\begin{figure}
  % http://homework.uoregon.edu/pub/class/es202/ztest.html
  % https://en.wikipedia.org/wiki/Standard_score
  \begin{align*}
    X &\hookrightarrow \mathcal{N}(\mu_X, \sigma_X^2) \\
    Y &\hookrightarrow \mathcal{N}(\mu_Y, \sigma_Y^2) \\
    s_X &= \frac{\sigma^{2\star}_X}{n_X} \\
    s_Y &= \frac{\sigma^{2\star}_Y}{n_Y} \\
    T &= \frac{\mu^{\star}_X - \mu^{\star}_Y}{\sqrt{s_X + s_Y}} \\
    f &= \frac{(s_X + s_Y)^2}{\frac{s_X^2}{n_X-1}+\frac{s_Y^2}{n_Y-1}} \\
    \text{Si $\mu_X = \mu_Y$, alors} &\; T \hookrightarrow t(0; f)
  \end{align*}
  \caption{Calcul du t-test}
  \label{ttest}
\end{figure}
