[pspp] / src / language / stats / oneway.c

/* PSPP - a program for statistical analysis.
   Copyright (C) 1997-9, 2000, 2007, 2009, 2010 Free Software Foundation, Inc.

   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 3 of the License, 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 program.  If not, see <http://www.gnu.org/licenses/>. */

#include <config.h>

#include <data/case.h>
#include <data/casegrouper.h>
#include <data/casereader.h>

#include <math/covariance.h>
#include <math/categoricals.h>
#include <math/moments.h>
#include <gsl/gsl_matrix.h>
#include <linreg/sweep.h>

#include <libpspp/ll.h>

#include <language/lexer/lexer.h>
#include <language/lexer/variable-parser.h>
#include <language/lexer/value-parser.h>
#include <language/command.h>

#include <data/procedure.h>
#include <data/value.h>
#include <data/dictionary.h>

#include <language/dictionary/split-file.h>
#include <libpspp/hash.h>
#include <libpspp/taint.h>
#include <math/group-proc.h>
#include <math/levene.h>
#include <libpspp/misc.h>

#include <output/tab.h>

#include <gsl/gsl_cdf.h>
#include <math.h>
#include <data/format.h>

#include <libpspp/message.h>

#include "gettext.h"
#define _(msgid) gettext (msgid)

enum missing_type
  {
    MISS_LISTWISE,
    MISS_ANALYSIS,
  };

enum statistics
  {
    STATS_DESCRIPTIVES = 0x0001,
    STATS_HOMOGENEITY = 0x0002
  };

struct coeff_node
{
  struct ll ll; 
  double coeff; 
};


struct contrasts_node
{
  struct ll ll; 
  struct ll_list coefficient_list;

  bool bad_count; /* True if the number of coefficients does not equal the number of groups */
};

struct oneway_spec
{
  size_t n_vars;
  const struct variable **vars;

  const struct variable *indep_var;

  enum statistics stats;

  enum missing_type missing_type;
  enum mv_class exclude;

  /* List of contrasts */
  struct ll_list contrast_list;

  /* The weight variable */
  const struct variable *wv;
};


/* Workspace variable for each dependent variable */
struct per_var_ws
{
  struct covariance *cov;

  double sst;
  double sse;
  double ssa;

  int n_groups;

  double cc;
};

struct oneway_workspace
{
  /* The number of distinct values of the independent variable, when all
     missing values are disregarded */
  int actual_number_of_groups;

  /* A  hash table containing all the distinct values of the independent
     variable */
  struct hsh_table *group_hash;

  struct per_var_ws *vws;

  struct moments1 *totals;
  double minimum;
  double maximum;
};

/* Routines to show the output tables */
static void show_anova_table (const struct oneway_spec *, const struct oneway_workspace *);
static void show_descriptives (const struct oneway_spec *, const struct oneway_workspace *);
static void show_homogeneity (const struct oneway_spec *, const struct oneway_workspace *);

static void output_oneway (const struct oneway_spec *, struct oneway_workspace *ws);
static void run_oneway (const struct oneway_spec *cmd, struct casereader *input, const struct dataset *ds);

int
cmd_oneway (struct lexer *lexer, struct dataset *ds)
{
  const struct dictionary *dict = dataset_dict (ds);  
  struct oneway_spec oneway ;
  oneway.n_vars = 0;
  oneway.vars = NULL;
  oneway.indep_var = NULL;
  oneway.stats = 0;
  oneway.missing_type = MISS_ANALYSIS;
  oneway.exclude = MV_ANY;
  oneway.wv = dict_get_weight (dict);

  ll_init (&oneway.contrast_list);

  
  if ( lex_match (lexer, '/'))
    {
      if (!lex_force_match_id (lexer, "VARIABLES"))
        {
          goto error;
        }
      lex_match (lexer, '=');
    }

  if (!parse_variables_const (lexer, dict,
                              &oneway.vars, &oneway.n_vars,
                              PV_NO_DUPLICATE | PV_NUMERIC))
    goto error;

  lex_force_match (lexer, T_BY);

  oneway.indep_var = parse_variable_const (lexer, dict);

  while (lex_token (lexer) != '.')
    {
      lex_match (lexer, '/');

      if (lex_match_id (lexer, "STATISTICS"))
        {
          lex_match (lexer, '=');
          while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
            {
              if (lex_match_id (lexer, "DESCRIPTIVES"))
                {
                  oneway.stats |= STATS_DESCRIPTIVES;
                }
              else if (lex_match_id (lexer, "HOMOGENEITY"))
                {
                  oneway.stats |= STATS_HOMOGENEITY;
                }
              else
                {
                  lex_error (lexer, NULL);
                  goto error;
                }
            }
        }
      else if (lex_match_id (lexer, "CONTRAST"))
        {
          struct contrasts_node *cl = xzalloc (sizeof *cl);

