Chapter Contents |
Previous |
Next |

Sample Size and Power Calculations |

The power for the one-sample *t*-test, the paired *t*-test,
and the two-sample *t*-test is computed in the
usual fashion. That is, power is the probability of correctly
rejecting the null hypothesis when the alternative is true.
The sample size is the number per group; these calculations assume
equally sized groups. To compute the power of a *t*-test, you make
use of the noncentral *t* distribution. The formula
(O'Brien and Lohr 1984) is given by

for a one-sided alternative hypothesis and

for a two-sided alternative hypothesis where *t* is
distributed as noncentral *t*(*NC*,*v*).

- is the () quantile
of the
*t*distribution with df - is the (1-) quantile of the
*t*distribution with df - is the () quantile of the
*t*distribution with df

For one sample and paired samples,

For two samples,

Note that

The other parameters are

Chapter Contents |
Previous |
Next |
Top |

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.