17.8.2.2 Algorithms ((PSS) Two-Sample T-Test)

For two equal size (n) samples, the Power with degrees of freedom v = 2(n-1) and pooled standard deviation s is calculated by:

 Power=Prob(t >t_{(1-\alpha ,\nu )},\nu ,\lambda )\,\!

for a one-sided test and

 Power=Prob(t >t_{(\alpha /2,\nu )},\nu ,\lambda )+Prob(t<t_{(1-\alpha /2,\nu )},\nu ,\lambda )\,\!

for a two-sided test.

Where the noncentrality parameter:

\lambda =\frac \delta {\sqrt{2/n}} \,\! and  \delta =\frac{\left| \mu _1-\mu _2\right| }s\,\!