Welch's t-test: Difference between revisions

\Beta(x,y) = \dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} =\exp(\ln\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)}) = \exp((\ln(\Gamma(x)) + \ln(\Gamma(y)) - \ln(\Gamma(x+y)))

<math> p=1-\frac{1}{2}\times\frac{\int_0^\frac{\nu}{t^2+\nu} r^{\frac{\nu}{2}-1}\,(1-r)^{-0.5}\,\mathrm{d}r}{\exp((\ln(\Gamma(x\frac{\nu}{2})) + \ln(\Gamma(y0.5)) - \ln(\Gamma(x\frac{\nu}{2}+y0.5)))} </math>

<math> p = 1-\frac{1}{2}\times\frac{\int_0^\frac{\nu}{t^2+\nu} \frac{r^{\frac{\nu}{2}-1}}{\sqrt{1-r}}\,\mathrm{d}r}{ \exp((\ln(\Gamma(x\frac{\nu}{2})) + \ln(\Gamma(y0.5)) - \ln(\Gamma(x\frac{\nu}{2}+y0.5))) }</math>