t_test.m

GNU Octave is a high-level language, primarily intended for numerical computations. It provides a c

## Copyright (C) 1995, 1996, 1997  Kurt Hornik
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
## 
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details. 
## 
## You should have received a copy of the GNU General Public License
## along with this file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## usage:  [pval, t, df] = t_test (x, m [, alt])
##
## For a sample x from a normal distribution with unknown mean and
## variance, perform a t-test of the null hypothesis mean(x) == m.
## Under the null, the test statistic t follows a Student distribution
## with df = length (x) - 1 degrees of freedom.
##
## With the optional argument string alt, the alternative of interest
## can be selected.  
## If alt is "!=" or "<>", the null is tested against the two-sided
## alternative mean(x) != m.
## If alt is ">", the one-sided alternative mean(x) > m is considered,
## similarly for "<".  
## The default is the two-sided case.
##
## pval is the p-value of the test.
##  
## If no output argument is given, the p-value of the test is displayed.
  
## Author:  KH <[e-mail]>
## Description:  Student's one-sample t test 

function [pval, t, df] = t_test (x, m, alt)
  
  if ((nargin < 2) || (nargin > 3))
    usage ("[pval, t, df] = t_test (x, m [, alt])");
  endif
    
  if (! is_vector (x))
    error ("t_test:  x must be a vector.");
  endif
  if (! is_scalar (m))
    error ("t_test:  m must be a scalar.");
  endif
  
  n   = length (x);
  df  = n - 1;
  t   = sqrt (n) * (sum (x) / n - m) / std (x);
  cdf = t_cdf (t, df);
  
  if (nargin == 2)
    alt  = "!=";
  endif

  if (! isstr (alt))
    error ("t_test:  alt must be a string");
  endif
  if (strcmp (alt, "!=") || strcmp (alt, "<>"))
    pval = 2 * min (cdf, 1 - cdf);
  elseif strcmp (alt, ">")
    pval = 1 - cdf;
  elseif strcmp (alt, "<")
    pval = cdf;
  else
    error (sprintf ("t_test:  option %s not recognized", alt));
  endif

  if (nargout == 0)
    printf ("  pval:  %g\n", pval);
  endif
  
endfunction