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From Wikipedia

Cluster sampling

Cluster sampling is a sampling technique used when "natural" groupings are evident in a statistical population. It is often used in marketing research. In this technique, the total population is divided into these groups (or clusters) and a sample of the groups is selected. Then the required information is collected from the elements within each selected group. This may be done for every element in these groups or a subsample of elements may be selected within each of these groups. A common motivation for cluster sampling is to reduce the average cost per interview. Given a fixed budget, this can allow an increased sample size. Assuming a fixed sample size, the technique gives more accurate results when most of the variation in the population is within the groups, not between them.

## Cluster elements

Elements within a cluster should ideally be as heterogeneous as possible, but there should be homogeneity between cluster means. Each cluster should be a small scale representation of the total population. The clusters should be mutually exclusive and collectively exhaustive. A random sampling technique is then used on any relevant clusters to choose which clusters to include in the study. In single-stage cluster sampling, all the elements from each of the selected clusters are used. In two-stage cluster sampling, a random sampling technique is applied to the elements from each of the selected clusters.

The main difference between cluster sampling and stratified sampling is that in cluster sampling the cluster is treated as the sampling unit so analysis is done on a population of clusters (at least in the first stage). In stratified sampling, the analysis is done on elements within strata. In stratified sampling, a random sample is drawn from each of the strata, whereas in cluster sampling only the selected clusters are studied. The main objective of cluster sampling is to reduce costs by increasing sampling efficiency. This contrasts with stratified sampling where the main objective is to increase precision.

There also exists multistage sampling, where more than two steps are taken in selecting clusters from clusters.

## Aspects of cluster sampling

One version of cluster sampling is area sampling or geographical cluster sampling. Clusters consist of geographical areas. Because a geographically dispersed population can be expensive to survey, greater economy than simple random sampling can be achieved by treating several respondents within a local area as a cluster. It is usually necessary to increase the total sample size to achieve equivalent precision in the estimators, but cost savings may make that feasible.

In some situations, cluster analysis is only appropriate when the clusters are approximately the same size. This can be achieved by combining clusters. If this is not possible, probability proportionate to size sampling is used. In this method, the probability of selecting any cluster varies with the size of the cluster, giving larger clusters a greater probability of selection and smaller clusters a lower probability. However, if clusters are selected with probability proportionate to size, the same number of interviews should be carried out in each sampled cluster so that each unit sampled has the same probability of selection.

Cluster sampling is used to estimate high mortalities in cases such as wars, famines and natural disasters.

• Can be cheaper than other methods - e.g. fewer travel expenses, administration costs

• Higher sampling error, which can expressed in the so-called "design effect", the ratio between the number of subjects in the cluster study and the number of subjects in an equally reliable, randomly sampled unclustered study.

Question:

Answers:The method that you choose to apply is dependent on your research aims and what resources you have available. If you want the purest form of sampling to find what is most likely the shared answer from the largest group of people you would choose random sampling. This way anyone has a chance and there is not bias. However there is a good chance that you will have some disproportiante results. Systematic sampling works well when you know you are unable to conduct a purely random sample and have some type of criteria for your sampling population. It is not random and will have some bias since you are controlling some factors, but it will give you potentially a more direct answer. Purposive sampling is most likely to be for a focus group type scenario where you want to make sure you have certain things represented in your sample. In this case you are going to get exactly what you want since you are setting the parameters to guarantee a certain result, however you have a lot of bias as you are kind of rigging the sample and this must be accounted for.

Question:In probability and statistics, what are the advantages and disadvantages of stratified sampling over random sampling?

Answers:The wiki (ref) lists four advantages and five disadvantages. The main advantage of stratified sampling is that you guarantee a balanced sample. The disadvantage of stratified sampling is that it's harder to do. One way to get the benefits of both is to take a random sample, and then weight your results based on your demographics. But if you under-sample a large group, your statistical uncertainty can go way up.

Question:Systematic Random Stratified?

Answers:Random sampling is the purest form of probability sampling. Each member of the population has an equal and known chance of being selected. When there are very large populations, it is often difficult or impossible to identify every member of the population, so the pool of available subjects becomes biased. Systematic sampling is often used instead of random sampling. It is also called an Nth name selection technique. After the required sample size has been calculated, every Nth record is selected from a list of population members. As long as the list does not contain any hidden order, this sampling method is as good as the random sampling method. Its only advantage over the random sampling technique is simplicity. Systematic sampling is frequently used to select a specified number of records from a computer file. Stratified sampling is commonly used probability method that is superior to random sampling because it reduces sampling error. A stratum is a subset of the population that share at least one common characteristic. Examples of stratums might be males and females, or managers and non-managers. The researcher first identifies the relevant stratums and their actual representation in the population. Random sampling is then used to select a sufficient number of subjects from each stratum. "Sufficient" refers to a sample size large enough for us to be reasonably confident that the stratum represents the population. Stratified sampling is often used when one or more of the stratums in the population have a low incidence relative to the other stratums.

Question:

Answers:when there is a lot production, it is difficult and cumbersome to inspect and test all the items of the lot so random acceptence sampling is followed for these lots for inspection. Advantge is that you can test any say 10 items of the 100 and have a feel of the lot !