Probability sampling is characterized by an element of chance and likelihood where every element of the population of interest has known and equal probability of being selected. But it does not mean that we know in advance which element will be selected next. In other words, no one can anticipate precisely that a particular element will be selected next. Probability sampling is considered to be the most reliable and dependable kind of sampling in the field of research. Since the element of biasness is very small or even zero in this kind of sampling. Following are the well known types of Probability Sampling.
1. Simple Random Sampling:
In simple random sampling there is an equal chance for every member of the population to be selected for the sample. When sampling in this way, we make a list of all the elements of the population of interest, then we randomly select elements from this list—Sampling Frame. Simple random sampling is used when we don’t have any prior knowledge about the distribution of the characteristic of interest across the population. Example: Random selection of 30 students from a class of 70, is an example of simple random sampling. Since there are 70 students in this class—sampling frame, wherein each student has an equal chance of being selected i.e. It’s probability of selection is 1/70.
2. Stratified Random Sampling:
In stratified random sampling we divide all the elements of the population of interest into different subgroups in such a way that they will be homogenous within groups and heterogeneous among groups. In other word all the strata will be disjoint and non-overlapping so that putting them together will make the population of interest. We then randomly select elements from each of these subgroups—strata. This kind of sampling is used when we know that the characteristic of interest is not equally distributed across the population, and its density and occurrence is different in different parts of the population of interest. It means that we should have prior knowledge about the distribution of the characteristics of interest in the population when using this type of sampling.
There are two types of stratified sampling which are given as under:
2.1 Proportional Stratified Sampling:
In proportional stratified sampling we select elements from each subgroup—stratum—according to their proportion in the population of interest. For example if we want to know public opinion about a certain national issue of a country whose population is divide into four ethnics groups as under:
Muslims = 40%
Christians = 30%
Hindus = 20%
Buddhists = 10%
Now, If we want to draw a sample of 1000 persons from the population , then, according to the proportional stratified sampling, the composition of our sample would be:
Muslims = 40/100 × 1000 = 400
Christians = 30/100 × 1000 = 300
Hindus = 20/100 × 1000 = 200
Buddhists = 10/100 × 1000 = 100
2.2. Disproportional Stratified Sampling:
In a disproportional stratified sampling we randomly select elements from the given strata not according to its ratio in the population of interest but according to our will or need.
3. Cluster Sampling:
Sometimes our population is consisted of different clusters i.e. schools, hospitals, industries etc. If we randomly select some cluster from the given population then it is called cluster sampling. Cluster sampling can be done in the following two ways:
3.1. Single Stage Cluster Sampling:
In single stage cluster sampling all the elements of a cluster are selected as a sample.
3.2. Two Stage Cluster Sampling:
In two stage cluster sampling, first we randomly select some clusters from the given population, then some elements from each cluster are randomly selected.
4. Stratified Cluster Sampling:
In order to minimize the occurrence of errors in cluster sampling, a new variety of cluster sampling has been introduced by combining stratified and cluster sampling which is called Stratified Cluster Sampling. In this kind of sampling, all the clusters having similar characteristics are stratified together and then at least one cluster is randomly selected from each stratum. After that either all or some elements of each selected cluster are sampled.
5. Systematic Sampling:
Unlike simple random sampling, in systematic sampling the selection of elements from a population— sampling frame— is not random, except the first element, but systematic. In systematic sampling we put all the elements of a population in such a sequence where every element has an equal chance of being selected. Then we divide this sequence in several groups of k elements each. In other words, to select a systematic sample of size n from a sample frame of size N, we divide N by n to get k. Then, we randomly select the first element (n1 )from the first group of k elements and then use the following rule.
k = N/n
First elements = n1
Second element = n1 + k = n2
Third element = n2 + k = n3 and so on.
Suppose N =20 and n = 5 then k = 20/5=4. Now we randomly select the first item from the integers 1 to 4. If the random number selected is 3, then our systematic sample will contain the elements 3, 3+4 = 7, 7 + 4 = 11, and so on until we have 5 elements in our sample.
k = N/n
First elements = n1
Second element = n1 + k = n2
Third element = n2 + k = n3 and so on.
Suppose N =20 and n = 5 then k = 20/5=4. Now we randomly select the first item from the integers 1 to 4. If the random number selected is 3, then our systematic sample will contain the elements 3, 3+4 = 7, 7 + 4 = 11, and so on until we have 5 elements in our sample.
6. Multi-Stage Sampling:
Multi-stage sampling is a process which involves several stages. First, the larger population is divided in different clusters, then all the clusters are divided in various groups—strata— according to their characteristics i.e. clusters with similar characteristics are grouped together. Next one or more clusters are randomly selected from each stratum. Then the selected clusters are further divided in smaller clusters. This process continues in the top down direction dividing bigger clusters into smaller clusters until they cannot be divided anymore. And finally individual unites are selected from each cluster. For example, a country is divided into different geographic areas i.e. states, cities, urban and rural. Than all the areas with identical characteristics are combined together to form one stratum. And in this way several strata are made.
