Statistics & graphs · SL/HL

Two-sample t-test

Compare independent or paired samples with a t-test.

Your values

Number formats & units

Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.

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Example

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\text{Welch:}\quad t=\frac{\bar x_1-\bar x_2}{\sqrt{s_1^2/n_1+s_2^2/n_2}}

\text{paired:}\quad t=\frac{\bar d}{s_d/\sqrt n}

What the variables mean

Symbol	Meaning
$p$	Two-tailed probability under the null model.
$\mathrm{df}$	Degrees of freedom.

t = -6.845792, p = 0.0001328

Follow the example steps

Use a paired test only for meaningfully matched observations.

Before 5, 10; after 6, 12 for the same two individuals: ignore the matching.

Analyse the paired changes 1, 2.

More checks before you submit

Method notes

Choose the test design before looking at the outcome. A statistical test does not repair poor sampling, lack of independence or confounding.