A sampling procedure that employs some type of random selection is known as probability sampling. Any element in the population has an equal probability of being picked for inclusion in the sample. Typically, random numbers are employed to choose such sampling. As a result, unbiased population estimates may be obtained by weighting sampled units based on their chance of selection. Discuss the use of the 4 categories of probability sampling as mentioned below, accompanied by relevant examples (unbiased population estimates), and argue which sampling is the most unbiased.

 

(a) Simple random sampling; 

(b) Systematic sampling; 

(c) Stratified random sampling; and 

(d) Cluster sampling. 

Answer is Given at the explanation

Step-by-step explanation

1. Simple random sampling

In a simple random sample, every member of the population has an equal chance of being selected. Your sampling frame should include the whole population.

To conduct this type of sampling, you can use tools like random number generators or other techniques that are based entirely on chance.

Example

You want to select a simple random sample of 100 employees of Company Y. You assign a number to every employee in the company database from 1 to 1000, and use a random number generator to select 100 numbers.

2. Systematic sampling

Systematic sampling is similar to simple random sampling, but it is usually slightly easier to conduct. Every member of the population is listed with a number, but instead of randomly generating numbers, individuals are chosen at regular intervals.

Example 

All employees of the company are listed in alphabetical order. From the first 10 numbers, you randomly select a starting point: number 6. From number 6 onwards, every 10th person on the list is selected (6, 16, 26, 36, and so on), and you end up with a sample of 100 people.

If you use this technique, it is important to make sure that there is no hidden pattern in the list that might skew the sample. For example, if the HR database groups employees by the team, and team members are listed in order of seniority, there is a risk that your interval might skip over people in junior roles, resulting in a sample that is skewed towards senior employees.

3. Stratified sampling

Stratified sampling involves dividing the population into subpopulations that may differ in important ways. It allows you draw more precise conclusions by ensuring that every subgroup is properly represented in the sample.

To use this sampling method, you divide the population into subgroups (called strata) based on the relevant characteristic (e.g. gender, age range, income bracket, job role).

Based on the overall proportions of the population, you calculate how many people should be sampled from each subgroup. Then you use random or systematic sampling to select a sample from each subgroup.

Example

     The company has 800 female employees and 200 male employees. You want to ensure that the sample reflects the gender balance         of the company, so you sort the population into two strata based on gender. Then you use random sampling on each group, selecting       80 women and 20 men, which gives you a representative sample of 100 people.

4. Cluster sampling

Cluster sampling also involves dividing the population into subgroups, but each subgroup should have similar characteristics to the whole sample. Instead of sampling individuals from each subgroup, you randomly select entire subgroups.

If it is practically possible, you might include every individual from each sampled cluster. If the clusters themselves are large, you can also sample individuals from within each cluster using one of the techniques above. This is called multistage sampling.

This method is good for dealing with large and dispersed populations, but there is more risk of error in the sample, as there could be substantial differences between clusters. It's difficult to guarantee that the sampled clusters are really representative of the whole population.

Example

     The company has offices in 10 cities across the country (all with roughly the same number of employees in similar roles). You don't             have the capacity to travel to every office to collect your data, so you use random sampling to select 3 offices - these are your 

      clusters.