Get point-wise values of psi (inverse of nu prime)
Usage
getPsi(nuPrime, conditionalPower)
Value
The value of alpha which corresponds to nuPrime and lies between 0 and conditionalPower.
Arguments
nuPrime
The function value to be inverted.
conditionalPower
The target conditional power \(CP\) of the design. Must be a numeric value.
Details
The function \(\psi\) is the inverse of:
$$\nu'(\alpha) = -2 \cdot(\Phi^{-1}(1-\alpha) + \Phi^{-1}(1-CP)) / \phi(\Phi^{-1}(1-\alpha))$$.
If the conditional power \(CP\) lies outside of the range \(1-\Phi(2) \leq CP \leq \Phi(2)\), the calculation is slightly more complicated.
The argument conditionalPower is either the fixed target conditional power or the value of the conditional power function at the corresponding first-stage p-value.