view scripts/statistics/tests/anova.m @ 17338:1c89599167a6

maint: End m-files with 1 blank line. Simplifies automated grammarchecking script. * scripts/@ftp/ascii.m, scripts/@ftp/binary.m, scripts/@ftp/cd.m, scripts/@ftp/close.m, scripts/@ftp/delete.m, scripts/@ftp/dir.m, scripts/@ftp/display.m, scripts/@ftp/ftp.m, scripts/@ftp/loadobj.m, scripts/@ftp/mget.m, scripts/@ftp/mkdir.m, scripts/@ftp/mput.m, scripts/@ftp/rename.m, scripts/@ftp/rmdir.m, scripts/@ftp/saveobj.m, scripts/audio/lin2mu.m, scripts/audio/loadaudio.m, scripts/audio/mu2lin.m, scripts/audio/record.m, scripts/audio/saveaudio.m, scripts/audio/setaudio.m, scripts/deprecated/__error_text__.m, scripts/deprecated/cut.m, scripts/deprecated/error_text.m, scripts/deprecated/isstr.m, scripts/deprecated/polyderiv.m, scripts/deprecated/studentize.m, scripts/deprecated/sylvester_matrix.m, scripts/general/bicubic.m, scripts/general/celldisp.m, scripts/general/colon.m, scripts/general/cplxpair.m, scripts/general/del2.m, scripts/general/display.m, scripts/general/isdir.m, scripts/general/isequaln.m, scripts/general/loadobj.m, scripts/general/private/__isequal__.m, scripts/general/private/__splinen__.m, scripts/general/profexplore.m, scripts/general/quadgk.m, scripts/general/randi.m, scripts/general/repmat.m, scripts/general/saveobj.m, scripts/geometry/delaunay.m, scripts/help/__unimplemented__.m, scripts/help/doc_cache_create.m, scripts/help/get_first_help_sentence.m, scripts/help/help.m, scripts/help/print_usage.m, scripts/help/private/__additional_help_message__.m, scripts/help/private/__strip_html_tags__.m, scripts/help/type.m, scripts/image/imfinfo.m, scripts/image/imformats.m, scripts/image/imread.m, scripts/image/imwrite.m, scripts/image/private/__imfinfo__.m, scripts/image/private/__imread__.m, scripts/image/private/__imwrite__.m, scripts/image/private/imageIO.m, scripts/image/private/imwrite_filename.m, scripts/image/private/ind2x.m, scripts/io/beep.m, scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m, scripts/linear-algebra/krylov.m, scripts/linear-algebra/subspace.m, scripts/miscellaneous/bug_report.m, scripts/miscellaneous/bunzip2.m, scripts/miscellaneous/cast.m, scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m, scripts/miscellaneous/dir.m, scripts/miscellaneous/dump_prefs.m, scripts/miscellaneous/error_ids.m, scripts/miscellaneous/fileattrib.m, scripts/miscellaneous/gunzip.m, scripts/miscellaneous/isdeployed.m, scripts/miscellaneous/ismac.m, scripts/miscellaneous/mex.m, scripts/miscellaneous/mexext.m, scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/movefile.m, scripts/miscellaneous/namelengthmax.m, scripts/miscellaneous/news.m, scripts/miscellaneous/pack.m, scripts/miscellaneous/perl.m, scripts/miscellaneous/private/display_info_file.m, scripts/miscellaneous/python.m, scripts/miscellaneous/rmappdata.m, scripts/miscellaneous/run.m, scripts/miscellaneous/tar.m, scripts/miscellaneous/tempname.m, scripts/miscellaneous/untar.m, scripts/miscellaneous/unzip.m, scripts/miscellaneous/what.m, scripts/miscellaneous/zip.m, scripts/optimization/fminunc.m, scripts/optimization/fsolve.m, scripts/optimization/fzero.m, scripts/optimization/glpk.m, scripts/optimization/optimget.m, scripts/optimization/optimset.m, scripts/optimization/qp.m, scripts/optimization/sqp.m, scripts/path/pathdef.m, scripts/pkg/pkg.m, scripts/pkg/private/build.m, scripts/pkg/private/describe.m, scripts/pkg/private/dirempty.m, scripts/pkg/private/get_forge_download.m, scripts/pkg/private/get_forge_pkg.m, scripts/pkg/private/get_unsatisfied_deps.m, scripts/pkg/private/install.m, scripts/pkg/private/is_architecture_dependent.m, scripts/pkg/private/list_forge_packages.m, scripts/pkg/private/rebuild.m, scripts/pkg/private/shell.m, scripts/pkg/private/uninstall.m, scripts/plot/axes.m, scripts/plot/box.m, scripts/plot/closereq.m, scripts/plot/diffuse.m, scripts/plot/ezpolar.m, scripts/plot/findfigs.m, scripts/plot/gco.m, scripts/plot/guidata.m, scripts/plot/guihandles.m, scripts/plot/hdl2struct.m, scripts/plot/linkprop.m, scripts/plot/peaks.m, scripts/plot/print.m, scripts/plot/private/__add_datasource__.m, scripts/plot/private/__axis_label__.m, scripts/plot/private/__clabel__.m, scripts/plot/private/__color_str_rgb__.m, scripts/plot/private/__contour__.