          struct ll_list *coefficient_list = &cl->coefficient_list;
          lex_match (lexer, '=');

          ll_init (coefficient_list);

          while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
            {
              if ( lex_is_number (lexer))
                {
                  struct coeff_node *cc = xmalloc (sizeof *cc);
                  cc->coeff = lex_number (lexer);

                  ll_push_tail (coefficient_list, &cc->ll);
                  lex_get (lexer);
                }
              else
                {
                  lex_error (lexer, NULL);
                  goto error;
                }
            }

          ll_push_tail (&oneway.contrast_list, &cl->ll);
        }
      else if (lex_match_id (lexer, "MISSING"))
        {
          lex_match (lexer, '=');
          while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
            {
              if (lex_match_id (lexer, "INCLUDE"))
                {
                  oneway.exclude = MV_SYSTEM;
                }
              else if (lex_match_id (lexer, "EXCLUDE"))
                {
                  oneway.exclude = MV_ANY;
                }
              else if (lex_match_id (lexer, "LISTWISE"))
                {
                  oneway.missing_type = MISS_LISTWISE;
                }
              else if (lex_match_id (lexer, "ANALYSIS"))
                {
                  oneway.missing_type = MISS_ANALYSIS;
                }
              else
                {
                  lex_error (lexer, NULL);
                  goto error;
                }
            }
        }
      else
        {
          lex_error (lexer, NULL);
          goto error;
        }
    }


  {
    struct casegrouper *grouper;
    struct casereader *group;
    bool ok;



    grouper = casegrouper_create_splits (proc_open (ds), dict);
    while (casegrouper_get_next_group (grouper, &group))
      run_oneway (&oneway, group, ds);
    ok = casegrouper_destroy (grouper);
    ok = proc_commit (ds) && ok;
  }

  free (oneway.vars);
  return CMD_SUCCESS;

 error:
  free (oneway.vars);
  return CMD_FAILURE;
}


\f

static int
compare_double_3way (const void *a_, const void *b_, const void *aux UNUSED)
{
  const double *a = a_;
  const double *b = b_;
  return *a < *b ? -1 : *a > *b;
}

static unsigned
do_hash_double (const void *value_, const void *aux UNUSED)
{
  const double *value = value_;
  return hash_double (*value, 0);
}

static void
free_double (void *value_, const void *aux UNUSED)
{
  double *value = value_;
  free (value);
}



static void postcalc (const struct oneway_spec *cmd);
static void  precalc (const struct oneway_spec *cmd);

struct descriptive_data
{
  struct moments1 *mom;
  double minimum;
  double maximum;
};

static void *
makeit (void)
{
  struct descriptive_data *dd = xmalloc (sizeof *dd);
  dd->mom = moments1_create (MOMENT_VARIANCE);
  dd->minimum = DBL_MAX;
  dd->maximum = -DBL_MAX;

  return dd;
}

static void 
updateit (void *user_data, const struct variable *wv, 
          const struct variable *catvar, const struct ccase *c, void *aux)
{
  const union value *val = case_data_idx (c, 0);
  struct descriptive_data *dd = user_data;
  struct oneway_workspace *ws = aux;

  double weight = 1.0;
  if (wv)
    weight = case_data (c, wv)->f;

  moments1_add (dd->mom, val->f, weight);
  moments1_add (ws->totals, val->f, weight);

  if (val->f * weight < dd->minimum)
    dd->minimum = val->f * weight;

  if (val->f * weight > dd->maximum)
    dd->maximum = val->f * weight;


  if (val->f * weight < ws->minimum)
    ws->minimum = val->f * weight;

  if (val->f * weight > ws->maximum)
    ws->maximum = val->f * weight;
}

static void
run_oneway (const struct oneway_spec *cmd,
            struct casereader *input,
            const struct dataset *ds)
{
  int v;
  struct taint *taint;
  struct dictionary *dict = dataset_dict (ds);
  struct casereader *reader;
  struct ccase *c;

  struct oneway_workspace ws;

  ws.vws = xmalloc (cmd->n_vars * sizeof (*ws.vws));

  ws.totals = moments1_create (MOMENT_VARIANCE);
  ws.minimum = DBL_MAX;
  ws.maximum = -DBL_MAX;


  for (v = 0; v < cmd->n_vars; ++v)
    {
      struct categoricals *cats = categoricals_create (&cmd->indep_var, 1,
                                                       cmd->wv, cmd->exclude, 
                                                       makeit,
                                                       updateit, &ws);

      ws.vws[v].cov = covariance_2pass_create (1, &cmd->vars[v],
                                               cats, 
                                               cmd->wv, cmd->exclude);
      ws.vws[v].cc = 0;
    }

