Comparing the efficiency of SRSWOR and SRSWR with the help of R Programming

 Kesia  Sara Koshy

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What is probability sampling?

Definition: Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.

The most critical requirement of probability sampling is that everyone in your population has a known and equal chance of getting selected. For example, if you have a population of 100 people, every person would have odds of 1 in 100 for getting selected. Probability sampling gives you the best chance to create a sample that is truly representative of the population.

Probability sampling uses statistical theory to randomly select a small group of people (sample) from an existing large population and then predict that all their responses will match the overall population.

What are the types of probability sampling?

Simple random sampling, as the name suggests, is an entirely random method of selecting the sample. This sampling method is as easy as assigning numbers to the individuals (sample) and then randomly choosing from those numbers through an automated process. Finally, the numbers that are chosen are the members that are included in the sample. 

Stratified random sampling involves a method where the researcher divides a more extensive population into smaller groups that usually don’t overlap but represent the entire population.

Random cluster sampling is a way to select participants randomly that are spread out geographically. For example, if you wanted to choose 100 participants from the entire population of the India., it is likely impossible to get a complete list of everyone. Instead, the researcher randomly selects areas (i.e., cities or counties) and randomly selects from within those boundaries.

Systematic sampling is when you choose every “nth” individual to be a part of the sample. There’s an equal opportunity for every member of a population to be selected using this sampling technique.

Applications of probability sampling

For example, an organization has 500,000 employees sitting at different geographic locations. The organization wishes to make certain amendments in its human resource policy, but before they roll out the change, they want to know if the employees will be happy with the change or not. However, it’s a tedious task to reach out to all 500,000 employees. This is where probability sampling comes handy. A sample from the larger population i.e., from 500,000 employees, is chosen. This sample will represent the population.

 

What are the steps involved in probability sampling?

Follow these steps to conduct probability sampling:

1. Choose your population of interest carefully: Carefully think and choose from the population, people you believe whose opinions should be collected and then include them in the sample. 

2. Determine a suitable sample frame: Your frame should consist of a sample from your population of interest and no one from outside to collect accurate data. 

3. Select your sample and start your survey: It can sometimes be challenging to find the right sample and determine a suitable sample frame. Even if all factors are in your favor, there still might be unforeseen issues like cost factor, quality of respondents, and quickness to respond. Getting a sample to respond to a probability survey accurately might be difficult but not impossible.

But, in most cases, drawing a probability sample will save you time, money, and a lot of frustration. 

When to use probability sampling?

Use probability sampling in these instances:

1. When you want to reduce the sampling bias: This sampling method is used when the bias has to be minimum.

2. When the population is usually diverse: Researchers use this method extensively as it helps them create samples that fully represent the population.

3. To create an accurate sample: Probability sampling help researchers create accurate samples of their population. 

 

Advantages of probability sampling

Here are the advantages of probability sampling:

1. It’s Cost-effective: This process is both cost and time effective, and a larger sample can also be chosen based on numbers assigned to the samples and then choosing random numbers from the more significant sample.

2. It’s simple and straightforward: Probability sampling is an easy way of sampling as it does not involve a complicated process. It’s quick and saves time. The time saved can thus be used to analyze the data and draw conclusions.

3. It is non-technical: This method of sampling doesn’t require any technical knowledge because of its simplicity. 

What is the difference between probability sampling and non-probability sampling?

Here’s how you differentiate probability sampling from non-probability sampling,

Probability sampling	Non-probability sampling
The samples are randomly selected.	Samples are selected on the basis of the researcher’s subjective judgment.
Everyone in the population has an equal chance of getting selected.	Not everyone has an equal chance to participate.
Researchers use this technique when they want to keep a tab on sampling bias.	Sampling bias is not a concern for the researcher.
Useful in an environment having a diverse population.	Useful in an environment that shares similar traits.
Used when the researcher wants to create accurate samples.	This method does not help in representing the population accurately.
Finding the correct audience is not simple.	Finding an audience is very simple.

 

R Analysis

print(sample(1:3))

## [1] 2 1 3

print(sample(1:3, size=3, replace=FALSE))  # same as previous line

## [1] 3 1 2

print(sample(c(2,5,3), size=4, replace=TRUE))

## [1] 3 5 3 3

print(sample(1:2, size=10, prob=c(1,3), replace=TRUE))

##  [1] 1 2 2 2 1 1 2 1 2 2

By default sample() randomly reorders the elements passed as the first argument. This means that the default size is the size of the passed array. replace=TRUE makes sure that no element occurs twice.

The last line uses a weighed random distribution instead of a uniform one. One out of four numbers are 1, the out of four are 3.

size:

This is the size of the returned list. If replace is disabled size must be no bigger than the length of the first argument.

replace:

If this is true a sample may contain an element several times while another element might not occur at all.

print(sample(c(2,5,3), size=3, replace=FALSE))

## [1] 5 2 3

print(sample(c(2,5,3), size=3, replace=TRUE))

## [1] 2 5 3

barplot(table(sample(1:3, size=1000, replace=TRUE, prob=c(.30,.60,.10))))

 

The prob=c(.30,.60,.10) cause 30% ones, 60% twos and 10% threes.

INTERPRETATION

This is a simple sampling R analysis done with certain datas. Here we have defined certain arguements and showed how they work. Also we have plotted a bargraph showing 30%, 60% and 10% porobabilities for the sample we’ve taken.

Conclusion

In conclusion the probability random sampling is more preferable because the researcher generate his data for the use of entire population by using probabilistic method to control biased during the sampling, based on evidence generated by the agencies of statistical official that the non-probability techniques is based on purpose that lead to assumption which resulting to risk. Basing on assumption means one will generate inappropriate generalization of the population.