17.9.2.2 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 $\delta =\frac{\left| \mu _1-\mu _2\right| }s\,\!$

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