Monday, May 4, 2009

Comparison Among the Designs and Methods

Simple random sampling is the basic building block and point of reference for all other designs discussed in this text. However, few large scale surveys use only simple random sampling, because other designs often provide greater accuracy or efficiency or both. The sample is chosen from the entire population, using a random number generator. Each member of the population has an equal chance of being selected. The selection of any particular individual does not affect the chances of any other individual being chosen. Every number of the population has an equal chance of being selected and the selection of any particular individual does not affect the chances of any other individual being chosen. Choosing the sample randomly reduces that selected members will not representative the whole population. You could select the sample by drawing names randomly or by assigning each member of population a unique number and then using a random number generator to determine which members to include

Stratified random sampling produces estimators with smaller variance than those from simple random sampling, for the same sample size, when the measurements under study are homogenous within strata but stratum means vary among themselves. The ideal situation for stratified random sampling is to have all measurements within any one stratum equal but have differences occurring as we move from stratum to stratum. Sometimes a population includes groups of members who share common characteristics, such as gender, age, or educational level. Such groups are called strata. A stratified sample has the same proportion of members from each stratum as the population does

A stratified sample is obtained by taking samples from each stratum or sub-group of a population. When we sample a population with several strata, we generally require that the proportion of each stratum in the sample should be the same as in the population.

Stratified sampling techniques are generally used when the population is heterogeneous, or dissimilar, where certain homogeneous, or similar, sub-populations can be isolated (strata). Simple random sampling is most appropriate when the entire population from which the sample is taken is homogeneous. Some reasons for using stratified sampling over simple random sampling are:

a) the cost per observation in the survey may be reduced;
b) estimates of the population parameters may be wanted for each sub-population;
c) increased accuracy at given cost.

Suppose a farmer wishes to work out the average milk yield of each cow type in his herd which consists of Ayrshire, Friesian, Galloway and Jersey cows. He could divide up his herd into the four sub-groups and take samples from these.
(Definition and example taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1)

Systematic sampling is used most often simply as a convenience. It is relatively easy to carry out. But this form of sampling may actually be better than simple random sampling, in terms of bounds on the error of estimation, if the correlation between pairs of elements within the same systematic sample is negative. The stratified and the systematic sample booth force the sampling to be carried out along the whole set of data, but stratified design offers more random selection and often produces a smaller bound on the error of estimation. A random starting point is chosen, using a random number generator. The sample is chosen by going through the population sequentially; the members of the sample are selected at regular intervals, e.g., every fifth person is selected. You go through the population sequentially and select members at regular intervals. The sample size and the population determine the sampling interval:
Interval = population size / sample size,
for example, if you wanted the sample to be a tenth of population, you would select every tenth member of the population, starting with one chosen randomly from among the first ten sequence

Stratified Cluster Sampling
• Combines elements of stratification and clustering
• First you define the clusters
• Then you group the clusters into strata of clusters, putting similar clusters together in a stratum
• Then you randomly pick one (or more) cluster from each of the strata of clusters
• Then you sample the subjects within the sampled clusters (either all the subjects, or a simple random sample of them)

Cluster sampling is generally employed because of cost effectiveness or because no adequate frame for elements is available. However, cluster sampling may be better than either simple or stratified random sampling if the measurements within clusters are heterogeneous and the cluster means are nearly equal. This condition is in contrast to that for stratified random sampling in which strata are to be homogeneous but stratum means are to differ.

Stratification vs. Clustering

• Divide population into groups different from each other: sexes, races, ages
• Sample randomly from each group
• Less error compared to simple random
• More expensive to obtain stratification information before sampling
The population is divided into groups that share a common characteristic. From each group a simple random sample of the members is taken. The size of each sample from each group is proportional to the size of each group. There may often be factors which divide up the population into sub-populations (groups / strata) and we may expect the measurement of interest to vary among the different sub-populations. This has to be accounted for when we select a sample from the population in order that we obtain a sample that is representative of the population. This is achieved by stratified sampling.

• Divide population into comparable groups: schools, cities
• Randomly sample some of the groups
• More error compared to simple random
• Reduces costs to sample only some areas or organizations
The population is divided into groups. A random sample of groups is chosen. All members from the
chosen group are surveyed.

Multi-stage Random Sampling
The population is organized into groups. A random sample of groups is chosen. From each group a random sample is chosen. This method uses several levels of random sampling. Multi-stage sampling is like cluster sampling, but involves selecting a sample within each chosen cluster, rather than including all units in the cluster. Thus, multi-stage sampling involves selecting a sample in at least two stages.

-. Richard L. Scheaffer, William Mendenhall, Lyman Ott; Elementary Survey Sampling, 4-th, PWS-Kent Publishing Company, 1990, Boston
-. Mugo Fridah W, Sampling in Research
-. SamplingBigSlides.pdf
-. St. Paul Mathematics Department

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