Selection of samples:SRSWR vs SRSWOR(2048114)
Selection of
samples(SRSWR VS SRSWOR)
Anindita Sarkar(2048114)
INTRODUCTION-
SIMPLE RANDOM
SAMPLING(with replacement Vs without replacement) :-
The simplest of the methods of probability sampling which is
usually called the method of random sampling. In this method, an equal
probability of selection is assigned to each available units of the population
at the first and each subsequent draw. Thus, if the number of units in the
population is N, then the probability of selection of any unit at first draw is
1/N and at the second draw is 1/N-1 etc, which are ultimately equal to 1/N. The
sample obtained using the above method is called “ Simple Random Sampling”.
Since this result is independent of the specified unit it follows that every
one of the units in the population has the same chance of being included in the
sample under the procedure of simple random sampling.
Difference Between SRSWOR and SRSWR:
(i)
If the selected units are not being replaced
back in the population before the second draw, it is called SRSWOR and if the
selected units are being replaced back in the population before the second
draw, it is called SRSWR
(ii)
In SRSWOR, at each draw ,new information on the
units will be generated while it may be possible to have the same kind of
information on the units in SRSWR.
(iii) SRSWOR method will cover
the whole population units while it is not true in the case of SRSWR.
Steps in Selecting a Simple Random Sample-
1. Define the target population.
2. Identify an existing sampling
frame of the target population or develop a new one.
3. Evaluate the sampling frame for
undercoverage, overcoverage, multiple coverage, and clustering, and make
adjustments where necessary.
4. Assign a unique number to each
element in the frame.
5. Determine the sample size.
6. Randomly select the targeted number of
population elements.
Samples of size m without replacement from Sn are all possible combinations of m
distinct elements from Sn. There are nC m such samples. Samples are unordered,
that is, different orderings of the same elements are considered the same sample.
There are m! ordered samples for each unordered sample as this is the number of ways to
permute m items.
Samples of size m with replacement (WR) from Sn can have any of the
n elements in each of the m positions. The elements are not required to be
distinct. There are nm such possible samples. Note that WR samples can have the
same element in more than one position.
Real world examples
of simple random sampling include:
- At a birthday party, teams
for a game are chosen by putting everyone's name into a jar, and then
choosing the names at random for each team.
- On an assembly line, each
employee is assigned a random number using computer software. The same
software is used periodically to choose a number of one of the employees
to be observed to ensure they are employing best practices.
- A restaurant leaves a fishbowl
on the counter for diners to drop their business cards. Once a month, a
business card is pulled out to award one lucky diner with a free meal.
- At a bingo game, balls with every possible number are placed inside a mechanical cage. The caller rotates the cage, tumbling around the balls inside. Then, she selects one of the balls at random to be called, like B-12 or O-65.
SIMPLE
RANDOM SAMPLING WITH REPLACEMENT (SRSWR): SRSWR is a method of selection of
n units out of the N units one by one such that at each stage of selection,
each unit has an equal chance of being selected, i.e., 1/ N
SIMPLE
RANDOM SAMPLING WITHOUT REPLACEMENT (SRSWOR): SRSWOR is a method of
selection of n units out of the N units one by one such that at any stage of
selection, any one of the remaining units have the same chance of being
selected, i.e. 1/N .
When
drawing a sample from a population, there are many different combinations of
people that could be selected. This formula is used to derive the number of
possible samples drawn with replacement :
N^n
where N is the number in the total
population and n is the number of units being sampled.
This
Formula is used to calculated the number of possible samples that can be drawn
without replacement, disregarding order,
N!/n!(N-n)!
where N is the number of people in the
population, n is the number of sampled persons, and ! is the factorial notation
for the sequential multiplication of a number times a number minus 1,
continuing until reaching 1.
CONCLUSION—In the analysis part I have taken a
dataset and I have selected a sample of 15 units from the population using both
SRSWR and SRSWOR. When we sample with replacement, the two sample values are
independent. Practically, this means that what we get on the first one doesn't
affect what we get on the second. Mathematically, this means that the
covariance between the two is zero. In sampling without replacement, the two sample values aren't
independent.
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