17.8.1.2 Algorithms ((PSS) One-Sample T-Test)

For given degrees of freedom  \nu =n-1\,\! and  s\,\! standard deviation , the Power for one sample t-Test 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 =\delta \sqrt{n} \,\!

and

 \delta =\frac{\left| \mu _\alpha -\mu _0\right| }s\,\!