17.9.1.2 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

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

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