1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2007, 2009, 2010, 2011 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 #include <gsl/gsl_cdf.h>
20 #include <gsl/gsl_matrix.h>
23 #include "data/case.h"
24 #include "data/casegrouper.h"
25 #include "data/casereader.h"
26 #include "data/dataset.h"
27 #include "data/dictionary.h"
28 #include "data/format.h"
29 #include "data/value.h"
30 #include "language/command.h"
31 #include "language/dictionary/split-file.h"
32 #include "language/lexer/lexer.h"
33 #include "language/lexer/value-parser.h"
34 #include "language/lexer/variable-parser.h"
35 #include "libpspp/ll.h"
36 #include "libpspp/message.h"
37 #include "libpspp/misc.h"
38 #include "libpspp/taint.h"
39 #include "linreg/sweep.h"
40 #include "tukey/tukey.h"
41 #include "math/categoricals.h"
42 #include "math/covariance.h"
43 #include "math/levene.h"
44 #include "math/moments.h"
45 #include "output/tab.h"
48 #define _(msgid) gettext (msgid)
49 #define N_(msgid) msgid
51 /* Workspace variable for each dependent variable */
54 struct categoricals *cat;
55 struct covariance *cov;
69 /* Per category data */
70 struct descriptive_data
72 const struct variable *var;
87 STATS_DESCRIPTIVES = 0x0001,
88 STATS_HOMOGENEITY = 0x0002
101 struct ll_list coefficient_list;
107 typedef double df_func (const struct per_var_ws *pvw, const struct moments1 *mom_i, const struct moments1 *mom_j);
108 typedef double ts_func (int k, const struct moments1 *mom_i, const struct moments1 *mom_j, double std_err);
109 typedef double p1tail_func (double ts, double df1, double df2);
111 typedef double pinv_func (double std_err, double alpha, double df, int k, const struct moments1 *mom_i, const struct moments1 *mom_j);
129 const struct variable **vars;
131 const struct variable *indep_var;
133 enum statistics stats;
135 enum missing_type missing_type;
136 enum mv_class exclude;
138 /* List of contrasts */
139 struct ll_list contrast_list;
141 /* The weight variable */
142 const struct variable *wv;
144 /* The confidence level for multiple comparisons */
152 df_common (const struct per_var_ws *pvw, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
154 return pvw->n - pvw->n_groups;
158 df_individual (const struct per_var_ws *pvw UNUSED, const struct moments1 *mom_i, const struct moments1 *mom_j)
164 moments1_calculate (mom_i, &n_i, NULL, &var_i, 0, 0);
165 moments1_calculate (mom_j, &n_j, NULL, &var_j, 0, 0);
167 nom = pow2 (var_i/n_i + var_j/n_j);
168 denom = pow2 (var_i/n_i) / (n_i - 1) + pow2 (var_j/n_j) / (n_j - 1);
173 static double lsd_pinv (double std_err, double alpha, double df, int k UNUSED, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
175 return std_err * gsl_cdf_tdist_Pinv (1.0 - alpha / 2.0, df);
178 static double bonferroni_pinv (double std_err, double alpha, double df, int k, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
180 const int m = k * (k - 1) / 2;
181 return std_err * gsl_cdf_tdist_Pinv (1.0 - alpha / (2.0 * m), df);
184 static double sidak_pinv (double std_err, double alpha, double df, int k, const struct moments1 *mom_i, const struct moments1 *mom_j)
186 const double m = k * (k - 1) / 2;
