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there are 2 types of Sampling techniques in Statistics. They are

a) Simple Random Sampling b) Stratified Sampling

a) Simple Random Sampling:

In this technique, every datapoint/record in the sample is picked randomly. Every datapoint/record has equal chances of being selected. The selection of one datapoint into the sample will not affect the selection of any other point in the population.

b) Stratified Sampling:

In this sampling technique, if we have different groups in the population, then the sample will be selected in such a way that the count of each group in the sample is proportional to the count of those groups in the population.

I can explain both these techniques with examples.

Problem Statement: We have to estimate the average score of 1000 students in Machine Learning Examination. (Note: In universities, ML is a subject and students from different streams can choose this subject as an elective)

Out of the 1000 students, 400 are from Engineering background, 300 are from Statistics background, 200 are from Pharmacy background(Data Science is also used in Pharmacy Domain), 100 are from Business background.

Here Population = Total number of students who have appeared for ML examination = 1000

Let us pick a sample of 250 students.

So sample size = 250

a) In simple random sampling, the sample may contain either all the 250 students from Engineering background, or all the 250 from Statistics background or a combination of Engineering and Pharmacy background, or smaller subsets of each background, or students from only engineering & statistics, etc. It could be any possible combination. It also may contain the population in equal proportions

This sample with improper proportions is called BIASED SAMPLE and using this biased sample leads to biased estimates.

b) In Stratified sampling technique, the sample is picked in such a way that the all the category sizes in the sample are proportional to the sizes in the population.

In total population of 1000,

Engineering - 400 (40% of 1000)

Statistics - 300 (30% of 1000)

Pharmacy - 200 (20% of 1000)

Business - 100 (10% of 1000)

So in Stratified sampling, the sample of 250 members is selected as below.

Engineering - 100 (40% of 250)

Statistics - 75 (30% of 250)

Pharmacy - 50 (20% of 250)

Business - 25 (10% of 250)

The sample selected in Stratified sampling is an UNBIASED SAMPLE. Using an Unbiased sample leads to accurate estimates.

CONCLUSION:

1) If there are no sub-groups in the population, then it is best to go for Simple random sampling as there are no chances for the samples to be BIASED. Samples may become BIASED in Simple random sampling only when there are sub-groups in the population.

2) If there are sub-groups in the population, it is recommended to go for Stratified Sampling as the samples need to be UNBIASED.