Power and Sample Size Determination When the Alternative Hypotheses are Given in Quantiles

The power of normal-theory tests about means depends on a noncentrality parameter which is a function of the unknown parameter ..In order to calculate power and to solve sample-size problems based on power, differences between hypothesized and alternative values of the means are frequently selected as a multiple of ., a choice which eliminates . from the noncentrality parameter and permits a solution.Perhaps a more natural (but equivalent) way to express alternatives is to give one or more means as the quantile of order p (say Qp ) of a distribution with another mean.As we will demonstrate, this kind of alternative also eliminates . from the problem.