\[s_p = \sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}\]
\[T=\frac{\bar{x}_1-\bar{x}_2}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}\]
\[SE = s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}\]
\[(\bar{x}_1-\bar{x}_2)\pm t^{\ast}_{df}\times SE\]
\[T=\frac{\bar{x}_{diff}}{s_{diff}/ \sqrt{n_{diff}}}\] \[\bar{x}_{diff}\pm t^{\ast}_{df}\cdot \frac{s_{diff}}{\sqrt{n_{diff}}}\] \[F=\frac{MSG}{MSE}\]