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:

  • For a Greater than Alternative Hypothesis:

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


  • For a Less than Alternative Hypothesis:

Power=Prob(t <t_{(\alpha ,\nu )},\nu ,\lambda )\,\!


  • For a Not Equal Alternative Hypothesis:

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


Where the noncentrality parameter:

\lambda =\delta \sqrt{n} \,\!

and

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

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