  c = casereader_peek (input, 0);
  if (c == NULL)
    {
      casereader_destroy (input);
      return;
    }
  output_split_file_values (ds, c);
  case_unref (c);

  taint = taint_clone (casereader_get_taint (input));

  ws.group_hash = hsh_create (4,
                                  compare_double_3way,
                                  do_hash_double,
                                  free_double,
                                  cmd->indep_var);

  precalc (cmd);

  input = casereader_create_filter_missing (input, &cmd->indep_var, 1,
                                            cmd->exclude, NULL, NULL);
  if (cmd->missing_type == MISS_LISTWISE)
    input = casereader_create_filter_missing (input, cmd->vars, cmd->n_vars,
                                              cmd->exclude, NULL, NULL);
  input = casereader_create_filter_weight (input, dict, NULL, NULL);

  reader = casereader_clone (input);

  for (; (c = casereader_read (reader)) != NULL; case_unref (c))
    {
      size_t i;

      const double weight = dict_get_case_weight (dict, c, NULL);

      const union value *indep_val = case_data (c, cmd->indep_var);
      void **p = hsh_probe (ws.group_hash, &indep_val->f);
      if (*p == NULL)
        {
          double *value = *p = xmalloc (sizeof *value);
          *value = indep_val->f;
        }

      for (i = 0; i < cmd->n_vars; ++i)
        {
          {
            struct per_var_ws *pvw = &ws.vws[i];

            pvw->cc += weight;
            covariance_accumulate_pass1 (pvw->cov, c);
          }

          const struct variable *v = cmd->vars[i];

          const union value *val = case_data (c, v);

          struct group_proc *gp = group_proc_get (cmd->vars[i]);
          struct hsh_table *group_hash = gp->group_hash;

          struct group_statistics *gs;

          gs = hsh_find (group_hash, indep_val );

          if ( ! gs )
            {
              gs = xmalloc (sizeof *gs);
              gs->id = *indep_val;
              gs->sum = 0;
              gs->n = 0;
              gs->ssq = 0;
              gs->sum_diff = 0;
              gs->minimum = DBL_MAX;
              gs->maximum = -DBL_MAX;

              hsh_insert ( group_hash, gs );
            }

          if (!var_is_value_missing (v, val, cmd->exclude))
            {
              struct group_statistics *totals = &gp->ugs;

              totals->n += weight;
              totals->sum += weight * val->f;
              totals->ssq += weight * pow2 (val->f);

              if ( val->f * weight  < totals->minimum )
                totals->minimum = val->f * weight;

              if ( val->f * weight  > totals->maximum )
                totals->maximum = val->f * weight;

              gs->n += weight;
              gs->sum += weight * val->f;
              gs->ssq += weight * pow2 (val->f);

              if ( val->f * weight  < gs->minimum )
                gs->minimum = val->f * weight;

              if ( val->f * weight  > gs->maximum )
                gs->maximum = val->f * weight;
            }

          gp->n_groups = hsh_count (group_hash );
        }

    }
  casereader_destroy (reader);
  reader = casereader_clone (input);
  for ( ; (c = casereader_read (reader) ); case_unref (c))
    {
      int i;
      for (i = 0; i < cmd->n_vars; ++i)
        {
          struct per_var_ws *pvw = &ws.vws[i];
          covariance_accumulate_pass2 (pvw->cov, c);
        }
    }
  casereader_destroy (reader);

  for (v = 0; v < cmd->n_vars; ++v)
    {
      struct per_var_ws *pvw = &ws.vws[v];
      gsl_matrix *cm = covariance_calculate_unnormalized (pvw->cov);
      const struct categoricals *cats = covariance_get_categoricals (pvw->cov);

      pvw->sst = gsl_matrix_get (cm, 0, 0);

      reg_sweep (cm, 0);

      pvw->sse = gsl_matrix_get (cm, 0, 0);

      pvw->ssa = pvw->sst - pvw->sse;

      pvw->n_groups = categoricals_total (cats);
    }

  postcalc (cmd);

  for (v = 0; v < cmd->n_vars; ++v)
    {
      struct categoricals *cats = covariance_get_categoricals (ws.vws[v].cov);

      categoricals_done (cats);
    }

  if ( cmd->stats & STATS_HOMOGENEITY )
    levene (dict, casereader_clone (input), cmd->indep_var,
            cmd->n_vars, cmd->vars, cmd->exclude);

  casereader_destroy (input);

  ws.actual_number_of_groups = hsh_count (ws.group_hash);

  if (!taint_has_tainted_successor (taint))
    output_oneway (cmd, &ws);

  taint_destroy (taint);
}

/* Pre calculations */
static void
precalc (const struct oneway_spec *cmd)
{
  size_t i = 0;

  for (i = 0; i < cmd->n_vars; ++i)
    {
      struct group_proc *gp = group_proc_get (cmd->vars[i]);
      struct group_statistics *totals = &gp->ugs;

