SIMPLE RANDOM SAMPLING

Simple Random Sampling :

 A random sample is known as a probability sample. Under this method the selection of items for a sample depends on chance. Each and every item of the population will have equal chance of being included in the sample.

 As a result, the element of personal bias is altogether avoided here. The researcher cannot exercise his discretion in the selection of sample items. It is expected that by allowing equal probability to all population units, the different characters that are present in the universe be given adequate representation to make it a probability sample. Adopting scientific rules of sample selection makes a deliberate effort. Therefore, the scope for bias is totally ruled out.

The method is formally deemed as follows: Suppose we take a sample of size n from a finite population of size N. Then there are ^NC_n samples has an equal chance of being selected is known as random sampling and the lot obtained by this technique is termed as a random sample.  It is not easy in practice to ensure true randomness in the selection of items in a sample.  However, to ensure randomness of selection one may adopt either the lottery method or consult the table of random numbers.

Method of Drawing Simple Random Sample

It has the advantage of ease of use because of the simple selection procedures and it requires only a listing of the entire population before the sample process can begin. The following methods are generally used in simple random sampling.

Lottery Method: This is a common technique adopted for selecting random samples. All the items in the universe are numbered or named on separate slips of equal size. Such slips are then folded and mixed up in a box thoroughly and shaken so that it is difficult to identify the units of universe. Then, a selection is made blindly of the number of slips that are required for the sample. This is expected to ensure randomness or equal probability to all units of the universe.

For instance, one is asked to make a random selection of 50 out of 500 students of MBA, first year class. In order to ensure randomness in the selection, first the names of the students must be written on separate slips, which are then uniformly folded. Put all the folded slips in a container and mix them thoroughly. Next, ask someone to pick 50 slips randomly one after another. Students thus selected constitute our random sample.

In the application of this method there exist two cases: 
(i) equal probability and
 (ii) varying probability. 

If one unit is selected out of 500 observations, there remain only 499 in the universe. When a second unit is selected out of 499 units of the universe, the chance of its selection is comparatively better than the earlier one. Therefore, to ensure equal chance to the entire population, a sample unit once selected is again replaced in the population. Thus, the total number of the population units remains unchanged giving equal opportunity to all units. In such cases, there is every possibility of repetition of units. This is called equal probability sampling technique or random sampling with replacement.