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