m, scripts/plot/private/__default_plot_options__.m, scripts/plot/private/__errcomm__.m, scripts/plot/private/__file_filter__.m, scripts/plot/private/__fltk_file_filter__.m, scripts/plot/private/__getlegenddata__.m, scripts/plot/private/__gnuplot_open_stream__.m, scripts/plot/private/__gnuplot_print__.m, scripts/plot/private/__go_draw_axes__.m, scripts/plot/private/__interp_cube__.m, scripts/plot/private/__is_function__.m, scripts/plot/private/__line__.m, scripts/plot/private/__marching_cube__.m, scripts/plot/private/__next_line_style__.m, scripts/plot/private/__patch__.m, scripts/plot/private/__pie__.m, scripts/plot/private/__pltopt__.m, scripts/plot/private/__quiver__.m, scripts/plot/private/__scatter__.m, scripts/plot/private/__stem__.m, scripts/plot/private/__uigetdir_fltk__.m, scripts/plot/private/__uigetfile_fltk__.m, scripts/plot/private/__uiobject_split_args__.m, scripts/plot/private/__uiputfile_fltk__.m, scripts/plot/refresh.m, scripts/plot/saveas.m, scripts/plot/shg.m, scripts/plot/specular.m, scripts/plot/sphere.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m, scripts/plot/uicontextmenu.m, scripts/plot/uicontrol.m, scripts/plot/uipanel.m, scripts/plot/uipushtool.m, scripts/plot/uiresume.m, scripts/plot/uitoggletool.m, scripts/plot/uitoolbar.m, scripts/plot/uiwait.m, scripts/plot/waitforbuttonpress.m, scripts/polynomial/pchip.m, scripts/polynomial/polyeig.m, scripts/polynomial/ppval.m, scripts/prefs/addpref.m, scripts/prefs/getpref.m, scripts/prefs/ispref.m, scripts/prefs/private/loadprefs.m, scripts/prefs/private/prefsfile.m, scripts/prefs/private/saveprefs.m, scripts/prefs/setpref.m, scripts/set/private/validargs.m, scripts/set/unique.m, scripts/signal/arch_fit.m, scripts/signal/arch_rnd.m, scripts/signal/arch_test.m, scripts/signal/arma_rnd.m, scripts/signal/durbinlevinson.m, scripts/signal/fractdiff.m, scripts/signal/freqz.m, scripts/signal/freqz_plot.m, scripts/signal/hurst.m, scripts/signal/periodogram.m, scripts/signal/private/rectangle_lw.m, scripts/signal/private/rectangle_sw.m, scripts/signal/private/triangle_sw.m, scripts/signal/spectral_adf.m, scripts/signal/spectral_xdf.m, scripts/signal/stft.m, scripts/signal/synthesis.m, scripts/signal/yulewalker.m, scripts/sparse/colperm.m, scripts/sparse/eigs.m, scripts/sparse/etreeplot.m, scripts/sparse/gmres.m, scripts/sparse/private/__sprand_impl__.m, scripts/sparse/spdiags.m, scripts/sparse/sprandn.m, scripts/specfun/bessel.m, scripts/specfun/betaln.m, scripts/specfun/expint.m, scripts/special-matrix/gallery.m, scripts/startup/__finish__.m, scripts/statistics/base/qqplot.m, scripts/statistics/distributions/tcdf.m, scripts/statistics/distributions/wienrnd.m, scripts/statistics/models/logistic_regression.m, scripts/statistics/models/private/logistic_regression_derivatives.m, scripts/statistics/models/private/logistic_regression_likelihood.m, scripts/statistics/tests/anova.m, scripts/statistics/tests/bartlett_test.m, scripts/statistics/tests/chisquare_test_homogeneity.m, scripts/statistics/tests/chisquare_test_independence.m, scripts/statistics/tests/cor_test.m, scripts/statistics/tests/f_test_regression.m, scripts/statistics/tests/hotelling_test.m, scripts/statistics/tests/hotelling_test_2.m, scripts/statistics/tests/kolmogorov_smirnov_test_2.m, scripts/statistics/tests/kruskal_wallis_test.m, scripts/statistics/tests/manova.m, scripts/statistics/tests/mcnemar_test.m, scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/run_test.m, scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m, scripts/statistics/tests/t_test_regression.m, scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m, scripts/statistics/tests/welch_test.m, scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m, scripts/statistics/tests/z_test_2.m, scripts/strings/strcat.m, scripts/strings/strjoin.m, scripts/strings/strsplit.m, scripts/testfun/__have_feature__.m, scripts/testfun/__printf_assert__.m, scripts/testfun/__prog_output_assert__.m, scripts/testfun/__run_test_suite__.m, scripts/time/clock.m, scripts/time/datenum.m, scripts/ui/errordlg.m, scripts/ui/private/message_dialog.m: End m-files with 1 blank line.
author Rik <rik@octave.org>
date Wed, 28 Aug 2013 08:33:02 -0700
parents d174210ce1ec
children d63878346099
line wrap: on
line source