      /* Create a hash for each of the dependent variables.
         The hash contains a group_statistics structure,
         and is keyed by value of the independent variable */

      gp->group_hash = hsh_create (4, compare_group, hash_group,
                                   (hsh_free_func *) free_group,
                                   cmd->indep_var);

      totals->sum = 0;
      totals->n = 0;
      totals->ssq = 0;
      totals->sum_diff = 0;
      totals->maximum = -DBL_MAX;
      totals->minimum = DBL_MAX;
    }
}

/* Post calculations for the ONEWAY command */
static void
postcalc (const struct oneway_spec *cmd)
{
  size_t i = 0;

  for (i = 0; i < cmd->n_vars; ++i)
    {
      struct group_proc *gp = group_proc_get (cmd->vars[i]);
      struct hsh_table *group_hash = gp->group_hash;
      struct group_statistics *totals = &gp->ugs;

      struct hsh_iterator g;
      struct group_statistics *gs;

      for (gs =  hsh_first (group_hash, &g);
           gs != 0;
           gs = hsh_next (group_hash, &g))
        {
          gs->mean = gs->sum / gs->n;
          gs->s_std_dev = sqrt (gs->ssq / gs->n - pow2 (gs->mean));

          gs->std_dev = sqrt (
                              gs->n / (gs->n - 1) *
                              ( gs->ssq / gs->n - pow2 (gs->mean))
                              );

          gs->se_mean = gs->std_dev / sqrt (gs->n);
          gs->mean_diff = gs->sum_diff / gs->n;
        }

      totals->mean = totals->sum / totals->n;
      totals->std_dev = sqrt (
                              totals->n / (totals->n - 1) *
                              (totals->ssq / totals->n - pow2 (totals->mean))
                              );

      totals->se_mean = totals->std_dev / sqrt (totals->n);
    }
}

static void show_contrast_coeffs (const struct oneway_spec *cmd, const struct oneway_workspace *ws);
static void show_contrast_tests (const struct oneway_spec *cmd, const struct oneway_workspace *ws);

static void
output_oneway (const struct oneway_spec *cmd, struct oneway_workspace *ws)
{
  size_t i = 0;

  /* Check the sanity of the given contrast values */
  struct contrasts_node *coeff_list  = NULL;
  ll_for_each (coeff_list, struct contrasts_node, ll, &cmd->contrast_list)
    {
      struct coeff_node *cn = NULL;
      double sum = 0;
      struct ll_list *cl = &coeff_list->coefficient_list;
      ++i;

      if (ll_count (cl) != ws->actual_number_of_groups)
        {
          msg (SW,
               _("Number of contrast coefficients must equal the number of groups"));
          coeff_list->bad_count = true;
          continue;
        }

      ll_for_each (cn, struct coeff_node, ll, cl)
        sum += cn->coeff;

      if ( sum != 0.0 )
        msg (SW, _("Coefficients for contrast %zu do not total zero"), i);
    }

  if (cmd->stats & STATS_DESCRIPTIVES)
    show_descriptives (cmd, ws);

  if (cmd->stats & STATS_HOMOGENEITY)
    show_homogeneity (cmd, ws);

  show_anova_table (cmd, ws);


  if (ll_count (&cmd->contrast_list) > 0)
    {
      show_contrast_coeffs (cmd, ws);
      show_contrast_tests (cmd, ws);
    }


  /* Clean up */
  for (i = 0; i < cmd->n_vars; ++i )
    {
      struct hsh_table *group_hash = group_proc_get (cmd->vars[i])->group_hash;

      hsh_destroy (group_hash);
    }

  hsh_destroy (ws->group_hash);
}


/* Show the ANOVA table */
static void
show_anova_table (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
{
  size_t i;
  int n_cols =7;
  size_t n_rows = cmd->n_vars * 3 + 1;

  struct tab_table *t = tab_create (n_cols, n_rows);

  tab_headers (t, 2, 0, 1, 0);

  tab_box (t,
           TAL_2, TAL_2,
           -1, TAL_1,
           0, 0,
           n_cols - 1, n_rows - 1);

  tab_hline (t, TAL_2, 0, n_cols - 1, 1 );
  tab_vline (t, TAL_2, 2, 0, n_rows - 1);
  tab_vline (t, TAL_0, 1, 0, 0);

  tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Sum of Squares"));
  tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df"));
  tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Mean Square"));
  tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("F"));
  tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));


  for (i = 0; i < cmd->n_vars; ++i)
    {
      const struct per_var_ws *pvw = &ws->vws[i];
      struct group_proc *gp = group_proc_get (cmd->vars[i]);
      const double df1 = pvw->n_groups - 1;
      const double df2 = pvw->cc - pvw->n_groups;
      const double msa = pvw->ssa / df1;

