1. Simple Random Sampling: A simple random sample (SRS) of size n is produced by a scheme that ensures that each subgroup of the population of size n has an equal probability of being chosen as the sample
2. Stratified Random Sampling: Divide the population into “strata”. There can be any number of these. Then choose a simple random sample from each stratum. Combine those into the overall sample. That is a stratified random sample. (Example: Mosque A has 600 women and 400 women as members. One way to get a stratified random sample of size 30 is to take an SRS of 18 women from the 600 women and another SRS of 12 men from the 400 men.)
3. Multi-Stage Sampling: Sometimes the population is too large and scattered for it to be practical to make a list of the entire population from which to draw an SRS. For instance, when the polling organization samples US voters, they do not do an SRS. Since voter lists are compiled by counties, they might first do a sample of the counties and then sample within the selected counties. This illustrates two stages. In some instances, they might use even more stages. At each stage, they might do a stratified random sample on sex, race, income level, or any other useful variable on which they could get information before sampling.
4. Cluster sampling. With cluster sampling, every member of the population is assigned to one, and only one, group. Each group is called a cluster. A sample of clusters is chosen, using a probability method (often simple random sampling). Only individuals within sampled clusters are surveyed.
Note the difference between cluster sampling and stratified sampling. With stratified sampling, the sample includes elements from each stratum. With cluster sampling, in contrast, the sample includes elements only from sampled clusters.
5. Systematic random sampling. With systematic random sampling, we create a list of every member of the population. From the list, we randomly select the first sample element from the first k elements on the population list. Thereafter, we select every kth element on the list.