There are various techniques within the Probability class: Under this technique, the probability of any particular Sampling Unit getting selected for study is known. This type of sampling follows the statistical principles and hence answers those research questions which require statistical inferences to be drawn from the study. It helps in **business research**.

## Methods of Probability Sampling

These techniques differ from one another in one aspect or another, like Whether there is any relaxation applied in the way of Sampling Units for getting selected or not. Variation optimizes a technique for different situations to take advantage of the ease, Cost, time, effectiveness etc.

As already explained, if any extreme values present in the population have sufficient quantum to distort the results by their inclusion or exclusion, they are not left to chance. Their effect becomes more significant with smaller people. However, as the population tends to become too small, one should prefer the census.

## 1. Simple Random Sampling

This method is like a pure lottery system. This offers an equal probability for all the sampling units to get chosen for the study. This is the basic technique under Probability Sampling, and the other methods of probability sampling of this class offer some variations of this methodology. In this method, every sampling unit of the population or any combination of sampling units has an equal chance of getting chosen for the study. This is based on pure luck, and no other cause can affect the inclusion or exclusion of any sampling unit in the study. There is no restriction of any kind. So this is an unrestrictive type of Probability Sampling. Also, there is no bias in this method.

## 2. Restrictive Random Sampling

### i) Systematic Sampling

This variation of simple random sampling restricts the random selection to a small predetermined group of sampling units only. Based on this first random selection, other teams are automatically selected without actually participating in the selection process. For example, if there are 0 to 1000 units in the population and the Sample sizes are 20 units, the value of period K is calculated as follows:

K=1000-0/20=50 Now, Simple Random Sampling is applied only to the first 50 units. One unit is selected; say, 8 are chosen. Then starting from 8, the period (50) is added repeatedly to get the number of other teams fixed.

Thus, the units selected will be 8, 58, 108, 158, 208, 258, 308, 358, 408, 458, 508, and 558. 608,658,708, 758, 808, 858, 908,958. This methods of probability sampling simplifies the procedure such that Simple random selection is restricted to the first unit only. It makes it less expensive, quick, and more suitable for prominent people and still offers the benefits of Simple Random Sampling. Another advantage is that the sample gets spread uniformly over the whole population.

If there exists a phenomenon of hidden periodicity in the characteristics of the population, one may end up gathering only one type of data, and the sample no more remains representative of the people. The disadvantage is that it needs to be more independent in selecting the first unit. It will be clear from the following examples:

If we select 3rd day every month to record the number of customers at a bank, we may always get a huge crowd, and if we get the 27th day of the month, there will be a considerably fewer number of customers. It is so because, generally, banks get a large number of customers during the first few days of every calendar month and get fewer numbers during the last few days of every calendar month.

So this system should not be used if the Frame has been naturally or deliberately ordered in respect of the studied variable, i.e. Frame arranged in ascending or descending order of Ranks of college students. Barring this pitfall, Systematic Sampling has all the advantages of Simple Random Sampling.

#### Advantages of Systematic Sampling

It is probability Sampling. So, all the advantages of Probability Sampling are found in this method also.

- The design is simple and easy to handle.
- Simple Random Sampling of only a part of some list is to be done.
- Quick and Cost-effective.
- Samples get uniformly distributed over the whole source list.

#### Disadvantages of Systematic Sampling

- Hidden periodicity, if present in the source list, hampers the performance result of this method.
- It should not be used on ordered or ranked source lists.

### ii) Stratified Random Sampling

This is also a restricted form of probability sampling. The methods of probability sampling helps handle the population’s heterogeneity concerning the studied variable. If the population is heterogeneous, it has significant variability, and then a simple Random Sampling may lose out on producing a representative sample of the people. In that situation, the two-step stratified sampling is more effective.

In the first step, the researcher divides the population into several strata. Each stratum is homogenous within itself and is heterogeneous to one another. The size of each stratum and the sample size due from each stratum is determined.

In the above figure, a total heterogeneous population of size N requires a sample size of n. If we create three strata, A, B and C having population sizes N, N, N, N, respectively (NN, +N,+N,) such that now A, B, and C are homogenous. (for example – low-income group, middle-income group and high-income group people living in a colony) The Sample Size due from each is n, n, and n, respectively. (n=n+n+n).

#### Advantages of Stratified Sampling

- Stratified sampling helps provide a sample representing a heterogeneous population more closely.
- As it helps reduce the effect of heterogeneity, the results are more precise.
- Homogeneous strata are easier to handle.

#### Disadvantages of Stratified Sampling

- The methods of probability sampling requires two steps. One for creating strata and the second for sampling.
- It requires close relation of the stratification variable to the variable under study.
- If strata are large in number, it increases CostCost and time.

#### Precautions while dividing the population into strata

- Strata should be small in number, generally up to 6; otherwise, handling and analysis become a complex task.
- Each stratum should be homogenous within itself.
- After stratification, each stratum should be sufficient, and the sample size should also be considerably large.
- The variable/basis chosen for creating strata should be relevant to the variables to be studied.
- Strata should be well boundaries and distinct; otherwise, the reason for stratification will be recovered.

### iii) Cluster Sampling

The cluster represents a large number of groups of sampling units such that each set may be heterogeneous within itself, but all collections are similar in the overall composition. For example, each college affiliated with a University forms a cluster, or each group of residential buildings in an area forms a set of buildings. It is one of the methods of probability sampling.

#### Advantages of Cluster Sampling

- It saves the researcher from creating a frame consisting of the sampling units in all the clusters. He will have to prepare a frame only for the finally selected collections.
- It saves on Cost, time, and travel as clusters are mainly concentrated geographically.

#### Disadvantages of Cluster Sampling

- This is a two-step process.
- Success depends upon successfully creating a large number of clusters.
- If clusters are not similar, it does not create a representative sample, and the sampling error will be higher.
- Response from complete enumeration may get typified as the sampling units knowing each other well and can mutually influence one another’s reaction.

### iv) Area Sampling

Area Sampling uses all principles of cluster sampling and is very similar to it. As the name suggests, ‘Area’ represents a geographically delimited boundary. It is one of the methods of probability sampling. This is a particular case where geographical boundaries form the clusters. Each ‘area’ represents a cluster, and we call it Area Sampling.

For example, villagers in a district or ‘wards’ in a city created by Govt. departments based on their official data. This makes it more accessible as a cluster, in this case, is already started, and that too based on authentic, official data.

### v) Multistage Sampling

Sampling is done at several stages, and the final sampling units are selected hierarchically. For example, they randomly selected two states out of the whole country in the first stage. In the second stage, 2 cities from each state are chosen randomly. In the third stage, 4 wards from each city are selected randomly, and 4 schools are selected from each community for the country’s final study on school education. This is similar to cluster sampling, but clusters are formed in stages of hierarchy.

It offers similar advantages as that of cluster sampling, and at each successive stage, the need for Frame preparation becomes narrower. It has disadvantages in that sampling error will accumulate if the units selected at each next step are not similar. Multistage sampling is one of the methods of probability sampling. If the number of stages is large, this error will also go on multiplying as the degree of sample representativeness is lost with each successive step.