**Probability Sampling Methods (Random Method)**

Under the probability sampling methods (Random Method), each unit of the population has a certain probability of being included in the sample. There are four methods under this probability.

## Types:

__1. Simple Random sampling: __

__1. Simple Random sampling:__

In this method, each and every unit of the population has a certain probability to be included in the sample. There are two methods under this method.

**Simple random sampling with replacement:** In this method, the population units which are selected in the sample are observed and replaced in the populations so that once selected units to have the same probability of selection in the successive sample draw. From the population of size N, a sample of size n can be selected in N^{n} ways. The chance of selection of each sample of size n is 1/ N^{n}

**Simple random sampling without replacement:** In this method, the population units which are selected in the sample are observed and will not be replaced in the populations so that once selected units to have no probability of selection in the successive sample draw. From the population of size N, a sample of size n can be selected in N_{Cn }ways. The chance of selection of each sample of size n is 1/ N_{Cn.}

**Advantages/merits and disadvantages/demerits of the simple random sampling:**

** ****Merits: **

- The sample units are selected based on the probability approach so that personal bias is completely eliminated.
- Sample Statistics is used to estimates the population parameters at a certain level of confidence.

** **

**Demerits:**

- This method required a complete and up to date frame/list which is not always available and it is a very cumbersome job to create frame/list.
- This method requires more cost and time compared to non-probability sampling.
- This method requires a large sample size compared to stratify sampling to achieve the same level of precision.
- In some cases, the sample may not be representative of the population.

### 2. __Systematic or serial random sampling__

__Systematic or serial random sampling__

In systematic sampling at first population is divided into an equal number of non-overlapping subpopulations based on sample size and population size. One sample unit will be selected from the first subpopulation and the remaining sample units from other subpopulations will be selected systematically based on the first selected sample units of the first subpopulation. For instance, to draw a sample of the size “n” from the population of size “N”. At first, the population has to divide into an “n” subpopulation with equal size. Each subpopulation contains the “k” units where ‘k’ is called the sampling interval i.e.

Then the first item will be select from 1 to k from the first subpopulation. Suppose the i^{th} sample is selected (i≤k). Then sample consists i, (i+k), i+2k), i+3k), ………., [i+(n-1)k] as the sample units.

** **

**Advantages/merits and disadvantages/demerits of the systematic random sampling:**

**Merits: **

- This method is more convenient to use than another probability sampling.
- This method draws the sample which is evenly spread over the entire population.
- The sample units are selected based on a probability approach so that personal bias is completely eliminated.
- Sample Statistics will be used to estimates the population parameters at a certain level of confidence.

** **

**Demerits:**

- This method required a complete and up to date frame/list which is not always available and it is a very cumbersome job to create frame/list.
- This method requires more cost and time compared to non-probability sampling.
- In some cases, the sample may not be representative of the population.

### 3. __Stratified Random Sampling: __

__Stratified Random Sampling:__

When the population under study is heterogeneous in nature then stratified sampling is more appropriate as compared to other sampling methods to draw the representative sample of the population. In this method, at first, the population is divided into the number of subpopulations and these subpopulations are called strata. As far as possible make the units within the strata homogenous and units between the strata heterogeneous in some attributes. The size of each stratum may or may not be equal. Then sample units will be selected from each stratum independently using simple random sampling. This is also called restricted random sampling. The stratification of the population could be done by ecological regions, development regions, rural/urban, sex, age, caste/ethnicity, etc.

** **** **

**Advantages/merits and disadvantages/demerits of the stratified random sampling:**

**Merits: **

- If the population is heterogeneous in nature then this method produces the representative sample than another sampling.
- This method draws the sample which is evenly spread over the entire population.
- The sample units are selected based on the probability approach so that personal bias is completely eliminated.
- Sample Statistics will be used to estimates the population parameters at a certain level of confidence.
- This method can be used if a complete and up to date frame/list is not available.

** **

**Demerits:**

- This method requires more cost and time compared to non-probability sampling.
- The stratification of the population is quite cumbersome.

### 4. __Cluster Random Sampling: __

__Cluster Random Sampling:__

In cluster sampling, at first, the population is divided into several small non-overlapping subpopulations and these subpopulations are called clusters. The size of the cluster may or may not be equal. As far as possible units within the cluster should be heterogeneous i.e. one cluster could represent the population and units between the clusters should be homogeneous. Then simple random sampling is used to select some sample cluster and all the units of the selected cluster are taken as sample units. The cluster sampling method can be more cost-effective than simple random sampling method, particularly if the population is spread over a wide geographical region. However, cluster sampling methods tend to be less efficient than either simple random sampling methods or stratified sampling method and often require a larger sample size.

** **

**Advantages/merits and disadvantages/demerits of the cluster random sampling:**

**Merits: **

- If the population is heterogeneous in nature then this method is better than simple random sampling and systematic random sampling.
- This method draws the sample which is evenly spread over the entire population.
- The sample units are selected based on a probability approach so that personal bias is completely eliminated.
- Sample Statistics will be used to estimates the population parameters at a certain level of confidence.
- This method can be used if a complete and up to date frame/list is not available.

** **

**Demerits:**

- This method requires more cost and time compared to non-probability sampling.
- The clustering of the population is cumbersome.

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