      const char *s = var_to_string (cmd->vars[i]);

      tab_text (t, 0, i * 3 + 1, TAB_LEFT | TAT_TITLE, s);
      tab_text (t, 1, i * 3 + 1, TAB_LEFT | TAT_TITLE, _("Between Groups"));
      tab_text (t, 1, i * 3 + 2, TAB_LEFT | TAT_TITLE, _("Within Groups"));
      tab_text (t, 1, i * 3 + 3, TAB_LEFT | TAT_TITLE, _("Total"));

      if (i > 0)
        tab_hline (t, TAL_1, 0, n_cols - 1, i * 3 + 1);


      gp->mse  = (pvw->sst - pvw->ssa) / df2;

      /* Sums of Squares */
      tab_double (t, 2, i * 3 + 1, 0, pvw->ssa, NULL);
      tab_double (t, 2, i * 3 + 3, 0, pvw->sst, NULL);
      tab_double (t, 2, i * 3 + 2, 0, pvw->sse, NULL);


      /* Degrees of freedom */
      tab_fixed (t, 3, i * 3 + 1, 0, df1, 4, 0);
      tab_fixed (t, 3, i * 3 + 2, 0, df2, 4, 0);
      tab_fixed (t, 3, i * 3 + 3, 0, pvw->cc - 1, 4, 0);

      /* Mean Squares */
      tab_double (t, 4, i * 3 + 1, TAB_RIGHT, msa, NULL);
      tab_double (t, 4, i * 3 + 2, TAB_RIGHT, gp->mse, NULL);

      {
        const double F = msa / gp->mse ;

        /* The F value */
        tab_double (t, 5, i * 3 + 1, 0,  F, NULL);

        /* The significance */
        tab_double (t, 6, i * 3 + 1, 0, gsl_cdf_fdist_Q (F, df1, df2), NULL);
      }
    }

  tab_title (t, _("ANOVA"));
  tab_submit (t);
}


/* Show the descriptives table */
static void
show_descriptives (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
{
  size_t v;
  int n_cols = 10;
  struct tab_table *t;
  int row;

  const double confidence = 0.95;
  const double q = (1.0 - confidence) / 2.0;

  const struct fmt_spec *wfmt = cmd->wv ? var_get_print_format (cmd->wv) : &F_8_0;

  int n_rows = 2;

  for (v = 0; v < cmd->n_vars; ++v)
    n_rows += ws->actual_number_of_groups + 1;

  t = tab_create (n_cols, n_rows);
  tab_headers (t, 2, 0, 2, 0);

  /* Put a frame around the entire box, and vertical lines inside */
  tab_box (t,
           TAL_2, TAL_2,
           -1, TAL_1,
           0, 0,
           n_cols - 1, n_rows - 1);

  /* Underline headers */
  tab_hline (t, TAL_2, 0, n_cols - 1, 2);
  tab_vline (t, TAL_2, 2, 0, n_rows - 1);

  tab_text (t, 2, 1, TAB_CENTER | TAT_TITLE, _("N"));
  tab_text (t, 3, 1, TAB_CENTER | TAT_TITLE, _("Mean"));
  tab_text (t, 4, 1, TAB_CENTER | TAT_TITLE, _("Std. Deviation"));
  tab_text (t, 5, 1, TAB_CENTER | TAT_TITLE, _("Std. Error"));


  tab_vline (t, TAL_0, 7, 0, 0);
  tab_hline (t, TAL_1, 6, 7, 1);
  tab_joint_text_format (t, 6, 0, 7, 0, TAB_CENTER | TAT_TITLE,
                         _("%g%% Confidence Interval for Mean"),
                         confidence*100.0);

  tab_text (t, 6, 1, TAB_CENTER | TAT_TITLE, _("Lower Bound"));
  tab_text (t, 7, 1, TAB_CENTER | TAT_TITLE, _("Upper Bound"));

  tab_text (t, 8, 1, TAB_CENTER | TAT_TITLE, _("Minimum"));
  tab_text (t, 9, 1, TAB_CENTER | TAT_TITLE, _("Maximum"));

  tab_title (t, _("Descriptives"));

  row = 2;
  for (v = 0; v < cmd->n_vars; ++v)
    {
      const char *s = var_to_string (cmd->vars[v]);
      const struct fmt_spec *fmt = var_get_print_format (cmd->vars[v]);

      int count = 0;

      struct per_var_ws *pvw = &ws->vws[v];
      const struct categoricals *cats = covariance_get_categoricals (pvw->cov);

      tab_text (t, 0, row, TAB_LEFT | TAT_TITLE, s);
      if ( v > 0)
        tab_hline (t, TAL_1, 0, n_cols - 1, row);

