Sampling
abstract:
Sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population.
Sampling, in simple terms, means selecting a group (a sample) from a population from which we will collect data for our research. Sampling is an important aspect of a research study as the results of the study majorly depend on the sampling technique used. So, in order to get accurate results or results that can estimate the population well, the sampling technique should be chosen wisely.
introduction:
why do we need sampling is that,It is nearly impossible to collect data from (or about) each and every individual (or element) of the population. Thus, sampling helps us in attaining information about the entire population. It is obvious that the results can’t be completely accurate but the closest approximation of the population. Also, it is important that the selected group should be representative of the population and not biased in any manner.
Samples can be divided based on the following criteria.
Probability samples - In such samples, each population element has a known probability or chance of being chosen for the sample.
Non-probability samples - In such samples, one can not be assured of having a known probability of each population element.
One of the best probability sampling techniques that helps in saving time and resources, is the Simple Random Sampling method.
Random Sampling Formula:
If P is the probability, n is the sample size, and N is the population. Then:
The chance of getting a sample selected only once is given by:
P = 1 – (N-1/N).(N-2/N-1)…..(N-n/N-(n-1))
Cancelling = 1-(N-n/n)
P = n/N
The chance of getting a sample selected more than once is given by:
P = 1-(1-(1/N))n
Real time application of Random sampling:
If the population size is small or the size of the individual samples and their number are relatively small, random sampling provides the best results since all candidates have an equal chance of being chosen.
Random assignment enhances the internal validity of the study, because it ensures that there are no systematic differences between the participants in each group. This helps you conclude that the outcomes can be attributed to the independent variable
The following are the real time suitiations where Random sampling is used :
1.the names of 25 employees being chosen out of a hat from a company of 250 employees. In this case, the population is all 250 employees, and the sample is random because each employee has an equal chance of being chosen.
2.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.
3.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.
4.A pharmaceutical company wants to test the effectiveness of a new drug. Volunteers are assigned randomly to one of two groups. The first group will receive the new drug; the second group will receive a placebo.
Problems based on Random sampling:
1.Assume a firm with 1000 employees, of the 100 are needed to complete an onsite work. Now all their names are in the basket and 100 will be picked from those. Now, in this instance, every employee has an equal chance of getting selected.
solution:
The chance of one-time selection is: P = n/N = 100/1000 = 10%
And, for more than once –
P = 1-(1-(1/N))nP = 1 – (999/1000)100
P = 0.952
P ≈ 9.5%
2.I roll a fair die twice and obtain two numbers X1= result of the first roll, and X2= result of the second roll. Find the probability of the following events:
A defined as “X1<X2”;
B defined as “You observe a 6 at least once”.
solution:
the sample space S has 36 elements.
a.We have
A={(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)}.
Then, we obtain
P(A)=|A|/|S|=15/36=5/12.
We have
B={(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(1,6),(2,6),(3,6),(4,6),(5,6)}.
b.We obtain
P(B)=|B|/|S|=11/36.
conclusion:
Random sampling helps to reduce the bias involved in the sample, compared to other methods of sampling and it is considered as a fair method of sampling.
This method does not require any technical knowledge, as it is a fundamental method of collecting the data.
The data collected through this method is well informed.
It is easy to pick the smaller sample size from the existing larger population.
references:
1.Frerichs, R.R. Rapid Surveys (unpublished), © 2008
2.Vitter, Jeffrey S. (1985-03-01). “Random Sampling with a Reservoir”. ACM Trans. Math. Softw.
3.Tille, Yves; Tillé, Yves (2006-01-01). Sampling Algorithms - Springer. Springer Series in Statistics.