rau=rau(X,N,opt)

function rau=rau(X,N,opt)

% RAU   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
%
% See also IRAU.

% 30.8.2007, Piotr Majdak
%

if exist('opt','var')
  if strcmp(upper(opt),'PC')
    X=X/100*N;
  elseif strcmp(upper(opt),'X')
  else
    error('OPT must be Pc (=percent correct) or X (=number of correct responses)');
  end
end
th=asin(sqrt(X/(N+1)))+asin(sqrt((X+1)/(N+1)));
rau=146/pi*(th)-23;