twostone(x,y,c,alpha)

function  twostone(x,y,c,alpha)
%TWOSTONE Two-sample Student's t-test when one has only one observation. 
% This file is a two-sample Student's t-test when one of the samples has 
% only one observation.
% 
% Syntax: function twostone(x,y,alpha)
%
% Inputs:
%     x - vector data of one of the samples
%     y - one data of the other sample
% alpha - significance value (=0.05 by default)
% Output:
%    Complete table of the Student's t-test
%
% Example: From the Box 9.7 of Sokal and Rohlf (1995) two places were
% sampled and one of them has a single observation. Data are the wing
% length (mm) of the mosquito Aedes canadiensis. With a significance of 
% 0.05We are interested to test if the places are equal. Data are:
%
%                        Observation        
% Place     1        2        3        4        5
%   1      4.02     3.88     3.34     3.87     3.18
%   2      3.02
%
%   x = [4.02,3.88,3.34,3.87,3.18];
%   y = 3.02;
%
% Calling on Matlab the function: 
%    twostone(x,y,1)
%
% Answer is:
%
% ---------------------------------------------
%  Sample-sizes       t         df        P
% ---------------------------------------------
%     5  1         -1.5637       4      0.1924
% ---------------------------------------------
% With a given significance level of: 0.025
% Null-hypothesis that samples are equal is not rejected
% It was asked for a two-tail t-test
%
% Created by A. Trujillo-Ortiz, R. Hernandez-Walls and K. Barba-Rojo
%            Facultad de Ciencias Marinas
%            Universidad Autonoma de Baja California
%            Apdo. Postal 453
%            Ensenada, Baja California
%            Mexico.
%            [e-mail]
%
% Copyright. April 25, 2008.
%
% To cite this file, this would be an appropriate format:
% Trujillo-Ortiz, A., R. Hernandez-Walls and K. Barba-Rojo. (2008). twostone:
%   Two-sample Student's t-test when one has only one observation. A MATLAB file.
%   [WWW document]. URL http://www.mathworks.com/matlabcentral/fileexchange/
%   loadFile.do?objectId=19787
%
% Reference:
% Sokal, R.S. and Rohlf, F.J. (1995), Biometry. 
%      W.H. Freeman and Company:New York
%

if nargin == 3,
    alpha = 0.05; %default
end

if ~isscalar(alpha)
   error('TWOSTONE requires a scalar ALPHA value.');
end
if ~isnumeric(alpha) || isnan(alpha) || (alpha <= 0) || (alpha >= 1)
   error('TWOSTONE requires 0 < ALPHA < 1.');
end

if ~isvector(x)
    error('TWOSTONE requires a x vector rather than matrix data.');
elseif length(x)==1
    error('TWOSTONE requires a x vector rather than a scalar.');
end

if ~isscalar(y)
    error('TWOSTONE requires a y scalar value.');
end

mx = mean(x);
sx = std(x);
n = length(x); 
v = n - 1; %degrees of freedom
t = (y - mx)/(sx*sqrt((n+1)/n)); %Student's t-statistic

if c == 1;
    alpha = alpha/2; %two-sided test
else
    alpha; %one-sided test
end

P = 1-tcdf(1-alpha,v); %P-value

n = [length(x) length(y)];
fprintf('---------------------------------------------\n');
disp('Sample-sizes       t         df        P')
fprintf('---------------------------------------------\n');
fprintf('   %d  %d%16.4f%8.i%12.4f\n',n,t,v,P);
fprintf('---------------------------------------------\n');
fprintf('With a given significance level of: %.3f\n', alpha);
     
if P >= alpha;
   disp('Null-hypothesis that samples are equal is not rejected');
   disp('It was asked for a two-tail t-test'); 
else
   disp('Null-hypothesis that samples are equal is rejected');
   disp('It was asked for an one-tail t-test'); 
end

return,