      for (count = 0; count < categoricals_total (cats); ++count)
        {
          double T;
          double n, mean, variance;

          const union value *gval = categoricals_get_value_by_subscript (cats, count);
          const struct descriptive_data *dd = categoricals_get_user_data_by_subscript (cats, count);

          moments1_calculate (dd->mom, &n, &mean, &variance, NULL, NULL);

          double std_dev = sqrt (variance);
          double std_error = std_dev / sqrt (n) ;

          struct string vstr;

          ds_init_empty (&vstr);

          var_append_value_name (cmd->indep_var, gval, &vstr);

          tab_text (t, 1, row + count,
                    TAB_LEFT | TAT_TITLE,
                    ds_cstr (&vstr));

          ds_destroy (&vstr);

          /* Now fill in the numbers ... */

          tab_fixed (t, 2, row + count, 0, n, 8, 0);

          tab_double (t, 3, row + count, 0, mean, NULL);

          tab_double (t, 4, row + count, 0, std_dev, NULL);


          tab_double (t, 5, row + count, 0, std_error, NULL);

          /* Now the confidence interval */

          T = gsl_cdf_tdist_Qinv (q, n - 1);

          tab_double (t, 6, row + count, 0,
                      mean - T * std_error, NULL);

          tab_double (t, 7, row + count, 0,
                      mean + T * std_error, NULL);

          /* Min and Max */

          tab_double (t, 8, row + count, 0,  dd->minimum, fmt);
          tab_double (t, 9, row + count, 0,  dd->maximum, fmt);
        }

      {
        double T;
        double n, mean, variance;

        moments1_calculate (ws->totals, &n, &mean, &variance, NULL, NULL);

        double std_dev = sqrt (variance);
        double std_error = std_dev / sqrt (n) ;

        tab_text (t, 1, row + count,
                  TAB_LEFT | TAT_TITLE, _("Total"));

        tab_double (t, 2, row + count, 0, n, wfmt);

        tab_double (t, 3, row + count, 0, mean, NULL);

        tab_double (t, 4, row + count, 0, std_dev, NULL);

        tab_double (t, 5, row + count, 0, std_error, NULL);

        /* Now the confidence interval */

        T = gsl_cdf_tdist_Qinv (q, n - 1);

        tab_double (t, 6, row + count, 0,
                    mean - T * std_error, NULL);

        tab_double (t, 7, row + count, 0,
                    mean + T * std_error, NULL);

        /* Min and Max */

        tab_double (t, 8, row + count, 0,  ws->minimum, fmt);
        tab_double (t, 9, row + count, 0,  ws->maximum, fmt);
      }

      row += categoricals_total (cats) + 1;
    }

  tab_submit (t);
}

/* Show the homogeneity table */
static void
show_homogeneity (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
{
  size_t v;
  int n_cols = 5;
  size_t n_rows = cmd->n_vars + 1;

  struct tab_table *t = tab_create (n_cols, n_rows);
  tab_headers (t, 1, 0, 1, 0);

  /* Put a frame around the entire box, and vertical lines inside */
  tab_box (t,
           TAL_2, TAL_2,
           -1, TAL_1,
           0, 0,
           n_cols - 1, n_rows - 1);


  tab_hline (t, TAL_2, 0, n_cols - 1, 1);
  tab_vline (t, TAL_2, 1, 0, n_rows - 1);

  tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("Levene Statistic"));
  tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("df1"));
  tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df2"));
  tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Significance"));

  tab_title (t, _("Test of Homogeneity of Variances"));

  for (v = 0; v < cmd->n_vars; ++v)
    {
      const struct per_var_ws *pvw = &ws->vws[v];
      const struct categoricals *cats = covariance_get_categoricals (pvw->cov);

      const struct variable *var = cmd->vars[v];
      const struct group_proc *gp = group_proc_get (cmd->vars[v]);
      const char *s = var_to_string (var);

      const double df1 = pvw->n_groups - 1;
      const double df2 = pvw->cc - pvw->n_groups;
      double F = gp->levene;

      tab_text (t, 0, v + 1, TAB_LEFT | TAT_TITLE, s);


      tab_double (t, 1, v + 1, TAB_RIGHT, F, NULL);
      tab_fixed (t, 2, v + 1, TAB_RIGHT, df1, 8, 0);
      tab_fixed (t, 3, v + 1, TAB_RIGHT, df2, 8, 0);

      /* Now the significance */
      tab_double (t, 4, v + 1, TAB_RIGHT, gsl_cdf_fdist_Q (F, df1, df2), NULL);
    }

  tab_submit (t);
}


/* Show the contrast coefficients table */
static void
show_contrast_coeffs (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
{
  int c_num = 0;
  struct ll *cli;

  int n_contrasts = ll_count (&cmd->contrast_list);
  int n_cols = 2 + ws->actual_number_of_groups;
  int n_rows = 2 + n_contrasts;

  struct tab_table *t;

  const struct covariance *cov = ws->vws[0].cov ;

  t = tab_create (n_cols, n_rows);
  tab_headers (t, 2, 0, 2, 0);

