Introduction to Sampling Techniques
In Statistics, we rarely have the time or money to ask every single person in a group for their opinion. This is where sampling comes in! Sampling is the process of selecting a small group (the sample) to represent the whole group (the population). In this chapter, we will look at different ways to choose that sample and how to make sure it is fair and accurate.
Note: This chapter focuses on how we pick people or items. To learn about how to design the actual questions or experiments, see the chapter on "Collecting data: sources, questionnaires and experiments".
Key Vocabulary
Before we look at the techniques, we need to understand three vital terms:
- Population: The entire group you are interested in (e.g., every student in your school).
- Sample: The small group you actually collect data from (e.g., 50 students from your school).
- Sampling Frame: A list of everyone in the population that you can choose from (e.g., the school register).
Non-Random Sampling (High Risk of Bias)
These methods are often quick and easy, but they carry a high risk of bias (where the results don't truly represent the population).
1. Opportunity (Convenience) Sampling
This involves picking whoever is available at the time.
Example: Standing outside a gym at 6:00 AM and asking the first 10 people you see about their exercise habits.
Risk: You only talk to people who wake up early and go to the gym, so your results won't represent the general public!
2. Judgement Sampling
The researcher uses their own "professional judgement" to pick who they think is representative.
Risk: Humans are naturally biased, even if they don't mean to be. You might accidentally pick people who look "friendly," which ruins the randomness.
Random and Systematic Sampling
These methods are much fairer because they use a clear system to avoid human bias.
3. Simple Random Sampling (SRS)
Every member of the population has an equal chance of being chosen. To do this, you need a sampling frame (a list).
Methods:
- Assigning everyone a number and using a random number generator on a calculator or computer.
- Using random number tables.
- Drawing names out of a hat.
4. Systematic Sampling
This involves picking a starting point at random and then choosing every \(n^{th}\) person.
Example: To get a sample of 20 from a list of 200, you would pick every \(10^{th}\) person (\(200 \div 20 = 10\)).
The "Periodicity" Trap: Be careful! If the list has a hidden pattern (periodicity) that matches your interval, the sample will be biased. For example, if you sample houses every \(8^{th}\) house, and every \(8^{th}\) house happens to be a large corner plot, your data won't represent the whole street.
5. Quota Sampling
In quota sampling, the researcher is told to collect data from a specific number of people in certain groups (e.g., "Find 20 men and 20 women"). Once a "quota" is full, they stop asking that group.
Advantage: You don't need a sampling frame (a list of names).
Disadvantage: It is not truly random because the researcher still chooses who to talk to on the street to fill the quota.
6. Stratified Sampling
This is a very popular method. The population is divided into groups called strata (e.g., by age, gender, or year group). The number of people picked from each group is proportional to the size of that group in the population.
How to calculate a Stratified Sample
Use this formula for each group (stratum):
\(\text{Number to sample} = \frac{\text{Number in stratum}}{\text{Total population}} \times \text{Total sample size}\)
Worked Example:
A school has 600 students: 350 are in Key Stage 3 and 250 are in Key Stage 4. You want a stratified sample of 60 students.
KS3 Sample: \(\frac{350}{600} \times 60 = 35\)
KS4 Sample: \(\frac{250}{600} \times 60 = 25\)
Check: \(35 + 25 = 60\). It adds up!
Higher Tier Note: At Higher Tier, you may be asked to stratify by more than one criterion (e.g., Age and Gender). You simply divide the population into more specific groups (e.g., KS3 Boys, KS3 Girls, KS4 Boys, KS4 Girls) and apply the same formula to each.
Higher Tier Only: Cluster Sampling
In Cluster Sampling, the population is already divided into groups that are similar to each other (clusters). Instead of picking individuals from everywhere, you pick a few whole clusters at random and survey everyone inside them.
Example: If you want to survey Year 10 students across the country, you might randomly pick 5 schools (clusters) and survey every Year 10 student in those specific schools.
Risk: If the clusters you pick aren't representative of the whole population, your results will be biased.
Quick Review: Which Method to Choose?
- Need it to be fair and you have a list? Use Simple Random or Systematic.
- Need to represent different groups fairly? Use Stratified.
- No list available but want specific groups? Use Quota.
- No time/money and just need a quick look? Use Opportunity (but beware of bias!).
Common Mistake to Avoid: In exams, students often forget that Systematic Sampling can only be used if there is no pattern in the list. Always check for "periodicity"!
Key Takeaway
The best sampling technique is usually the one that gives every member of the population a known (usually equal) chance of being selected, minimizing bias and making your conclusions more reliable.