## Copyright (C) 1995-2012 Kurt Hornik
##
## This file is part of Octave.
##
## Octave 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 3 of the License, or (at
## your option) any later version.
##
## Octave 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 Octave; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{pval}, @var{f}, @var{df_b}, @var{df_w}] =} anova (@var{y}, @var{g})
## Perform a one-way analysis of variance (ANOVA).  The goal is to test
## whether the population means of data taken from @var{k} different
## groups are all equal.
##
## Data may be given in a single vector @var{y} with groups specified by
## a corresponding vector of group labels @var{g} (e.g., numbers from 1
## to @var{k}).  This is the general form which does not impose any
## restriction on the number of data in each group or the group labels.
##
## If @var{y} is a matrix and @var{g} is omitted, each column of @var{y}
## is treated as a group.  This form is only appropriate for balanced
## ANOVA in which the numbers of samples from each group are all equal.
##
## Under the null of constant means, the statistic @var{f} follows an F
## distribution with @var{df_b} and @var{df_w} degrees of freedom.
##
## The p-value (1 minus the CDF of this distribution at @var{f}) is
## returned in @var{pval}.
##
## If no output argument is given, the standard one-way ANOVA table is
## printed.
## @end deftypefn

## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: One-way analysis of variance (ANOVA)

function [pval, f, df_b, df_w] = anova (y, g)

  if ((nargin < 1) || (nargin > 2))
    print_usage ();
  elseif (nargin == 1)
    if (isvector (y))
      error ("anova: for 'anova (Y)', Y must not be a vector");
    endif
    [group_count, k] = size (y);
    n = group_count * k;
    group_mean = mean (y);
  else
    if (! isvector (y))
      error ("anova: for 'anova (Y, G)', Y must be a vector");
    endif
    n = length (y);
    if (! isvector (g) || (length (g) != n))
      error ("anova: G must be a vector of the same length as Y");
    endif
    s = sort (g);
    i = find (s (2 : n) > s(1 : (n-1)));
    k = length (i) + 1;
    if (k == 1)
      error ("anova: there should be at least 2 groups");
    else
      group_label = s ([1, (reshape (i, 1, k-1) + 1)]);
    endif
    for i = 1 : k;
      v = y (find (g == group_label (i)));
      group_count (i) = length (v);
      group_mean (i) = mean (v);
    endfor

  endif

  total_mean = mean (y(:));
  SSB = sum (group_count .* (group_mean - total_mean) .^ 2);
  SST = sumsq (reshape (y, n, 1) - total_mean);
  SSW = SST - SSB;
  df_b = k - 1;
  df_w = n - k;
  v_b = SSB / df_b;
  v_w = SSW / df_w;
  f = v_b / v_w;
  pval = 1 - fcdf (f, df_b, df_w);

  if (nargout == 0)
    ## This eventually needs to be done more cleanly ...
    printf ("\n");
    printf ("One-way ANOVA Table:\n");
    printf ("\n");
    printf ("Source of Variation   Sum of Squares    df  Empirical Var\n");
    printf ("*********************************************************\n");
    printf ("Between Groups       %15.4f  %4d  %13.4f\n", SSB, df_b, v_b);
    printf ("Within Groups        %15.4f  %4d  %13.4f\n", SSW, df_w, v_w);
    printf ("---------------------------------------------------------\n");
    printf ("Total                %15.4f  %4d\n", SST, n - 1);
    printf ("\n");
    printf ("Test Statistic f     %15.4f\n", f);
    printf ("p-value              %15.4f\n", pval);
    printf ("\n");
  endif

endfunction