Sampling Methods (Edexcel GCSE Maths): Revision Notes

Sampling methods

When conducting statistical research, you need to collect data from a sample that accurately represents the entire population you're studying. This is where sampling methods become essential - they help ensure your sample gives you reliable results that can be applied to the whole population.

Simple random sampling

Simple random sampling is the most basic method of selecting a representative sample. In this approach, every member of the population has an equal chance of being chosen, which helps eliminate bias and ensures fairness in your selection process.

How to conduct simple random sampling

The process involves three straightforward steps that guarantee randomness in your selection:

First, you need to assign a unique number to every single member of your population. This creates a complete list where each person or item has their own identifier.

Second, generate a list of random numbers. You can do this using a computer programme, a calculator with a random number function, or even by drawing numbers from a bag. The key is that the selection process must be completely random.

Finally, match your random numbers to the corresponding members of your population. The people or items whose numbers come up in your random selection become your sample.

This method works particularly well when your population is fairly uniform and you don't need to worry about representing different subgroups within it.

Stratified sampling

Sometimes your population contains distinct groups or categories that you want to ensure are properly represented in your sample. This is where stratified sampling becomes incredibly useful.

When to use stratified sampling

Use stratified sampling when your population can be divided into groups where members share common characteristics. For example, you might have different age groups, genders, year groups in a school, or job categories in a workplace. The key is that these groups should be meaningful for your research question.

How stratified sampling works

The principle behind stratified sampling is proportional representation. Larger groups in your population should have more representatives in your sample, while smaller groups should have fewer. This ensures your sample maintains the same proportions as the original population.

To calculate how many sample members you need from each group, you use a simple formula: find the proportion of the population that belongs to each group, then multiply this proportion by your desired sample size.

The calculation follows this pattern:

$\text{Sample size from group} = \frac{\text{Number in group}}{\text{Total population}} \times \text{Sample size}$

After you've calculated how many people you need from each group, you then use simple random sampling within each group to select the actual participants.

Worked examples

Let's look at a practical example to see how these calculations work in real situations.

	Year 9	Year 10	Year 11
Boys	206	219	120
Girls	194	181	80

Consider a secondary school with students distributed across different year groups and genders. The school has specific numbers of boys and girls in Years 9, 10, and 11, and you want to create representative samples for different research purposes.

Choosing the right method

The choice between simple random sampling and stratified sampling depends on your research needs and population characteristics. Simple random sampling works well when your population is relatively uniform, while stratified sampling is essential when you need to ensure representation from different subgroups.

Both methods rely on randomness to eliminate bias, but stratified sampling gives you additional control over the composition of your sample, making it particularly valuable for research where group differences might be important.