187 double lp = 1.0 - exp (log (1.0 - alpha) / m ) ;
188 return std_err * gsl_cdf_tdist_Pinv (1.0 - lp / 2.0, df);
191 static double tukey_pinv (double std_err, double alpha, double df, int k, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
193 return std_err / sqrt (2.0) * qtukey (1 - alpha, 1.0, k, df, 1, 0);
196 static double scheffe_pinv (double std_err, double alpha, double df, int k, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
198 double x = (k - 1) * gsl_cdf_fdist_Pinv (1.0 - alpha, k - 1, df);
199 return std_err * sqrt (x);
202 static double gh_pinv (double std_err UNUSED, double alpha, double df, int k, const struct moments1 *mom_i, const struct moments1 *mom_j)
204 double n_i, mean_i, var_i;
205 double n_j, mean_j, var_j;
208 moments1_calculate (mom_i, &n_i, &mean_i, &var_i, 0, 0);
209 moments1_calculate (mom_j, &n_j, &mean_j, &var_j, 0, 0);
211 m = sqrt ((var_i/n_i + var_j/n_j) / 2.0);
213 return m * qtukey (1 - alpha, 1.0, k, df, 1, 0);
218 multiple_comparison_sig (double std_err,
219 const struct per_var_ws *pvw,
220 const struct descriptive_data *dd_i, const struct descriptive_data *dd_j,
221 const struct posthoc *ph)
223 int k = pvw->n_groups;
224 double df = ph->dff (pvw, dd_i->mom, dd_j->mom);
225 double ts = ph->tsf (k, dd_i->mom, dd_j->mom, std_err);
226 return ph->p1f (ts, k - 1, df);
230 mc_half_range (const struct oneway_spec *cmd, const struct per_var_ws *pvw, double std_err, const struct descriptive_data *dd_i, const struct descriptive_data *dd_j, const struct posthoc *ph)
232 int k = pvw->n_groups;
233 double df = ph->dff (pvw, dd_i->mom, dd_j->mom);
235 return ph->pinv (std_err, cmd->alpha, df, k, dd_i->mom, dd_j->mom);
238 static double tukey_1tailsig (double ts, double df1, double df2)
240 double twotailedsig = 1.0 - ptukey (ts, 1.0, df1 + 1, df2, 1, 0);
242 return twotailedsig / 2.0;
245 static double lsd_1tailsig (double ts, double df1 UNUSED, double df2)
247 return ts < 0 ? gsl_cdf_tdist_P (ts, df2) : gsl_cdf_tdist_Q (ts, df2);
250 static double sidak_1tailsig (double ts, double df1, double df2)
252 double ex = (df1 + 1.0) * df1 / 2.0;
253 double lsd_sig = 2 * lsd_1tailsig (ts, df1, df2);
255 return 0.5 * (1.0 - pow (1.0 - lsd_sig, ex));
258 static double bonferroni_1tailsig (double ts, double df1, double df2)
260 const int m = (df1 + 1) * df1 / 2;
262 double p = ts < 0 ? gsl_cdf_tdist_P (ts, df2) : gsl_cdf_tdist_Q (ts, df2);
265 return p > 0.5 ? 0.5 : p;
268 static double scheffe_1tailsig (double ts, double df1, double df2)
270 return 0.5 * gsl_cdf_fdist_Q (ts, df1, df2);
274 static double tukey_test_stat (int k, const struct moments1 *mom_i, const struct moments1 *mom_j, double std_err)
276 double n_i, mean_i, var_i;
277 double n_j, mean_j, var_j;
279 moments1_calculate (mom_i, &n_i, &mean_i, &var_i, 0, 0);
280 moments1_calculate (mom_j, &n_j, &mean_j, &var_j, 0, 0);
282 double ts = (mean_i - mean_j) / std_err;
283 ts = fabs (ts) * sqrt (2.0);
288 static double lsd_test_stat (int k, const struct moments1 *mom_i, const struct moments1 *mom_j, double std_err)
290 double n_i, mean_i, var_i;
291 double n_j, mean_j, var_j;
