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:

  • 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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