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

IA idea · Statistics & hypothesis testing

Can statistics tell two authors apart?

AI SLAI HLAA SL Solid Also in: Art & music

Research question

Is there a significant difference between the mean sentence lengths of [two authors] in comparable texts, and can sentence and word length identify which author wrote an unattributed passage?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

Stylometry has been used to settle real authorship disputes. Using free public-domain texts, you can test whether two authors differ — and then try to identify a “mystery” passage.

The mathematics you'll need

Sampling from a text
Descriptive statistics and box plots
Two-sample t-test (AI)
Normal approximation and conditions
Chi-squared test on word-length categories

The statistics, step by step

Worked with every number shown, with what examiners look for and the common mistakes: t-test: two-sample and paired · Is my data normal? · Descriptive statistics and box plots · Sampling and collecting data. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.

Where the data comes from

Download texts from Project Gutenberg; sample random chapters and count sentence lengths with a spreadsheet or short script.

Project Gutenberg — 70,000+ free public-domain books as plain text — ideal for letter and word frequency counts.

Real data for this idea

Primary source: Project Gutenberg: Free ebooks. Download two or three books as “Plain Text UTF-8” by hand and remove the licence header before counting. Licence: Public domain in the US; download a few books by hand (the site blocks bulk robots).

Links checked October 2026; we link to the data and never copy it. More free data sets.

A possible outline

Choose authors from the same era and genre.
Design a random sampling method for sentences.
Compare distributions and test means.
Use your findings to classify a passage.
Reflect on editing, genre and definitions of a sentence.

Pitfalls that cost marks

Comparing a novel with a play.
Non-random sampling (e.g., only first chapters).
Assuming normality without checking.

Showing personal engagement

Choose authors you have read in English class.
Test your own essays against a classmate's (with permission).
Discuss real stylometry cases.

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	Sampling from a text; Descriptive statistics and box plots
AA HL	Not a natural fit	The mathematics is mainly from the AI course; at AA HL the exploration would need an AA-level approach (calculus, proof or probability theory) to reach the top of Criterion E.
AI SL	Good fit	Sampling from a text; Descriptive statistics and box plots
AI HL	Good fit	Sampling from a text; Descriptive statistics and box plots

Level: Solid. Needs some independent work beyond class examples. 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: comparing a novel with a play; and non-random sampling (e.g., only first chapters). Say how each one affects your answer.

Use of mathematics (E)

SL: sampling from a text; descriptive statistics and box plots; two-sample t-test; normal approximation and conditions; chi-squared test on word-length categories, 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

Combine several features into a simple classifier and test its accuracy on passages you hold back.

Extending it for HL

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

See a complete IA, marked

Should I lease or buy my first car? (AI SL) is a complete statistics exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI SL, AI HL and AA SL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Sampling from a text, descriptive statistics and box plots, two-sample t-test (AI), normal approximation and conditions and chi-squared test on word-length categories.

Where can I get data for this IA?

Download texts from Project Gutenberg; sample random chapters and count sentence lengths with a spreadsheet or short script. Checked sources and tools: Project Gutenberg.

Turn this idea into your IA

The planner opens with “Can statistics tell two authors apart?” filled in: the question, the maths and the data sources.

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