293 moments1_calculate (mom_i, &n_i, &mean_i, &var_i, 0, 0);
294 moments1_calculate (mom_j, &n_j, &mean_j, &var_j, 0, 0);
296 return (mean_i - mean_j) / std_err;
299 static double scheffe_test_stat (int k, const struct moments1 *mom_i, const struct moments1 *mom_j, double std_err)
301 double n_i, mean_i, var_i;
302 double n_j, mean_j, var_j;
304 moments1_calculate (mom_i, &n_i, &mean_i, &var_i, 0, 0);
305 moments1_calculate (mom_j, &n_j, &mean_j, &var_j, 0, 0);
307 double t = (mean_i - mean_j) / std_err;
314 static double gh_test_stat (int k, const struct moments1 *mom_i, const struct moments1 *mom_j, double std_err)
316 double n_i, mean_i, var_i;
317 double n_j, mean_j, var_j;
319 moments1_calculate (mom_i, &n_i, &mean_i, &var_i, 0, 0);
320 moments1_calculate (mom_j, &n_j, &mean_j, &var_j, 0, 0);
322 double thing = var_i / n_i + var_j / n_j;
324 thing = sqrt (thing);
326 double ts = (mean_i - mean_j) / thing;
333 static const struct posthoc ph_tests [] =
335 { "LSD", N_("LSD"), df_common, lsd_test_stat, lsd_1tailsig, lsd_pinv},
336 { "TUKEY", N_("Tukey HSD"), df_common, tukey_test_stat, tukey_1tailsig, tukey_pinv},
337 { "BONFERRONI", N_("Bonferroni"), df_common, lsd_test_stat, bonferroni_1tailsig, bonferroni_pinv},
338 { "SCHEFFE", N_("Scheffé"), df_common, scheffe_test_stat, scheffe_1tailsig, scheffe_pinv},
339 { "GH", N_("Games-Howell"), df_individual, gh_test_stat, tukey_1tailsig, gh_pinv},
340 { "SIDAK", N_("Šidák"), df_common, lsd_test_stat, sidak_1tailsig, sidak_pinv}
344 struct oneway_workspace
346 /* The number of distinct values of the independent variable, when all
347 missing values are disregarded */
348 int actual_number_of_groups;
350 struct per_var_ws *vws;
352 /* An array of descriptive data. One for each dependent variable */
353 struct descriptive_data **dd_total;
356 /* Routines to show the output tables */
357 static void show_anova_table (const struct oneway_spec *, const struct oneway_workspace *);
358 static void show_descriptives (const struct oneway_spec *, const struct oneway_workspace *);
359 static void show_homogeneity (const struct oneway_spec *, const struct oneway_workspace *);
361 static void output_oneway (const struct oneway_spec *, struct oneway_workspace *ws);
362 static void run_oneway (const struct oneway_spec *cmd, struct casereader *input, const struct dataset *ds);
365 cmd_oneway (struct lexer *lexer, struct dataset *ds)
367 const struct dictionary *dict = dataset_dict (ds);
368 struct oneway_spec oneway ;
371 oneway.indep_var = NULL;
373 oneway.missing_type = MISS_ANALYSIS;
374 oneway.exclude = MV_ANY;
375 oneway.wv = dict_get_weight (dict);
377 oneway.posthoc = NULL;
378 oneway.n_posthoc = 0;
380 ll_init (&oneway.contrast_list);
383 if ( lex_match (lexer, T_SLASH))
385 if (!lex_force_match_id (lexer, "VARIABLES"))
389 lex_match (lexer, T_EQUALS);
392 if (!parse_variables_const (lexer, dict,
393 &oneway.vars, &oneway.n_vars,
394 PV_NO_DUPLICATE | PV_NUMERIC))
397 lex_force_match (lexer, T_BY);
399 oneway.indep_var = parse_variable_const (lexer, dict);
401 while (lex_token (lexer) != T_ENDCMD)
403 lex_match (lexer, T_SLASH);
405 if (lex_match_id (lexer, "STATISTICS"))
