Getting honest answers: the randomised response technique

AA HLAI HLAA SL Ambitious Also in: Probability, Statistics

Research question

If respondents secretly flip a coin to decide whether to answer truthfully or say 'yes', can you still estimate the true proportion who would say yes, and how much bigger a sample does the privacy cost?

Adapt it: change the place, the data or the comparison until the question is yours.

Free: the A–E checklist an examiner uses, by email ↓

Why it makes a good exploration

A clever probability design that protects respondents. Working out the estimator and its variance, then comparing with a direct question, is a complete investigation.

The mathematics you'll need

Conditional probability and the law of total probability
An unbiased estimator for the true proportion (derived)
Variance of the estimator compared with direct questioning
Sample size for a given margin of error
Comparing the estimate with a direct-question group

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Use a mildly personal question approved by your teacher (for example 'Have you ever handed in homework late?'). Anonymous forms, consent and school approval.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain the method.
Derive the estimator and its variance.
Run the survey with two groups: direct and randomised.
Compare estimates and their margins of error.
Reflect on whether people trusted the method.

Pitfalls that cost marks

Questions that are truly sensitive; keep it mild and approved.
Coin tosses people can be seen doing.
Not accounting for the extra variance.

Showing personal engagement

Design the coin procedure yourself.
Predict the difference between groups.
Test a die-based variant.

See Criterion C: personal engagement for what examiners look for.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Fits — ambitious at SL	Conditional probability and the law of total probability; An unbiased estimator for the true proportion (derived)
AA HL	Good fit	Conditional probability and the law of total probability; An unbiased estimator for the true proportion (derived)
AI SL	Not a natural fit	The mathematics is mainly AA or HL (calculus or proof beyond AI SL); an AI SL version would need a data-driven, technology-based approach.
AI HL	Good fit	Conditional probability and the law of total probability; An unbiased estimator for the true proportion (derived)

Level: Ambitious. Suits confident students; expect to learn some mathematics on your own. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Personal engagement (C)

Design every part yourself: the question, the sampling frame, the wording and the analysis plan. Piloting the questionnaire and changing it is engagement an examiner can see.

Reflection (D)

Reflect on bias (who answered, who didn't, how wording steered answers) and on what a significant result can and can't show about the whole population. For this idea, start with: questions that are truly sensitive; keep it mild and approved — say how it affects your answer.

Use of mathematics (E)

SL: A sampling method justified, a sample size worked out from the test you plan, the test's conditions checked, one calculation shown and the p-value interpreted in context.

HL: Confidence intervals, a justified choice between tests, a test of a model's fit, or a statistical estimate of how much bias could change the conclusion.

Criteria A and B (presentation and communication) work the same way for every idea: see the guides to Criterion A and Criterion B.

Taking it further

Choose the probability of a forced 'yes' that balances privacy and precision.

Extending it for HL

Add confidence intervals for the proportions you report, and estimate how large a non-response bias would have to be to overturn your result.

See a complete IA, marked

Our annotated exemplar Do students who sleep less react more slowly? (AI SL) asks a different question, but shows how a complete surveys exploration is structured and marked, with an examiner's comment on every criterion. Free excerpts and the full marking table are on its page.

Before you start: the checklist an examiner uses

Every check for Criteria A–E in a 4-page PDF, the mistakes that cost the most marks and a self-assessment grid. We'll email it with a short IA tip every few days, timed to your deadline if you give it. Free — no account, no payment.

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Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Criteria checklistCheck your plan or draft against the A–E descriptors and self-grade before you hand it in. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, an IB examiner, reads your draft and talks it through with you (€100).