# Probability-Based Sampling:

Sampling techniques falling under this category ensure that the sample taken is random. These techniques help in taking bias-free samples but these techniques are harder to conduct.

1) Simple Random Sampling:

In this technique, the probability of selecting any item from a population is equally likely.

Consider that we have ‘n’ items in a basket, the probability of selecting any one item is equal to 1 / n.

After picking the first item, the probability of pulling any second item from the basket is equal to 1 / (n - 1)

Similarly for selecting 3rd item from the basket, the basket has only (n-2) items left and all of them have an equal chance of getting selected which is 1 / (n - 2)

Result: What we finally get is a reliable random sample and it is representative of the whole population

Example:

Did you notice something:

Though the sample taken looks random but seems like ‘grapes’ are not at all there in the sample. Why So? This is the disadvantage of Simple Random sampling. It does not understand the categories of data. This problem has been solved by Stratified Sampling.

2) Linear Systematic Sampling:

In this technique, items are picked after a fixed interval.

To use this technique, you need to perform the below operations

• Arrange your items in a linear fashion
• Suppose we want to choose a sample of size ‘n’ from population ‘N’
• Calculate the value of ‘k' which is k = N / n
• Select one starting point between 1 and K (any random guess)
• Now pick every kth element

Let us understand the steps with the below example:

3) Stratified Sampling:

This sampling is random and it also takes care of the disadvantage of Simple Random Sampling.

A population can have data of multiple categories and it is necessary to pick random samples from each category. In Stratified Sampling, population data is divided into multiple groups according to the category and then items are picked randomly.

E.g.

• A Bank can have two types of borrowers, A (those who pay their loans) and B (those who don’t pay their loans)
• In one college, there will be Male Students and also there will be Female Students
• A company can have full time as well as part-time employees

Therefore in this technique, first we divide our population into multiple sets (sets can be 2, 3, 4 or so on, depending on the no. of categories present in the data). Once the homogeneous sets are formed, pick the items randomly from each of them.

4) Clustered Sampling:

In this technique, we form multiple clusters/groups of heterogeneous nature such that each cluster/group is representative of a whole population. Once the clusters are formed, then some of the clusters (out of all) are chosen randomly and after that, we apply one of the below technique:

i) Single Stage Cluster Sampling: wherein the randomly selected clusters are considered completely as a sample.

ii) Two-Stage Cluster Sampling: wherein the items are chosen randomly from the selected clusters.

• Homogeneous set: A set that contains items of a single category only. For e.g. A basket of apples
• Heterogeneous set: A set that contains items of multiple categories. For e.g. A basket containing different types of fruits.
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