407 lex_match (lexer, T_EQUALS);
408 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
410 if (lex_match_id (lexer, "DESCRIPTIVES"))
412 oneway.stats |= STATS_DESCRIPTIVES;
414 else if (lex_match_id (lexer, "HOMOGENEITY"))
416 oneway.stats |= STATS_HOMOGENEITY;
420 lex_error (lexer, NULL);
425 else if (lex_match_id (lexer, "POSTHOC"))
427 lex_match (lexer, T_EQUALS);
428 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
432 for (p = 0 ; p < sizeof (ph_tests) / sizeof (struct posthoc); ++p)
434 if (lex_match_id (lexer, ph_tests[p].syntax))
437 oneway.posthoc = xrealloc (oneway.posthoc, sizeof (*oneway.posthoc) * oneway.n_posthoc);
438 oneway.posthoc[oneway.n_posthoc - 1] = p;
443 if ( method == false)
445 if (lex_match_id (lexer, "ALPHA"))
447 if ( !lex_force_match (lexer, T_LPAREN))
449 lex_force_num (lexer);
450 oneway.alpha = lex_number (lexer);
452 if ( !lex_force_match (lexer, T_RPAREN))
457 msg (SE, _("The post hoc analysis method %s is not supported."), lex_tokcstr (lexer));
458 lex_error (lexer, NULL);
464 else if (lex_match_id (lexer, "CONTRAST"))
466 struct contrasts_node *cl = xzalloc (sizeof *cl);
468 struct ll_list *coefficient_list = &cl->coefficient_list;
469 lex_match (lexer, T_EQUALS);
471 ll_init (coefficient_list);
473 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
475 if ( lex_is_number (lexer))
477 struct coeff_node *cc = xmalloc (sizeof *cc);
478 cc->coeff = lex_number (lexer);
480 ll_push_tail (coefficient_list, &cc->ll);
485 lex_error (lexer, NULL);
490 ll_push_tail (&oneway.contrast_list, &cl->ll);
492 else if (lex_match_id (lexer, "MISSING"))
494 lex_match (lexer, T_EQUALS);
495 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
497 if (lex_match_id (lexer, "INCLUDE"))
499 oneway.exclude = MV_SYSTEM;
501 else if (lex_match_id (lexer, "EXCLUDE"))
503 oneway.exclude = MV_ANY;
505 else if (lex_match_id (lexer, "LISTWISE"))
507 oneway.missing_type = MISS_LISTWISE;
509 else if (lex_match_id (lexer, "ANALYSIS"))
511 oneway.missing_type = MISS_ANALYSIS;
515 lex_error (lexer, NULL);
522 lex_error (lexer, NULL);
529 struct casegrouper *grouper;
530 struct casereader *group;
533 grouper = casegrouper_create_splits (proc_open (ds), dict);
534 while (casegrouper_get_next_group (grouper, &group))
535 run_oneway (&oneway, group, ds);
536 ok = casegrouper_destroy (grouper);
537 ok = proc_commit (ds) && ok;
552 static struct descriptive_data *
553 dd_create (const struct variable *var)
555 struct descriptive_data *dd = xmalloc (sizeof *dd);
557 dd->mom = moments1_create (MOMENT_VARIANCE);
558 dd->minimum = DBL_MAX;
559 dd->maximum = -DBL_MAX;
566 dd_destroy (struct descriptive_data *dd)
568 moments1_destroy (dd->mom);
573 makeit (void *aux1, void *aux2 UNUSED)
575 const struct variable *var = aux1;
577 struct descriptive_data *dd = dd_create (var);
583 updateit (void *user_data,
584 enum mv_class exclude,
585 const struct variable *wv,
586 const struct variable *catvar UNUSED,
587 const struct ccase *c,
588 void *aux1, void *aux2)
590 struct descriptive_data *dd = user_data;
592 const struct variable *varp = aux1;
594 const union value *valx = case_data (c, varp);
