If a simple random subsample of elements is selected within each of these groups, this is referred to as a "two-stage" cluster sampling plan. A common motivation for cluster sampling is to reduce the total number of interviews and costs given the desired accuracy. For a fixed sample size, the expected random error is smaller when most of the variation in the population is present internally within the groups, and not between the groups.
The population within a cluster should ideally be as heterogeneous as possible, but there should be homogeneity between clusters. 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 sampled. 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 sampling is done on a population of clusters at least in the first stage.
In stratified sampling, the sampling is done on elements within each strata. In stratified sampling, a random sample is drawn from each of the strata, whereas in cluster sampling only the selected clusters are sampled.
A common motivation of cluster sampling is to reduce costs by increasing sampling efficiency. This contrasts with stratified sampling where the motivation is to increase precision. There is also multistage cluster sampling , where at least two stages are taken in selecting elements from clusters. Without modifying the estimated parameter, cluster sampling is unbiased when the clusters are approximately the same size.
In this case, the parameter is computed by combining all the selected clusters. When the clusters are of different sizes, probability proportionate to size sampling is used.
In this sampling plan, the probability of selecting a cluster is proportional to its size, so that a large clusters has a greater probability of selection than a small cluster. However, when 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. An example of cluster sampling is area sampling or geographical cluster sampling.
Each cluster is a geographical area. Because a geographically dispersed population can be expensive to survey, greater economy than simple random sampling can be achieved by grouping several respondents within a local area into a cluster. It is usually necessary to increase the total sample size to achieve equivalent precision in the estimators , but cost savings may make such an increase in sample size feasible.
Cluster sampling is used to estimate high mortalities in cases such as wars , famines and natural disasters.
The other probabilistic methods give fewer errors than this method. For this reason, it is discouraged for beginners. Two-stage cluster sampling, a simple case of multistage sampling , is obtained by selecting cluster samples in the first stage and then selecting sample of elements from every sampled cluster.
Consider a population of N clusters in total. Where do they make those things, anyway? Is there a ball machine industry? Neither of these mechanical procedures is very feasible and, with the development of inexpensive computers there is a much easier way.
Here's a simple procedure that's especially useful if you have the names of the clients already on the computer. Many computer programs can generate a series of random numbers. Then, sort both columns -- the list of names and the random number -- by the random numbers.
This rearranges the list in random order from the lowest to the highest random number. Then, all you have to do is take the first hundred names in this sorted list. You could probably accomplish the whole thing in under a minute. Simple random sampling is simple to accomplish and is easy to explain to others. Because simple random sampling is a fair way to select a sample, it is reasonable to generalize the results from the sample back to the population.
Simple random sampling is not the most statistically efficient method of sampling and you may, just because of the luck of the draw, not get good representation of subgroups in a population. To deal with these issues, we have to turn to other sampling methods. Stratified Random Sampling , also sometimes called proportional or quota random sampling, involves dividing your population into homogeneous subgroups and then taking a simple random sample in each subgroup.
In more formal terms:. Divide the population into non-overlapping groups i. There are several major reasons why you might prefer stratified sampling over simple random sampling. First, it assures that you will be able to represent not only the overall population, but also key subgroups of the population, especially small minority groups. If you want to be able to talk about subgroups, this may be the only way to effectively assure you'll be able to. If the subgroup is extremely small, you can use different sampling fractions f within the different strata to randomly over-sample the small group although you'll then have to weight the within-group estimates using the sampling fraction whenever you want overall population estimates.
When we use the same sampling fraction within strata we are conducting proportionate stratified random sampling. When we use different sampling fractions in the strata, we call this disproportionate stratified random sampling. Second, stratified random sampling will generally have more statistical precision than simple random sampling.
This will only be true if the strata or groups are homogeneous. If they are, we expect that the variability within-groups is lower than the variability for the population as a whole. Stratified sampling capitalizes on that fact.
For example, let's say that the population of clients for our agency can be divided into three groups: Caucasian, African-American and Hispanic-American.
And, by chance, we could get fewer than that! If we stratify, we can do better. First, let's determine how many people we want to have in each group. Let's say we still want to take a sample of from the population of clients over the past year.
But we think that in order to say anything about subgroups we will need at least 25 cases in each group. Finally, by subtraction we know that there are Caucasian clients. Because the groups are more homogeneous within-group than across the population as a whole, we can expect greater statistical precision less variance. And, because we stratified, we know we will have enough cases from each group to make meaningful subgroup inferences.
Here are the steps you need to follow in order to achieve a systematic random sample:. All of this will be much clearer with an example.
To use systematic sampling, the population must be listed in a random order. Now, select a random integer from 1 to 5. In our example, imagine that you chose 4. You would be sampling units 4, 9, 14, 19, and so on to and you would wind up with 20 units in your sample.
For this to work, it is essential that the units in the population are randomly ordered, at least with respect to the characteristics you are measuring. Retrieved Sep 14, from Explorable. The text in this article is licensed under the Creative Commons-License Attribution 4. You can use it freely with some kind of link , and we're also okay with people reprinting in publications like books, blogs, newsletters, course-material, papers, wikipedia and presentations with clear attribution.
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Cluster sampling (also known as one-stage cluster sampling) is a technique in which clusters of participants that represent the population are identified and included in the sample. Cluster sampling involves identification of cluster of participants representing the population and their inclusion in .
Sampling Methods. Sampling and types of sampling methods commonly used in quantitative research are discussed in the following module. Learning Objectives: Define sampling and randomization. Explain probability and non-probability sampling and describes the different types of each.
a method of sampling in which every sample element is selected only on the basis of chance through a random process replacement sampling a method of sampling in which sample elements are returned to the sampling frame after being selected, so they may be sampled again. Once you know your population, sampling frame, sampling method, and sample size, you can use all that information to choose your sample. Importance As you can .
The main difference between cluster sampling and stratified sampling lies with the inclusion of the cluster or strata. In stratified random sampling, all the strata of the population is sampled while in cluster sampling, the researcher only randomly selects a number of clusters from the collection of clusters of the entire population. Cluster sampling refers to a sampling method that has the following properties. The population is divided into N groups, called clusters. The researcher randomly selects n clusters to include in the sample. The number of observations within each cluster M i is known.