Stratified sampling (Edexcel GCSE Statistics): Revision Notes
Two-way tables
When conducting stratified sampling, two-way tables provide an excellent framework for organising your data and ensuring representative samples. This method allows you to treat each cell in the table as a separate stratum, making your sampling both systematic and fair.
This systematic approach ensures that every subgroup in your population gets proper representation, making your research findings more reliable and accurate.
Understanding stratified sampling with two-way tables
In stratified sampling using two-way tables, each cell becomes a distinct stratum that you need to sample from. The key principle to remember is that the proportion of each stratum in your sample must match its proportion in the total population. This ensures your sample accurately represents the population you're studying.
For example, if females aged 25+ make up 30% of your population, they should also represent 30% of your sample. This proportional representation is what makes stratified sampling so powerful for collecting reliable data.
The calculation method
To determine how many people to sample from each stratum, follow this systematic approach:
Step 1: Calculate the total population size by adding all the numbers in your two-way table.
Step 2: For each stratum (cell), find its proportion of the total population:
Step 3: Multiply each proportion by your desired total sample size:
Step 4: Round to the nearest whole number, as you cannot sample part of a person.
Worked Example: Library Usage Study
Jan wants to investigate library usage and has data showing:
- Under 25, Female: 1543 people
- Under 25, Male: 878 people
- 25 and over, Female: 5060 people
- 25 and over, Male: 3789 people
She wants a stratified sample of 120 library users.
Step 1: Find the total population
Step 2: Calculate proportions for each group
- Under 25, Female:
- 25 and over, Female:
Step 3: Calculate sample sizes
- Under 25, Female: people
- 25 and over, Female: people
Step 4: Check your total sample size matches your target (120 in this case).
The Golden Rule for Small Samples
If your calculated sample size is too small, you need to add 1 to the largest stratum. This ensures you maintain statistical validity even with smaller samples.
In our example, after rounding, we got 16 + 9 + 54 + 40 = 119 people, which is 1 short of our target of 120. Following the golden rule, we add 1 to the largest stratum (25+ females), making it 55 instead of 54.
Why this method works so well
Using two-way tables for stratified sampling produces highly representative samples because:
- Every subgroup in your population is properly represented
- The sampling maintains the same demographic balance as the original population
- It reduces sampling bias that might occur with simpler random sampling
- Your results will be more reliable and generalizable to the whole population
Benefits of This Approach
This method is particularly powerful because it eliminates the risk of accidentally over-representing or under-representing certain groups in your sample, which is a common problem with simple random sampling.
Common exam tips and traps
Always remember to:
- Calculate the total population size first
- Keep your proportions as decimals until the final step
- Round sensibly to whole numbers
- Check your final sample adds up to the target size
- Apply the golden rule when numbers don't quite match
Watch out for:
- Forgetting to add all cells to get the total population
- Rounding too early in your calculations
- Not checking that your final sample size matches what was asked for
Key Points to Remember:
- Each cell in a two-way table can be used as a stratum for sampling
- Sample proportions must match population proportions exactly
- Always calculate total population size first, then work out individual proportions
- Use the golden rule: add 1 to the largest stratum if your sample size is slightly too small
- Check your final sample size matches the target - this is a common place to lose marks in exams!