statistik:t-test

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Zweistichproben-t-Test

Verschiedene Samplegrößen, gleiche Varianz

$$ t = \frac{\bar{X_1}-\bar{X_2}}{S_{X_1 X_2} * \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} $$

$$ S_{X_1 X_2} = \sqrt{\frac{(n_1-1)S^2_{X_1} + (n_2-1)S^2_{X_2}}{n_1+n_2-2}} $$

Verschiedene Samplegrößen, verschiedene Varianz (Welch's test)

$$ t = \frac{\bar{X_1}-\bar{X_2}}{s_{\bar{X_1}-\bar{X_2}}} $$

$$ s_{\bar{X_1}-\bar{X_2}} = \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}} $$

$$ z_0 = \frac{\bar{X_1}-\bar{X_2}}{\sqrt{\frac{o^2_1}{n_1}+\frac{o^2_2}{n_2}}} $$

$$ t = \frac{\bar{X_1}-\bar{X_2}-\omega_0}{S_{X_1 X_2} * \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} $$

Für $n_1 = n_2$ und $\omega_0 = 0$

$$ t = \frac{\bar{X_1}-\bar{X_2}}{S_{X_1 X_2} * \sqrt{\frac{2}{n}}} $$

$$ n_{res} = 2*(\frac{S_{X_1 X_2}*t}{\bar{X_1}-\bar{X_2}})^2 $$

$$ df = n_1 + n_2 - 2 $$ $$ t = t(\alpha,df) $$

n df (2n-2) t-value $n_{res}$ $\delta (n-n_{res})$
1 0 -…
kleinstes $| \delta |$
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