Random Sampling. In this case the sample units are selected at random and the drawback of purposive sampling, viz, favoritism or subjective element, is completely overcome. A random sample is one in which each unit of population has an equal chance of being included in it.
Suppose we take a
sample of size n from a finite population of size N. Then there are N Cn possible
samples, A sampling technique in which each of the N Cn
samples has an equal chance of being selected is known as random sampling and
the sample obtained by this technique is termed as a random sample.
SIMPLE RANDOM SAMPLING
The simplest and
most common method of sampling is simple random sampling in which the sample is
drawn unit by unit, with equal probability of selection for each unit at each
draw.
Simple sampling is random sampling in which each unit of the
population has an equal chance, say p, of being included in the sample and that
this probability is independent of the previous drawings. Thus a sample
of size n from a population may be defined with a series of n independent
trials with constant probability ‘p’ of success for each trial.
Therefore, simple
random sampling is a method of selecting n units out of a population of size N
by giving equal probability to all units, or a sampling procedure in which all
possible combinations of n units that may be formed from the population of N
units have the same probability of selection. If a unit is selected and
noted and then returned to the population before the next drawing is made and
this procedure repeated n times, it gives rise to a-simple random sample of n
units. This procedure is generally known as simple random sampling with
replacement (srswr). On the other hand if sample is selected without returning
unit back to the population till sample is drawn, it is called a simple
random sampling without replacement (srswor).
PROCEDURE OF SELECTING A RANDOM SAMPLE
Some of the procedures used for selecting a random sample are as
follows;
(i) Lottery Method (ii) Use of Random
Number Tables
Lottery Method
In practice, a
ticket/chit may be associated with each unit of the population. Thus, each
sampling unit has its identification mark from 1 to N. The procedure of
selecting an individual is simple. All the tickets/ chits are placed in a
container, drum or metallic spherical device, in which a thorough mixing or
reshuffling is possible, before each draw. Draws of tickets/chits may be
continued until a sample of the required size is obtained. This procedure of
numbering units on tickets/chits and selecting one after reshuffling becomes
cumbersome when the population size is large.
Use of Random Number Tables
A random number table
is an arrangement of digits 0 to 9, in either a linear or rectangular pattern,
where each position is filled with one of these digits. A table of random
numbers is so constructed that all numbers 0, 1, 2,...,9 appear independent of
each other. Some random number tables in common use are:
(i) Tippett’s randon number
tables (ii) Fisher and Yates tables (iii) Kendall and Smith tables . (iv) A
million random digits
Example ; To select a random sample of 11 households from a list of 112
households in a village?
Ans ;033,051,052,099,102,081,092,013,017,076,079, this is
the selected sample of 11 households by using random table.
Example ; Select 10 out of 115 households?
Examples solved;
Rearrange the above table in three digit numbers as;
(first three numbers of first number,295,now match last number with next numbers two digits as ,266, 66 is first two digits of next number, also 413,is next number as 41of 6641 and 3 of ,3992, makes next number as 413, and so on
295 266 413 992
979 279 795 911
317 056 244 167
952 415 451 396
720 353 561 300
269 and so on
Example 1. Select a sample of 10 students out of 400 by using Tippett s Tables.
Solution; The number of students who will be selected on the basis of 3 digit numbers formed above and have a value upto 400 would be
295 266 279 317 056 244 167 396 353 300
Units in the universe which have been assigned these values will constitute a sample of 10 students from the universe of 400.
Universe size less than 100
If the universe size is of 2 digits only, Tippett’s numbers should be converted into two digit numbers by breaking each number into two equal parts and then a sample should be selected.
Two digit numbers taken column-wise(in the last illustration they were row-wise) would be :( to make this we have to use first 4 digit numbers as half part as 2952 ,29, 52, next 4167 as 41, 67, also 2370 as 23, 70 and so on;
29 52 41 67 23 70 05
60 27 54 66 41 95 24
74 83 52 46 91 43 and so on
Example 2. Pick up a sample of 5 students out of 50 Tippett’s table of random numbers.
Solution. The first five numbers less than 50 in 2 digit tippett’s Table numbers as pointed out above which have values upto 50 would be;
from ippett Table of Random numbers. . have values upto 50 would be :
29 23 05 27 41
Units of the universe bearing these numbers will conistutute sample.s