596 struct descriptive_data *dd_total = aux2;
600 if ( var_is_value_missing (varp, valx, exclude))
603 weight = wv != NULL ? case_data (c, wv)->f : 1.0;
605 moments1_add (dd->mom, valx->f, weight);
606 if (valx->f < dd->minimum)
607 dd->minimum = valx->f;
609 if (valx->f > dd->maximum)
610 dd->maximum = valx->f;
613 const struct variable *var = dd_total->var;
614 const union value *val = case_data (c, var);
616 moments1_add (dd_total->mom,
620 if (val->f < dd_total->minimum)
621 dd_total->minimum = val->f;
623 if (val->f > dd_total->maximum)
624 dd_total->maximum = val->f;
629 run_oneway (const struct oneway_spec *cmd,
630 struct casereader *input,
631 const struct dataset *ds)
635 struct dictionary *dict = dataset_dict (ds);
636 struct casereader *reader;
639 struct oneway_workspace ws;
641 ws.actual_number_of_groups = 0;
642 ws.vws = xzalloc (cmd->n_vars * sizeof (*ws.vws));
643 ws.dd_total = xmalloc (sizeof (struct descriptive_data) * cmd->n_vars);
645 for (v = 0 ; v < cmd->n_vars; ++v)
646 ws.dd_total[v] = dd_create (cmd->vars[v]);
648 for (v = 0; v < cmd->n_vars; ++v)
650 ws.vws[v].cat = categoricals_create (&cmd->indep_var, 1, cmd->wv,
651 cmd->exclude, makeit, updateit,
652 CONST_CAST (struct variable *,
656 ws.vws[v].cov = covariance_2pass_create (1, &cmd->vars[v],
658 cmd->wv, cmd->exclude);
659 ws.vws[v].nl = levene_create (var_get_width (cmd->indep_var), NULL);
662 c = casereader_peek (input, 0);
665 casereader_destroy (input);
668 output_split_file_values (ds, c);
671 taint = taint_clone (casereader_get_taint (input));
673 input = casereader_create_filter_missing (input, &cmd->indep_var, 1,
674 cmd->exclude, NULL, NULL);
675 if (cmd->missing_type == MISS_LISTWISE)
676 input = casereader_create_filter_missing (input, cmd->vars, cmd->n_vars,
677 cmd->exclude, NULL, NULL);
678 input = casereader_create_filter_weight (input, dict, NULL, NULL);
680 reader = casereader_clone (input);
681 for (; (c = casereader_read (reader)) != NULL; case_unref (c))
684 double w = dict_get_case_weight (dict, c, NULL);
686 for (i = 0; i < cmd->n_vars; ++i)
688 struct per_var_ws *pvw = &ws.vws[i];
689 const struct variable *v = cmd->vars[i];
690 const union value *val = case_data (c, v);
692 if ( MISS_ANALYSIS == cmd->missing_type)
694 if ( var_is_value_missing (v, val, cmd->exclude))
698 covariance_accumulate_pass1 (pvw->cov, c);
699 levene_pass_one (pvw->nl, val->f, w, case_data (c, cmd->indep_var));
702 casereader_destroy (reader);
704 reader = casereader_clone (input);
705 for ( ; (c = casereader_read (reader) ); case_unref (c))
708 double w = dict_get_case_weight (dict, c, NULL);
709 for (i = 0; i < cmd->n_vars; ++i)
711 struct per_var_ws *pvw = &ws.vws[i];
712 const struct variable *v = cmd->vars[i];
713 const union value *val = case_data (c, v);
715 if ( MISS_ANALYSIS == cmd->missing_type)
717 if ( var_is_value_missing (v, val, cmd->exclude))
721 covariance_accumulate_pass2 (pvw->cov, c);
722 levene_pass_two (pvw->nl, val->f, w, case_data (c, cmd->indep_var));
725 casereader_destroy (reader);
727 reader = casereader_clone (input);
728 for ( ; (c = casereader_read (reader) ); case_unref (c))
