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T test diff of mean

From OPOSSEM

<math> t = \frac{\bar{y}_2 - \bar{y}_1}{s_{\bar{y}_2-\bar{y}_1}}</math>, where <math>s_{\bar{y}_2-\bar{y}_1} = \sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}\sqrt{{\frac{1}{n_1}}+{\frac{1}{n_2}}}</math> with <math>df = n_1+n_2-2</math>