  /* Put a frame around the entire box, and vertical lines inside */
  tab_box (t,
           TAL_2, TAL_2,
           -1, TAL_1,
           0, 0,
           n_cols - 1, n_rows - 1);

  tab_box (t,
           -1, -1,
           TAL_0, TAL_0,
           2, 0,
           n_cols - 1, 0);

  tab_box (t,
           -1, -1,
           TAL_0, TAL_0,
           0, 0,
           1, 1);

  tab_hline (t, TAL_1, 2, n_cols - 1, 1);
  tab_hline (t, TAL_2, 0, n_cols - 1, 2);

  tab_vline (t, TAL_2, 2, 0, n_rows - 1);

  tab_title (t, _("Contrast Coefficients"));

  tab_text (t,  0, 2, TAB_LEFT | TAT_TITLE, _("Contrast"));


  tab_joint_text (t, 2, 0, n_cols - 1, 0, TAB_CENTER | TAT_TITLE,
                  var_to_string (cmd->indep_var));

  for ( cli = ll_head (&cmd->contrast_list);
        cli != ll_null (&cmd->contrast_list);
        cli = ll_next (cli))
    {
      int count = 0;
      struct contrasts_node *cn = ll_data (cli, struct contrasts_node, ll);
      struct ll *coeffi ;

      tab_text_format (t, 1, c_num + 2, TAB_CENTER, "%d", c_num + 1);

      for (coeffi = ll_head (&cn->coefficient_list);
           coeffi != ll_null (&cn->coefficient_list);
           ++count, coeffi = ll_next (coeffi))
        {
          const struct categoricals *cats = covariance_get_categoricals (cov);
          const union value *val = categoricals_get_value_by_subscript (cats, count);
          struct string vstr;

          ds_init_empty (&vstr);

          var_append_value_name (cmd->indep_var, val, &vstr);

          tab_text (t, count + 2, 1, TAB_CENTER | TAT_TITLE, ds_cstr (&vstr));

          ds_destroy (&vstr);

          if (cn->bad_count)
            tab_text (t, count + 2, c_num + 2, TAB_RIGHT, "?" );
          else
            {
              struct coeff_node *coeffn = ll_data (coeffi, struct coeff_node, ll);

              tab_text_format (t, count + 2, c_num + 2, TAB_RIGHT, "%g", coeffn->coeff);
            }
        }
      ++c_num;
    }

  tab_submit (t);
}


/* Show the results of the contrast tests */
static void
show_contrast_tests (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
{
  int n_contrasts = ll_count (&cmd->contrast_list);
  size_t v;
  int n_cols = 8;
  size_t n_rows = 1 + cmd->n_vars * 2 * n_contrasts;

  struct tab_table *t;

  t = tab_create (n_cols, n_rows);
  tab_headers (t, 3, 0, 1, 0);

  /* Put a frame around the entire box, and vertical lines inside */
  tab_box (t,
           TAL_2, TAL_2,
           -1, TAL_1,
           0, 0,
           n_cols - 1, n_rows - 1);

  tab_box (t,
           -1, -1,
           TAL_0, TAL_0,
           0, 0,
           2, 0);

  tab_hline (t, TAL_2, 0, n_cols - 1, 1);
  tab_vline (t, TAL_2, 3, 0, n_rows - 1);

  tab_title (t, _("Contrast Tests"));

  tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Contrast"));
  tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Value of Contrast"));
  tab_text (t,  4, 0, TAB_CENTER | TAT_TITLE, _("Std. Error"));
  tab_text (t,  5, 0, TAB_CENTER | TAT_TITLE, _("t"));
  tab_text (t,  6, 0, TAB_CENTER | TAT_TITLE, _("df"));
  tab_text (t,  7, 0, TAB_CENTER | TAT_TITLE, _("Sig. (2-tailed)"));

  for (v = 0; v < cmd->n_vars; ++v)
    {
      struct ll *cli;
      int i = 0;
      int lines_per_variable = 2 * n_contrasts;

      tab_text (t,  0, (v * lines_per_variable) + 1, TAB_LEFT | TAT_TITLE,
                var_to_string (cmd->vars[v]));

      for ( cli = ll_head (&cmd->contrast_list);
            cli != ll_null (&cmd->contrast_list);
            ++i, cli = ll_next (cli))
        {
          struct contrasts_node *cn = ll_data (cli, struct contrasts_node, ll);
          struct ll *coeffi = ll_head (&cn->coefficient_list);
          int ci;
          double contrast_value = 0.0;
          double coef_msq = 0.0;
          struct group_proc *grp_data = group_proc_get (cmd->vars[v]);
          struct hsh_table *group_hash = grp_data->group_hash;

          void *const *group_stat_array;

          double T;
          double std_error_contrast;
          double df;
          double sec_vneq = 0.0;

