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# difference between stratified and cluster sampling

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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.

Random sample

A sample is a subject chosen from a population for investigation. A random sample is one chosen by a method involving an unpredictable component. Random sampling can also refer to taking a number of independent observations from the same probability distribution, without involving any real population. The sample usually is not a representative of the population from which it was drawn&mdash; this random variation in the results is known as sampling error. In the case of random samples, mathematical theory is available to assess the 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.

## Types of random sample

• A simple random sample is hi selected so that all samples of the same size have an equal chance of being selected from the population.
• A self-weighting sample, also known as an EPSEM (Equal Probability of Selection Method) sample, is one in which every individual, or object, in the population of interest has an equal opportunity of being selected for the sample. Simple random samples are self-weighting.
• Stratified sampling involves selecting independent samples from a number of subpopulations, group or strata within the population. Great gains in efficiency are sometimes possible from judicious stratification.
• Cluster sampling involves selecting the sample units 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.

## Methods of producing random samples

Quota sampling

Quota sampling is a method for selecting survey participants. In quota sampling, a population is first segmented into mutually exclusive sub-groups, just as in stratified sampling. Then judgment is used to select the subjects or units from each segment based on a specified proportion. For example, an interviewer may be told to sample 200 females and 300 males between the age of 45 and 60. This means that individuals can put a demand on who they want to sample (targeting)

This second step makes the technique non-probability sampling. In quota sampling, the selection of the sample is non-random unlike random sampling and can often be found unreliable. For example interviewers might be tempted to interview those people in the street who look most helpful, or may choose to use accidental sampling to question those closest to them, for time-keeping sake. The problem is that these samples may be biased because not everyone gets a chance of selection. This non-random element is its greatest weakness and quota versus probability has been a matter of controversy for many years.

Quota sampling is useful when time is limited, a sampling frame is not available, the research budget is very tight or when detailed accuracy is not important. You can also choose how many of each category is selected.

A quota sample is a convenience sample, with an effort made to ensure a certain distribution of demographic variables. Subjects are recruited as they arrive, and the researcher assigns them to demographic groups based on variables like age and gender. When the quota for a given demographic group is filled, the researcher stops recruiting subjects from that particular group.

This is the non probability version of stratified sampling. Subsets are chosen and then either convenience or judgment sampling is used to choose people from each subset.

Stratified sampling is probably the most commonly used probability method. Subsets of the population are created so that each subset has a common characteristic, such as gender. Random sampling chooses a number of subjects from each subset.

Question:

Answers:Here are some sites that should help: http://ccnmtl.columbia.edu/projects/qmss/samp_type.html http://psychology.ucdavis.edu/sommerb/sommerdemo/sampling/types.htm http://edf5481-01.fa02.fsu.edu/Sampling.html http://www.bsos.umd.edu/hesp/newman/newman_classes/newman724/sampling6.pdf

Question:

Answers:In a probability sample, each item has a known probability of being IN the sample. A random sample is one chosen by a method involving an unpredictable component. So there is the known probability in the probability sample.

Question:This question is in reference to statistics and sampling methods. I would appreciate greatly if someone helps me understand the difference between these two types of sampling methods. Thank you in advance!

Answers:i think: a stratified random sample is a random sample of a population which has been divided in strata, taking an equal sample from each stratum. a weighted sample is one where the samples taken from different strata of the population under study are weighted.. that is, taken so that they are representative of the proportion of that stratum/group in the population. hope this helped!

Question:

Answers:When sub-populations vary considerably, it is advantageous to sample each subpopulation (stratum) independently. Stratification is the process of grouping members of the population into relatively homogeneous subgroups before sampling. The strata should be mutually exclusive: every element in the population must be assigned to only one stratum. The strata should also be collectively exhaustive: no population element can be excluded. Then random or systematic sampling is applied within each stratum. This often improves the representativeness of the sample by reducing sampling error. It can produce a weighted mean that has less variability than the arithmetic mean of a simple random sample of the population. Advantages over other sampling methods Focuses on important subpopulations and ignores irrelevant ones. Allows use of different sampling techniques for different subpopulations. Improves the accuracy/efficiency of estimation. Permits greater balancing of statistical power of tests of differences between strata by sampling equal numbers from strata varying widely in size.