Simple Random Sampling
It
is a technique of drawing a sample in such a way that each unit of population
has an equal and independent chance of being included in the sample. In this
method, an equal probability of selection is assigned to each unit of the
population at the first draw. It also implies an equal probability of selecting
any unit from the available units at subsequent draws. There are two simple random sampling plans that
is Simple Random sampling Without Replacement (SRSWOR) and Simple Random
sampling With Replacement (SRSWR).
If
the unit selected in any draw is not replaced in the population before making
the next draw, then it is known as Simple Random sampling Without Replacement
(SRSWOR)
If
the unit selected in any draw is replaced in the population before making the
next draw, then the sampling plan is known as Simple Random sampling With
Replacement (SRSWR).
Simple Random Sampling has an important and interesting feature is that, “the probability of selecting a specified unit of population at any given draw is equal to the probability of its being selected at the first draw”. This implies that in this case from a population of size N, the probability that any sampling unit is included in the sample is 1/N and this probability remains constant throughout the drawing.
Selection methods of Simple Random Samples:
Random
sample reefers to that method of sample selection in which every item has an
equal chance of being selected. But random sample does not depend upon the
method of selection but also on the size and nature of population. Some
procedures which are simple and good for small population and is not so for
large population. In general the method of selection should be independent of
the properties of sampled population. If the selected sample should be random,
one can take proper care. Human is inherent in nature and especially is more in
sampling schemes. Hence random samples can be obtained by any one of the
following methods.
(i). Lottery Method
(ii). Mechanical randomization
or Random Numbers method.
(i). Lottery Method: It is the simplest method of
selecting random sample from the population under study. The procedure of lottery method described as:
Suppose we want to select n units out of N units.
Let
assign the numbers 1 to N (i.e., one number to one unit) to all population
units in the Universe and write these numbers on n slips, which are made as
homogeneous with respect to shape, size, colour, etc. Then, these slips are put
in a big bag and thoroughly shuffled and then n slips are drawn one by one. The
n slips units are constitute as random sample of size n.
Merit: 1. It is simplest method of drawing random samples from the Universe.
Demerit:1. If the population is sufficiently
large, then it is time consuming and cumbersome to use.
(ii).
Mechanical
randomization or Random Numbers method: It is the most practical and
inexpensive method of selecting a random sample consists in the use of Random
Number Tables. The procedure of selecting Random samples through this method
described as;
Step 1:
Identify or note N units in the population with the numbers 1 to N
Step 2:
Select at random, any page of the random number table and pickup the numbers in
any row or column or diagonal at random
Step 3:
The population units corresponding to the numbers selected in step (2) constitutes
the random sample.
Let
us consider finite units of population of size N and the requires sample size
is n. Let Yi (i=1, 2, 3, ……N) be considered as the value of the
character for the ith unit of the population and corresponding small
letters considered as the value of the character for the ith unit of
sample. Generally population parameters will be usually be denoted by either
the capital letters of the English alphabet or by Greek letters and their estimates
which are functions of the sample observation, are denoted by either small
letters or putting the symbol caps on the corresponding parameters. Thus Y hat indicates the estimate of the population mean.
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