Distinguish between random sampling and stratified random sampling’. Clearly explaining the two in details. Give examples of both.

The selection procedure must guarantee this property. The selection procedures are illustrated below :

Suppose there are 40 students in a class, and we are required to select a random sample of 4. We may adopt the following procedure :

(i) Prepare 40 slips of paper of identical shapes and size.

(ii) Write the names of students on the slips (one slip for each student),

(iii) Place the prepared slips in a box and thoroughly mix them.

(iv) Finally, without looking in the box, draw four slips.

(v) The students whose names appear on the slips drawn, constitute the required random sample.

In lotteries, the tickets bought by the people are numbered. They are put in a box and mixed mechanically. Then a required number of tickets are drawn. People holding counterfoils of tickets, bearing the numbers drawn, are the winners. This method is used when the population is homogeneous.

Startified Random Sampling : The method of stratified random sampling requires that:

(i) we subdivide the whole population into a number of homogeneous strata, and

(ii) draw a fixed proportion (say 1% or 1/2% etc.) of individual units from each stratum, by the random sampling method.

This method is used when the population is not homogeneous with regard to the characteristics under investigation. The homogeneity of each stratum, with regard to the characteristics under investigation, is the essential features of this method. The strata may differ significantly from each other.