Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

IA idea · Statistics & hypothesis testing

Do students who sleep less react more slowly?

AI SLAI HLAA SLAA HL Accessible Also in: Health & biology, Surveys

Research question

Is there a significant correlation between hours slept the previous night and simple reaction time among students in my year group, and does the relationship hold after removing students who drank caffeine that morning?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

Sleep matters to every student, and reaction time is measurable in seconds rather than by opinion. The confounding variable (caffeine) gives you a genuine methodological decision to reflect on.

The mathematics you'll need

Scatter diagrams, Pearson's r and Spearman's rank (AI)
Linear regression and interpretation of the gradient
Hypothesis test for correlation or a t-test comparing groups (AI)
Chi-squared test of independence on categorised data (AI)
Sampling methods and bias

Modelling the data, step by step

This idea usually needs a straight-line model. See it worked step by step, with a criterion tip at every step: Straight line y = mx + c.

Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for you.

The statistics, step by step

Worked with every number shown, with what examiners look for and the common mistakes: Chi-squared test for independence · Spearman's rank correlation · t-test: two-sample and paired · Pearson's correlation and regression. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.

Where the data comes from

With consent, measure each participant's reaction time (mean of 5 trials on the same online test and device) and record self-reported sleep and caffeine; aim for 40+ students.

phyphox (RWTH Aachen) — Free app that turns your phone's accelerometer, microphone, barometer and gyroscope into data loggers with CSV export.

A possible outline

Define variables precisely (what counts as sleep, how reaction time is measured).
Justify sampling and sample size; collect data ethically.
Describe the data, then compute r and r_s; interpret both.
Test significance; split by caffeine and compare.
Reflect on self-reporting, the test device and causation.

Pitfalls that cost marks

Claiming causation from correlation.
Using different devices (screen lag varies).
Skipping the conditions for the test you use.

Showing personal engagement

Test yourself on nights of different sleep as a mini case study.
Predict the strength of the relationship before collecting.
Explain why Spearman's and Pearson's r differ in your data.

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

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Linear regression and interpretation of the gradient; Sampling methods and bias
AA HL	Fits, but add an HL technique	Linear regression and interpretation of the gradient; Sampling methods and bias
AI SL	Good fit	Scatter diagrams, Pearson's r and Spearman's rank; Linear regression and interpretation of the gradient
AI HL	Fits, but add an HL technique	Scatter diagrams, Pearson's r and Spearman's rank; Linear regression and interpretation of the gradient

Level: Accessible. A good first extended piece of maths, with room to go deeper. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: claiming causation from correlation; and using different devices (screen lag varies). Say how each one affects your answer.

Use of mathematics (E)

SL: scatter diagrams, Pearson's r and Spearman's rank; linear regression and interpretation of the gradient; hypothesis test for correlation or a t-test comparing groups; chi-squared test of independence on categorised data; sampling methods and bias, each explained in your own words and carried out correctly.

How statistics explorations reach the top bands in general: Statistics & hypothesis testing IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Fit a regression with a caffeine indicator, or use a t-test to compare reaction times of students above and below 7 hours of sleep.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL statistics exploration adds.

See a complete IA, marked

Do students who sleep less react more slowly? (AI SL) explores a question like this one, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI SL, AI HL, AA SL and AA HL. We rate it Accessible: a good first extended piece of maths, with room to go deeper.

What mathematics does this IA use?

Scatter diagrams, Pearson's r and Spearman's rank (AI), linear regression and interpretation of the gradient, hypothesis test for correlation or a t-test comparing groups (AI), chi-squared test of independence on categorised data (AI) and sampling methods and bias.

Where can I get data for this IA?

With consent, measure each participant's reaction time (mean of 5 trials on the same online test and device) and record self-reported sleep and caffeine; aim for 40+ students. Checked sources and tools: phyphox (RWTH Aachen).

Turn this idea into your IA

The planner opens with “Do students who sleep less react more slowly?” filled in: the question, the maths and the data sources.

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