Random Sampling

Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling. The counterpart of this sampling is Non-probability sampling or Non-random sampling. The primary types of this sampling are simple random sampling, stratified sampling, cluster sampling, and multistage sampling. In the sampling methods, samples which are not arbitrary are typically called convenience samples.

The primary feature of probability sampling is that the choice of observations must occur in a ‘random’ way such that they do not differ in any significant way from observations not sampled. We assume here that statistical experiments contain data that is gathered through random sampling.

Type of Random Sampling

The random sampling method uses some manner of a random choice. In this method, all the suitable individuals have the possibility of choosing the sample from the whole sample space. It is a time consuming and expensive method. The advantage of using probability sampling is that it ensures the sample that should represent the population. There are four major types of this sampling method, they are;

  1. Simple Random Sampling
  2. Systematic Sampling
  3. Stratified Sampling
  4. Clustered Sampling

Now let us discuss its types one by one here.

Simple random sampling

In this sampling method, each item in the population has an equal and likely possibility of getting selected in the sample (for example, each member in a group is marked with a specific number). Since the selection of item completely depends on the possibility, therefore this method is called “Method of chance Selection”. Also, the sample size is large and the item is selected randomly, thus it is known as “Representative Sampling”.

Systematic Random Sampling

In this method, the items are chosen from the destination population by choosing the random selecting point and picking the other methods after a fixed sample period. It is equal to the ratio of the total population size and the required population size.

Stratified Random Sampling

In this sampling method, a population is divided into subgroups to obtain a simple random sample from each group and complete the sampling process (for example, number of girls in a class of 50 strength). These small groups are called strata. The small group is created based on a few features in the population. After dividing the population into smaller groups, the researcher randomly selects the sample.

Clustered Sampling

Cluster sampling is similar to stratified sampling, besides the population is divided into a large number of subgroups (for example, hundreds of thousands of strata or subgroups). After that, some of these subgroups are chosen at random and simple random samples are then gathered within these subgroups. These subgroups are known as clusters. It is basically utilised to lessen the cost of data compilation.

Random Sampling Formula

If P is the probability, n is the sample size and N is the population. Then;

  • The chance of getting a sample selected only once is given by;

P = 1 – (N-1/N).(N-2/N-1)…..(N-n/N-(n-1))

Cancelling = 1-(N-n/n)

P = n/N

  • The chance of getting a sample selected more than once is given by;

P = 1-(1-(1/N))n

Random Sampling Example

Suppose a firm has 1000 employees in which 100 of them have to be selected for onsite work. All their names will be put in a basket to pull 100 names out of those. Now, each employee has an equal chance of getting selected, so we can also easily calculate the probability (P) of a given employee being selected, since we know the sample size (n) and the population size(N).

Therefore, the chance of selection of an employee only once is;

P = n/N = 100/1000 = 10%

And the chance of selection of an employee more than once is;

P = 1-(1-(1/N))n

P = 1 – (999/1000)100

P = 0.952

P ≈ 9.5%