731 double w = dict_get_case_weight (dict, c, NULL);
733 for (i = 0; i < cmd->n_vars; ++i)
735 struct per_var_ws *pvw = &ws.vws[i];
736 const struct variable *v = cmd->vars[i];
737 const union value *val = case_data (c, v);
739 if ( MISS_ANALYSIS == cmd->missing_type)
741 if ( var_is_value_missing (v, val, cmd->exclude))
745 levene_pass_three (pvw->nl, val->f, w, case_data (c, cmd->indep_var));
748 casereader_destroy (reader);
751 for (v = 0; v < cmd->n_vars; ++v)
753 struct per_var_ws *pvw = &ws.vws[v];
754 gsl_matrix *cm = covariance_calculate_unnormalized (pvw->cov);
755 const struct categoricals *cats = covariance_get_categoricals (pvw->cov);
757 moments1_calculate (ws.dd_total[v]->mom, &pvw->n, NULL, NULL, NULL, NULL);
759 pvw->sst = gsl_matrix_get (cm, 0, 0);
763 pvw->sse = gsl_matrix_get (cm, 0, 0);
765 pvw->ssa = pvw->sst - pvw->sse;
767 pvw->n_groups = categoricals_total (cats);
769 pvw->mse = (pvw->sst - pvw->ssa) / (pvw->n - pvw->n_groups);
771 gsl_matrix_free (cm);
774 for (v = 0; v < cmd->n_vars; ++v)
776 const struct categoricals *cats = covariance_get_categoricals (ws.vws[v].cov);
778 categoricals_done (cats);
780 if (categoricals_total (cats) > ws.actual_number_of_groups)
781 ws.actual_number_of_groups = categoricals_total (cats);
784 casereader_destroy (input);
786 if (!taint_has_tainted_successor (taint))
787 output_oneway (cmd, &ws);
789 taint_destroy (taint);
792 for (v = 0; v < cmd->n_vars; ++v)
794 covariance_destroy (ws.vws[v].cov);
795 levene_destroy (ws.vws[v].nl);
796 dd_destroy (ws.dd_total[v]);
802 static void show_contrast_coeffs (const struct oneway_spec *cmd, const struct oneway_workspace *ws);
803 static void show_contrast_tests (const struct oneway_spec *cmd, const struct oneway_workspace *ws);
804 static void show_comparisons (const struct oneway_spec *cmd, const struct oneway_workspace *ws, int depvar);
807 output_oneway (const struct oneway_spec *cmd, struct oneway_workspace *ws)
811 /* Check the sanity of the given contrast values */
812 struct contrasts_node *coeff_list = NULL;
813 struct contrasts_node *coeff_next = NULL;
814 ll_for_each_safe (coeff_list, coeff_next, struct contrasts_node, ll, &cmd->contrast_list)
816 struct coeff_node *cn = NULL;
818 struct ll_list *cl = &coeff_list->coefficient_list;
821 if (ll_count (cl) != ws->actual_number_of_groups)
824 _("In contrast list %zu, the number of coefficients (%d) does not equal the number of groups (%d). This contrast list will be ignored."),
825 i, ll_count (cl), ws->actual_number_of_groups);
827 ll_remove (&coeff_list->ll);
831 ll_for_each (cn, struct coeff_node, ll, cl)
835 msg (SW, _("Coefficients for contrast %zu do not total zero"), i);
838 if (cmd->stats & STATS_DESCRIPTIVES)
839 show_descriptives (cmd, ws);
841 if (cmd->stats & STATS_HOMOGENEITY)
842 show_homogeneity (cmd, ws);
844 show_anova_table (cmd, ws);
846 if (ll_count (&cmd->contrast_list) > 0)
848 show_contrast_coeffs (cmd, ws);
849 show_contrast_tests (cmd, ws);
855 for (v = 0 ; v < cmd->n_vars; ++v)
856 show_comparisons (cmd, ws, v);
861 /* Show the ANOVA table */
863 show_anova_table (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