          /* Note: The calculation of the degrees of freedom in the
             "variances not equal" case is painfull!!
             The following formula may help to understand it:
             \frac{\left (\sum_{i=1}^k{c_i^2\frac{s_i^2}{n_i}}\right)^2}
             {
             \sum_{i=1}^k\left (
             \frac{\left (c_i^2\frac{s_i^2}{n_i}\right)^2}  {n_i-1}
             \right)
             }
          */

          double df_denominator = 0.0;
          double df_numerator = 0.0;
          if ( i == 0 )
            {
              tab_text (t,  1, (v * lines_per_variable) + i + 1,
                        TAB_LEFT | TAT_TITLE,
                        _("Assume equal variances"));

              tab_text (t,  1, (v * lines_per_variable) + i + 1 + n_contrasts,
                        TAB_LEFT | TAT_TITLE,
                        _("Does not assume equal"));
            }

          tab_text_format (t,  2, (v * lines_per_variable) + i + 1,
                           TAB_CENTER | TAT_TITLE, "%d", i + 1);


          tab_text_format (t,  2,
                           (v * lines_per_variable) + i + 1 + n_contrasts,
                           TAB_CENTER | TAT_TITLE, "%d", i + 1);

          if (cn->bad_count)
            continue;

          group_stat_array = hsh_sort (group_hash);

          for (ci = 0;
               coeffi != ll_null (&cn->coefficient_list) && 
                 ci < hsh_count (group_hash);
               ++ci, coeffi = ll_next (coeffi))
            {
              struct coeff_node *cn = ll_data (coeffi, struct coeff_node, ll);
              const double coef = cn->coeff; 
              struct group_statistics *gs = group_stat_array[ci];

              const double winv = pow2 (gs->std_dev) / gs->n;

              contrast_value += coef * gs->mean;

              coef_msq += (coef * coef) / gs->n;

              sec_vneq += (coef * coef) * pow2 (gs->std_dev) /gs->n;

              df_numerator += (coef * coef) * winv;
              df_denominator += pow2((coef * coef) * winv) / (gs->n - 1);
            }

          sec_vneq = sqrt (sec_vneq);

          df_numerator = pow2 (df_numerator);

          tab_double (t,  3, (v * lines_per_variable) + i + 1,
                      TAB_RIGHT, contrast_value, NULL);

          tab_double (t,  3, (v * lines_per_variable) + i + 1 +
                      n_contrasts,
                      TAB_RIGHT, contrast_value, NULL);

          std_error_contrast = sqrt (grp_data->mse * coef_msq);

          /* Std. Error */
          tab_double (t,  4, (v * lines_per_variable) + i + 1,
                      TAB_RIGHT, std_error_contrast,
                      NULL);

          T = fabs (contrast_value / std_error_contrast);

          /* T Statistic */

          tab_double (t,  5, (v * lines_per_variable) + i + 1,
                      TAB_RIGHT, T,
                      NULL);

          df = grp_data->ugs.n - grp_data->n_groups;

          /* Degrees of Freedom */
          tab_fixed (t,  6, (v * lines_per_variable) + i + 1,
                     TAB_RIGHT,  df,
                     8, 0);


          /* Significance TWO TAILED !!*/
          tab_double (t,  7, (v * lines_per_variable) + i + 1,
                      TAB_RIGHT,  2 * gsl_cdf_tdist_Q (T, df),
                      NULL);

          /* Now for the Variances NOT Equal case */

          /* Std. Error */
          tab_double (t,  4,
                      (v * lines_per_variable) + i + 1 + n_contrasts,
                      TAB_RIGHT, sec_vneq,
                      NULL);

          T = contrast_value / sec_vneq;
          tab_double (t,  5,
                      (v * lines_per_variable) + i + 1 + n_contrasts,
                      TAB_RIGHT, T,
                      NULL);

          df = df_numerator / df_denominator;

          tab_double (t,  6,
                      (v * lines_per_variable) + i + 1 + n_contrasts,
                      TAB_RIGHT, df,
                      NULL);

          /* The Significance */
          tab_double (t, 7, (v * lines_per_variable) + i + 1 + n_contrasts,
                      TAB_RIGHT,  2 * gsl_cdf_tdist_Q (T,df),
                      NULL);
        }

      if ( v > 0 )
        tab_hline (t, TAL_1, 0, n_cols - 1, (v * lines_per_variable) + 1);
    }

  tab_submit (t);
}