The Road to Convey Rational Views: December 2022

Random sampling

Random sampling is also known as probability sampling. It means a process of a sample of observations from a population. It is for generating assumptions about the population characteristics. It is classified into simple random sampling, stratified sampling, cluster sampling, and multistage sampling.

Simple Random Sampling

Each item in the population has an equal and likely possibility of getting selected in the sample. Because the sample size is large, and the item is selected randomly, it is usually called Representative Sampling.

Systematic Random Sampling

It is equal to the ratio between the total population size and the required population size. Here, the samples are selected from the destination population by choosing the random selection point and choosing others after a fixed sampling period.

Stratified Random Sampling

A population is subdivided into small groups called strata. This is for obtaining a simple random sample from each group. Therefore, the samples are randomly selected from the strata.

Clustered Sampling

Cluster sampling is similar to stratified sampling. However, here, the large population is divided into several numbers, subgroups, or strata. Then, these subdivisions are randomly choosen and then, simple random samples are gathered within these subdivisions. These subdivisions are actually called clusters.

Random Sampling

Advantages of random sampling

1. It is simple.

2. Its sample size is unrestricted.

3. It is easier.

4. If not got previous literature, we can assume p =50%, q=50%.

5. It is actually unbiased.

6. It is fair as well.

7. Chance of selection of each member of a community or group or region is equal.

Limitation/Disadvantages of random sampling

1. It is time-consuming.

2. It is less efficient if sample selection is unrestricted.

3. It is expensive.

4. Researchers sometimes are biased for calculating the numbers of sample population. For example, they can increase error values from 5% to more to reduce the sample number.

Random Sampling Formula

P= Probability

n= sample size

N= Population,

Then,

P = 1-(1-(1/N))ⁿ

Random Sampling Example

A researcher began a research on the milk productivity of the buffaloes in a village. There are 1000 buffaloes in a village. Among them, 100 individuals are essential for study of their milk productivity. What is the probability (P) of a given individual buffalo being selected.

Here, n =100, N = 1000

Chance of selection of each buffalo only once is:

P = n/N = 100/1000 = 10%

Chance of selection of each buffalo more than once is:

P = 1-(1-(1/N))ⁿ

P = 1 – (999/1000)¹⁰⁰

P = 0.952

P ≈ 9.5%

Formulae for calculating population numbers (Sample size) by using random sampling technique

Process of sample size calculation

1. Count the total population (N).

2. Determine the critical value (Z) of the normal distribution at the defined significance level (Interval) or confidence level (Interval). Critical value at 95% confidence interval = 1.96.

Confidence Level	Z-score
80%	1.28
85%	1.44
90%	1.65
95%	1.96
99%	2.58

3. Determine the sample proportion.

If p= 1%, q=100%-1%= 99%= 0.99, so, p=0.01

If p=25%, q= 100%-25%=75%=0.75, so, p=0.25

If the literature shows p values = 10%-50%, p = average of 10 % and 50%, p=30%, q=70%.

If there is no literature regarding p values, use p=50% (0.5) and q= 50% (0.5).

4. Calculate margin of error (e).

If you test at 95% confidence interval, margin of error (e) =5%=0.05, If you test at 99% confidence interval, margin of error (e) = 1%=0.01.

5. Calculate the required sample numbers (n) using the formula above.

Example: A researcher prepared a proposal of an area to do an interview survey research on ethnomedicinal knowledge of the local ethnic people. The area consists of 10,000 population. How many individuals should she consider for an interview in her research?

Here,

N=10,000

Confidence interval = 95%

Error = 5% =0.05

Z= 1.96 (at 95% confidence interval)

p=50%=0.5

q=50%=0.5

Therefore,

n= 370

Conclusion: A total of 370 individuals should be included for an interview survey research by her.

Example: A researcher proposed studying intestinal parasites of fish of a pond with 2000 fish population. Previous researches have shown that fish were positive with intestinal parasites of 5% in 2021 and 20% in 2022. Calculate how many fish should be captured randomly for the collection of gastrointestinal contents (or fecal samples).

N=2000

Confidence interval = 95%

Error = 5% =0.05

Z= 1.96 (at 95% confidence interval)

p=5%-20%=average of 5% AND 20% =12.5% =0.125

q= 87.5%= 0.875

Therefore,

Calculate yourself the value of n.

Calculating Random Sampling Size via Online

Sometimes, it is difficult to manually calculate sample size thus, there is another idea. You can calculate the size via Online. There are several Online Calculator Sites via which you can easily determine the sample size.

You can visit the following Websites for Online calculation (These are external Websites and I am not owner of these Websites):

1. Survey Tools - Random Sample Calculator (custominsight.com)

2. Sample Size Calculator

3. Sampling Distribution Calculator - Statology

4. Sample Size Calculator | Good Calculators

5. Sample Size Calculator: Understanding Sample Sizes | SurveyMonkey

6. Random Sample Generator - MathCracker.com

7. Sample Size Calculator (abs.gov.au)

8. Normal Probability Calculator for Sampling Distributions - MathCracker.com

9. FREE Sample Size Calculator + 8 Types of Sampling to Rock Your Survey (leadquizzes.com)

10. Sample Size: Simple Random Sample (stattrek.com)

11. Sample Size Calculator - Confidence Level, Confidence Interval, Sample Size, Population Size, Relevant Population - Creative Research Systems (surveysystem.com)