strata as part of a survey of poverty in the population as a whole which would permit the total sample size to be reduced because the investigator would know that the groups most affected by poverty were guaranteed inclusion.

### Cluster sampling

Cluster sampling is sometimes used when the population naturally congregates into clusters. For example, managers are clustered in organizations, so a sample of managers could be obtained by taking a random sample of organizations and investigating the managers in each of these. Interviewing or observing managers on this basis would be cheaper and easier than using a simple random sample of managers scattered across all organizations in the country. This is usually less precise than a simple random sample of the same size, but in practice the reduction in cost per element more than compensated for the decrease in precision.

### Multi-stage sampling

Sampling may be done as one process or in stages, known as multi-stage sampling .Multi-stage designs are common when populations are widely dispersed. Thus a survey of business managers might proceed by selecting a sample of corporations as first stage units, perhaps choosing these corporations with a probability proportionate to their size, and then selecting a sample of managers within these corporations at the second stage. Alternatively, a sample of individual factories or office buildings within each corporation could be chosen as the second stage units, followed by sample of managers in each of these as a third stage. Stratification can also be used in the design, if for example occupational sub-groups are known to differ from each other, by selecting state such as personnel, production, and finance management and sampling within each of these. For sampling to be representative, one needs a complete and accurate list of the first stage units that make up the relevant population, a basic requirement that is not always easily met. This forms the sampling frame. Selection from the frame is best done by numbering the items and using a table of random numbers to identify which items form the sample, though a quasi-random method of simply taking every item from the list is often appropriate. The reliability of a sample taken from a population can be assessed by the spread of the sampling distribution, measured by the standard deviation of this distribution, called the standard error. As a general rule, the larger is the size of the sample the smaller the standard error.

### Area sampling

In sampling of this kind small areas are designated as sampling units and the households interviewed include all or a specified fraction of those found in a canvass of these designated small areas. The basic sampling units or segments chosen may be relatively large or relatively small depending on such factors as the type of area being studied, population distribution, the availability of suitable maps and other information and the nature and desired accuracy of the data being collected.

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