X=irau(rau,N,opt)

function X=irau(rau,N,opt)

% IRAU   rationalized arcsine transform
% IRAU(RAU,N) transforms the RAU values to the number of correct responses 
% using the rationalized arcsine transform. N gives the number of repetitions.
% 
% IRAU(RAU,N,opt) defines one of the following options:
%  'Pc'  ... IRAU returns the percent correct scores (0..100%)
%  'X'   ... IRAU returns the number of correct responses (0..N, default)
%
% The formula are based on Sherbecoe and Studebaker,
% Int. J. of Audiology 2004; 43; 442-448
% 
% See also RAU.

% 30.8.2007, Piotr Majdak
%


th=(pi/146*(rau+23));
X=50*(1-(sqrt(N*(N+2)-cot(th).^2)/N).*cos(th));

if exist('opt','var')
  if strcmp(upper(opt),'PC')
    
  elseif strcmp(upper(opt),'X')
    X=X/100*N;
  else
    error('OPT must be Pc (=percent correct) or X (=number of correct responses)');
  end
else
  X=X/100*N;
end