Example:

Differences between Stratified and Cluster:

**Stratified and Cluster Sampling Techniques**

**Stratified and Cluster Sampling Techniques**

Cluster

A method of sampling that involves the division of a population into smaller groups known as strata. In stratified random sampling, the strata are formed based on members' shared attributes or characteristics. A random sample from each stratum is taken in a number proportional to the stratum's size when compared to the population. These subsets of the strata are then pooled to form a random sample.

Cluster sampling refers to a type of sampling method . With cluster sampling, the researcher divides the population into separate groups, called clusters. Then, a simple random sample of clusters is selected from the population. The researcher conducts his analysis on data from the sampled clusters.

Stratified

Sampling

In statistics, stratified sampling is a method of sampling from a population.

Stratification is the process of dividing members of the population into 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.

Advantages:

If the population is large and enough resources are available, usually one will use multi-stage sampling. In such situations, usually stratified sampling will be done at some stages. However the main advantage remains stratified sampling being the most representative of a population.

Disadvantages:

Stratified sampling is not useful when the population cannot be exhaustively partitioned into disjoint subgroups. It would be a misapplication of the technique to make subgroups' sample sizes proportional to the amount of data available from the subgroups, rather than scaling sample sizes to subgroup sizes.

Data representing each subgroup are taken to be of equal importance if suspected variation among them warrants stratified sampling. If subgroups' variances differ significantly and the data need to be stratified by variance, then there is no way to make the subgroup sample sizes proportional (at the same time) to the subgroups' sizes within the total population.

Example:

Suppose that in a company there are the following staff:

•male, full-time: 90

•male, part-time: 18

•female, full-time: 9

•female, part-time: 63

•Total: 180

and we are asked to take a sample of 40 staff, stratified according to the above categories. The first step is to find the total number of staff (180) and calculate the percentage in each group.

Now, multiply each group size by the sample size and divide by the total population size (size of entire staff):

•male, full-time = 90 x (40 / 180) = 20

•male, part-time = 18 x (40 / 180) = 4

•female, full-time = 9 x (40 / 180) = 2

•female, part-time = 63 x (40 / 180) = 14

Cluster sampling is a sampling technique used when "natural" but relatively homogeneous 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 simple random sample of the groups is selected.

Cluster

Sampling

Then the required information is collected from a simple random sample of 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 total number of interviews and costs given the desired accuracy. 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.

Advantage:

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

Disadvantage:

Higher sampling error, which can be 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 nonclustered study.

Suppose that the Department of Agriculture wishes to investigate the use of pesticides by farmers in England. A cluster sample could be taken by identifying the different counties in England as clusters. A sample of these counties (clusters) would then be chosen at random, so all farmers in those counties selected would be included in the sample. It can be seen here then that it is easier to visit several farmers in the same county than it is to travel to each farm in a random sample to observe the use of pesticides.

The main difference between cluster sampling and stratified sampling is that in cluster sampling the cluster is treated as the sampling unit, therefore, 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 taken into consideration. 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.)

Website links:

http://rchsbowman.wordpress.com/2009/08/16/statistics-notes-sampling-techniques-2/

http://rchsbowman.files.wordpress.com/2009/08/081609_2352_4.png

http://rchsbowman.files.wordpress.com/2009/08/081609_2352_6.png

http://faculty.elgin.edu/dkernler/statistics/ch01/images/cluster-sample.gif

http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Cluster_sampling.html

http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Stratified_sampling.html

QUESTIONS:

1) What's the difference between Stratified and Clustered Sampling?

a) No difference, they're the same

b) Clustered: analysis is done on a population of clusters. Stratified: analysis is done on elements within strata.

c) For clustered, analysis is done in convenience to the interviewer, whereas Stratified is not.

2) Stratification is:

a) the least expensive and least time-consuming of all sampling techniques

b) a fast and easy technique

c) the process of dividing members of the population into homogeneous subgroups before sampling.

3) An advantage of Clustered Sampling is:

a) Can be cheaper than other methods – e.g. fewer travel expenses

b) Higher sampling error

c) having gotten the most representative of a population

ANSWERS: 1b, 2c, 3a

VIDEO LINKS for further clarification:

Stratified: Clustered:

THE END! :)