Questionnaires and interviews (AQA GCSE Statistics): Revision Notes
Pilot surveys and random response method
Pilot surveys
A pilot survey is a small-scale trial run of your questionnaire before conducting the full survey. Think of it as a "test drive" for your questions. The main purpose is to check that your questions work properly and will collect the data you actually need.
Pilot surveys help you identify potential problems early on. You can test whether respondents understand your questions correctly and whether they can answer them in ways that give you useful, valid results. This preliminary testing is usually carried out on a small portion of your total sample population rather than everyone you plan to survey.
Why Pilot Surveys Matter:
The key benefits of running a pilot survey include:
- Spotting confusing or unclear questions before it's too late
- Making sure your questionnaire will collect the specific information you need
- Identifying any technical problems with response options or format
- Ensuring your questions are appropriate for your target audience
Random response method
Sometimes people don't answer questions truthfully, especially when the questions are about sensitive or embarrassing topics. The random response method is a clever statistical technique designed to encourage honest answers by giving people a bit of privacy protection.
Here's how it works: instead of asking the sensitive question directly, you introduce a random element (like tossing a coin) that determines which question the person actually answers. This way, you as the researcher don't know which specific question each individual responded to, making people more likely to be honest.
The Key to Success: Anonymity
The random response method only works because people feel more comfortable answering honestly when they know the researcher can't identify their specific response. This privacy protection is what makes the technique effective.
How the random response method works
Let's say you want to find out how many students have been bullied. You might set up your question like this:
Example Setup:
"Toss a coin. If it lands on heads, tick 'Yes' below. If it lands on tails, answer this question truthfully: Have you ever been bullied? Yes ☐ No ☐"
Since you don't know what each person's coin showed, you can't tell who was answering the actual question versus who was just following the "tick yes if heads" instruction. This anonymity encourages truthful responses.
Worked example: calculating with the random response method
Let's work through a complete example to see how the mathematics works:
Worked Example: Student Bullying Survey
The setup: 50 students are asked the bullying question using the random response method described above.
The results: 34 students ticked "Yes"
The calculation process:
Step 1: Work out how many people would tick "Yes" just because of the coin toss
- We'd expect about half the coins to land on heads
- Expected number who tick "Yes" due to heads = out of 50
Step 2: Find how many ticked "Yes" because they were actually bullied
- Total who ticked "Yes" = 34
- Those who ticked "Yes" due to coin heads = 25
- Those who ticked "Yes" because bullied =
Step 3: Calculate the estimated proportion
- 9 out of the remaining 25 students (who got tails) were bullied
- Proportion bullied =
- This suggests about 36% of students have been bullied
Another worked example
Worked Example: Identity Deception Survey
Question: "Have you ever pretended to be someone else?" Method: Flip a coin. If heads, answer "Yes". If tails, answer truthfully. Results: 520 people answered "Yes", 480 people answered "No"
Step 1: Calculate total responses and expected coin results
- Total responses = people
- Expected "Yes" from coin heads = people
Step 2: Find truthful "Yes" responses
- Actual "Yes" responses = 520
- "Yes" due to coin = 500
- Truthful "Yes" responses =
Step 3: Calculate the proportion
- People who got tails = 500
- Truthful "Yes" among tails group = 20
- Estimated proportion =
So we estimate that 4% of people have pretended to be someone else.
Key exam tips
Essential Exam Strategy for Random Response Method:
When tackling random response method questions:
- Always identify the total sample size first - you'll need this for your calculations
- Work out the expected results from the random element - usually half for a fair coin
- Subtract to find the truthful responses - take away the random "Yes" answers
- Calculate the proportion carefully - use the number who got the "answer truthfully" option as your denominator
Remember: Always double-check your arithmetic in exam questions - these calculations involve several steps where errors can accumulate.
Key Points to Remember:
- Pilot surveys are trial runs that help you test and improve your questionnaire before the main study
- Random response method encourages honest answers to sensitive questions by using random elements like coin tosses
- The key calculation steps are: find total responses, subtract random "Yes" answers, then calculate proportion from the remaining group
- Privacy protection is what makes the random response method effective - people answer more truthfully when they feel anonymous