Using sampling to obtain information - FMA

Sampling means taking samples from a population. Why we only take samples? This is because we don't have enough time to obtain information from the whole population. Sampling is particularly useful in auditing, but here we focus on the sampling techniques identified in FMA syllabus. I will first explain the theories, then I will provide an example for each technique using Zodiac signs. Let's take our objective as understanding the characteristics of Gemini. ;)

Random sampling
Sample will be chosen in a way that every item in the population has a chance of being selected, probably using random number table or random number generator. This is suitable when the population is known and not too big.
With our objective in mind, our population is the Gemini people. If our sample size is 20, we will generate 20 random numbers (each Gemini people is given a number) and interview the corresponding Gemini people to understand them.

Systematic sampling
The starting point is random, then sample is picked with fixed intervals. This is useful if population is logically same type but can introduce bias if population has a repetitive pattern.
In our case, again sample size is 20 and let's say we have 100 Gemini people, then our fixed interval can be determined as 5 (100/20), this means that 1 in every 5 Gemini people is chosen. Now, our random start can be from 1st to 5th Gemini people, let's say we choose 4th, then our samples will be taken as the 9th, 14th, 19th, 24th, 29th, 34th and until 99th Gemini people, total will be 20 Gemini people chosen to be interviewed.

Stratified sampling
The population will be divided into sub-populations (strata) and random samples are taken from each stratum. This technique requires prior knowledge of each item of population.
In our case, from 100 Gemini, we may categorise into "0-18 years old", "19-37 years old", "38-56 years old" and "57 years old and above". Then from each strata, we pick samples randomly to interview.

Multi-stage sampling
Population will be divided into sub-populations, and then divide again to sub-sub-populations until it is small enough, then random sample is selected from the small sub-populations. This is useful if the population is very large.
In our case, let's say our population is the Gemini people in whole Malaysia, there are too many to interview so we might only want to interview Gemini people in Selangor, but still this is too large, so we further divide into Gemini people in Subang and Klang. From here, we use random sampling technique to select Gemini people in Subang and Klang for interview.

Cluster sampling
This is similar to multi-stage sampling but at the end, all items in the small sub-populations will be selected. Again, this is useful if the population is very large.
Using the same example, we will interview all Gemini people in Subang and Klang.

Quota sampling
Investigators are told to interview all the people they meet up to a certain quota. This is very biased because they choose how to fill the quota.
In our case, we told the investigators to interview 200 Gemini people, they will decide who to interview. This is biased because if the investigator is a boy, he might interview more girls.