statistik:t-test

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statistik:t-test [2012/04/22 23:55] phreazerstatistik:t-test [2014/02/11 21:49] (current) – external edit 127.0.0.1
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 ===== 2 unabhängige Stichproben ===== ===== 2 unabhängige Stichproben =====
  
-==== Verschiedene Samplegrößen, gleiche Varianz ====+==== Unbekannte Varianz ==== 
 + 
 +=== Verschiedene Samplegrößen, gleiche Varianz ===
  
 $$ t = \frac{\bar{X_1}-\bar{X_2}}{S_{X_1 X_2} *  \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} $$ $$ t = \frac{\bar{X_1}-\bar{X_2}}{S_{X_1 X_2} *  \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} $$
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-==== Verschiedene Samplegrößen, verschiedene Varianz (Welch's test) ====+=== Verschiedene Samplegrößen, verschiedene Varianz (Welch's test) ===
  
 $$ t = \frac{\bar{X_1}-\bar{X_2}}{s_{\bar{X_1}-\bar{X_2}}} $$ $$ t = \frac{\bar{X_1}-\bar{X_2}}{s_{\bar{X_1}-\bar{X_2}}} $$
  
 $$ s_{\bar{X_1}-\bar{X_2}} = \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}} $$ $$ s_{\bar{X_1}-\bar{X_2}} = \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}} $$
 +
 +==== Bekannte Varianz ====
 +
 +$$ z_0 = \frac{\bar{X_1}-\bar{X_2}}{\sqrt{\frac{o^2_1}{n_1}+\frac{o^2_2}{n_2}}} $$
 +
 +
 +==== Beispiel ====
 +
 +$$ t = \frac{\bar{X_1}-\bar{X_2}-\omega_0}{S_{X_1 X_2} *  \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} $$
 +
 +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 $| \delta |$ |
  • statistik/t-test.1335131757.txt.gz
  • Last modified: 2014/02/11 21:48
  • (external edit)