Rationalized Arcsine Transform

RAU calculates the rationalized arcsine transform

% RAU(X,N) transforms the number of correct responses X to the
% rationalized arcsine (rau). N gives the number of repetitions.
%
% This function allows to use ANOVA statistics with percent correct scores
% because: 1) RAUs are normally distributed; 2) mean and variance of RAUs
% are not correlated with eachother; and 3) likelihood that a score will
% increase/decrease will remain constant over the range.
%
% RAU=RAU(X,N,opt) defines one of the following options:
% 'Pc' ... X is given in percent correct scores (0..100%)
% 'X' ... X is given in the number of correct responses (default)
%
% The formula are based on Sherbecoe and Studebaker,
% Int. J. of Audiology 2004; 43; 442-448