17.9.2.2 Algorithms ((PSS) Two-Sample T-Test)
For two equal size (n) samples, the Power with degrees of freedom /math-320b62a6ef11c47ea23bbad3ca3ebbcd.png?v=0 "v = 2(n-1)")
and pooled standard deviation /math-03c7c0ace395d80182db07ae2c30f034.png?v=0 "s")
is calculated by:
- For a Greater than Alternative Hypothesis:
/math-90e72b5bba11abb5d294d2587220648a.png?v=0 "Power=Prob(t >t_{(1-\alpha ,\nu )},\nu ,\lambda )\,\!")
- For a Less than Alternative Hypothesis:
/math-f314baa848ab627af0377b75dec94180.png?v=0 "Power=Prob(t <t_{(\alpha ,\nu )},\nu ,\lambda )\,\!")
- For a Not Equal Alternative Hypothesis:
/math-d8f208a36656f1255c4485c4edf1053e.png?v=0 "Power=Prob(t >t_{(1-\alpha /2,\nu )},\nu ,\lambda )+ Prob(t <t_{(\alpha /2,\nu )},\nu ,\lambda )\,\!")
Where the noncentrality parameter:
/math-569b2398820839ab74c83de61237cfde.png?v=0 "\lambda =\delta \sqrt{n} \,\!")
and
/math-8c1c98afea981ae924673f23068851a6.png?v=0 "\delta =\frac{ \mu _\alpha -\mu _0 }s\,\!")