Sampling Techniques

Year 12 Mathematics: Understanding Probability & Non-Probability Sampling

Introduction

When we want to find out information about a large group (the population), it's often too expensive or time-consuming to ask everyone. Instead, we select a smaller group (a sample). How we choose that sample determines whether our results are biased or accurately represent the population.

Probability (Random) Sampling

1. Simple Random Sampling

Definition: Every member of the population has an equal and independent chance of being selected.

Requirement: Needs a complete list of the population (sampling frame).

Example: Assigning a number to all 500 students in a school and using a computer to randomly generate 50 numbers.
2. Systematic Sampling

Definition: Selecting a random starting point, then picking every k-th item/person from the list.

Warning: Can introduce bias if the list has a hidden periodic pattern.

Example: Picking a random number between 1 and 10 (e.g., 4). Then surveying the 4th, 14th, 24th, etc., person on a register.
Uses Random!
3. Stratified Sampling

Definition: The population is divided into subgroups (strata). A proportional random sample is taken from each group using Simple Random or Systematic sampling.

Benefit: Guarantees all minority groups are proportionally represented.

Example: A school is 60% boys and 40% girls. To sample 100 students, you randomly draw 60 boys from the boys' register and 40 girls from the girls' register.

Non-Probability (Non-Random)

4. Convenience Sampling

Definition: Selecting individuals who are simply easiest to reach or readily available.

Warning: Highly prone to bias. The sample is rarely representative of the whole population.

Example: A researcher stands outside a library and asks the first 20 people who walk out to fill out a survey.
Uses Convenience!
5. Quota Sampling

Definition: The population is divided into subgroups. Participants are selected using Convenience sampling until a specific quota is filled for each group.

Key Difference: Unlike Stratified, there is no random selection from a list.

Example: A researcher needs 10 men and 10 women. They stand on the street and ask whoever walks past until they reach exactly 10 of each.