There are many methods of probability sampling. The commonly used methods are as follows:

1. Simple random sampling

2. Systematic random sampling

3. Stratified sampling

4. Area sampling

We will briefly explain each of these methods.

Simple random sampling: A simple random sample is a sample wherein any item of the population is as likely to be selected as any other item. In other words, all items of the population have equal chances of being selected in the sample. Lottery is one method of selecting a simple random sample. In fact, the simple random method is commonly known by the name as â€˜lottery samplingâ€™. When the size of the population is manageable, selecting a random sample by picking lotteries will be practicable.

Researchers often turn to the random table or the table of random numbers. This is a table that has been prepared by statisticians for the purpose of selecting random samples. This table can be readily used by any one for developing a random sample out of a given population. It is a set of numbers in which each of the digits from 0 to 9 has the same chance of appearing in all positions. Different random tables have been created for helping the selection of random samples. The tables of Tippet, Isher, Kendall and Mahalonobis are some commonly used random tables.

If the population is infinite or unlimited, then a random table may not help. It will be helpful only when the population is finite, well-defined and a complete list of the units of the population is available.

Systematic sampling: There is only a small difference between simple random sampling and systematic sampling. Systematic sampling involves selecting every nth unit from the population after the beginning unit is selected at random. The interval â€˜nâ€™ is fixed by dividing the population by sample size. For example, if the population consists of 500 elements and a sample of 50 elements is required, the sample interval will be fixed as 500/50 = 10. Thus, every tenth unit from the previously ordered population can be taken to get the systematic sample of 50 elements. Normally, the start is fixed by selecting a random number â€“ in the above case, between 1 and 10. If this happens to be 5, every tenth number from it i.e. 15, 25, 35 and so on are selected to get the sample required.

Systematic sampling can increase the sampleâ€™s representation when the population elements can be ordered in some pattern with regard to the characteristic being investigated.

Stratified sampling: In this case, the population is divided into a few strata according to certain characteristics common to members within the strata. From each stratum, a specified number of units is picked by random means. These units together constitute a stratified sample. While resorting to stratified sampling, it is essential that the criteria used to stratify the population is directly associated with what the study is going to measure. In other words, stratification of a population should be done only if a direct correlation exists between the criteria for stratifying and the data sought by the study. Within stratified samples, there are two kinds: the proportional sample and the disproportional sample. In some cases, the number of sample units selected from each stratum may be proportional to the stratumâ€™s share in the total population. In these cases, the samples are proportional samples. In certain marketing situations, sample units from each stratum may be taken based on certain assigned priorities and not on the basis of the stratumâ€™s share in the total population. The samples in these cases are disproportional samples.

Area sampling: Area sampling is also a form of stratified sampling. In this case, the stratification is based on the criterion of locations. This method selects the sample units in several stages. At each stage a series of intermediary geographical blocks are selected on random basis. Finally, from within these blocks, the sample units are selected at random. The area and sub-area selections at each stage have to be validated to ensure randomness in the sample finally selected.