867 size_t n_rows = cmd->n_vars * 3 + 1;
869 struct tab_table *t = tab_create (n_cols, n_rows);
871 tab_headers (t, 2, 0, 1, 0);
877 n_cols - 1, n_rows - 1);
879 tab_hline (t, TAL_2, 0, n_cols - 1, 1 );
880 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
881 tab_vline (t, TAL_0, 1, 0, 0);
883 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Sum of Squares"));
884 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df"));
885 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Mean Square"));
886 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("F"));
887 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
890 for (i = 0; i < cmd->n_vars; ++i)
895 const char *s = var_to_string (cmd->vars[i]);
896 const struct per_var_ws *pvw = &ws->vws[i];
898 moments1_calculate (ws->dd_total[i]->mom, &n, NULL, NULL, NULL, NULL);
900 df1 = pvw->n_groups - 1;
901 df2 = n - pvw->n_groups;
902 msa = pvw->ssa / df1;
904 tab_text (t, 0, i * 3 + 1, TAB_LEFT | TAT_TITLE, s);
905 tab_text (t, 1, i * 3 + 1, TAB_LEFT | TAT_TITLE, _("Between Groups"));
906 tab_text (t, 1, i * 3 + 2, TAB_LEFT | TAT_TITLE, _("Within Groups"));
907 tab_text (t, 1, i * 3 + 3, TAB_LEFT | TAT_TITLE, _("Total"));
910 tab_hline (t, TAL_1, 0, n_cols - 1, i * 3 + 1);
913 /* Sums of Squares */
914 tab_double (t, 2, i * 3 + 1, 0, pvw->ssa, NULL);
915 tab_double (t, 2, i * 3 + 3, 0, pvw->sst, NULL);
916 tab_double (t, 2, i * 3 + 2, 0, pvw->sse, NULL);
919 /* Degrees of freedom */
920 tab_fixed (t, 3, i * 3 + 1, 0, df1, 4, 0);
921 tab_fixed (t, 3, i * 3 + 2, 0, df2, 4, 0);
922 tab_fixed (t, 3, i * 3 + 3, 0, n - 1, 4, 0);
925 tab_double (t, 4, i * 3 + 1, TAB_RIGHT, msa, NULL);
926 tab_double (t, 4, i * 3 + 2, TAB_RIGHT, pvw->mse, NULL);
929 const double F = msa / pvw->mse ;
932 tab_double (t, 5, i * 3 + 1, 0, F, NULL);
934 /* The significance */
935 tab_double (t, 6, i * 3 + 1, 0, gsl_cdf_fdist_Q (F, df1, df2), NULL);
939 tab_title (t, _("ANOVA"));
944 /* Show the descriptives table */
946 show_descriptives (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
953 const double confidence = 0.95;
954 const double q = (1.0 - confidence) / 2.0;
956 const struct fmt_spec *wfmt = cmd->wv ? var_get_print_format (cmd->wv) : &F_8_0;
960 for (v = 0; v < cmd->n_vars; ++v)
961 n_rows += ws->actual_number_of_groups + 1;
963 t = tab_create (n_cols, n_rows);
964 tab_headers (t, 2, 0, 2, 0);
966 /* Put a frame around the entire box, and vertical lines inside */
971 n_cols - 1, n_rows - 1);
973 /* Underline headers */
974 tab_hline (t, TAL_2, 0, n_cols - 1, 2);
975 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
977 tab_text (t, 2, 1, TAB_CENTER | TAT_TITLE, _("N"));
978 tab_text (t, 3, 1, TAB_CENTER | TAT_TITLE, _("Mean"));
979 tab_text (t, 4, 1, TAB_CENTER | TAT_TITLE, _("Std. Deviation"));
980 tab_text (t, 5, 1, TAB_CENTER | TAT_TITLE, _("Std. Error"));
983 tab_vline (t, TAL_0, 7, 0, 0);
984 tab_hline (t, TAL_1, 6, 7, 1);
985 tab_joint_text_format (t, 6, 0, 7, 0, TAB_CENTER | TAT_TITLE,
986 _("%g%% Confidence Interval for Mean"),
989 tab_text (t, 6, 1, TAB_CENTER | TAT_TITLE, _("Lower Bound"));
990 tab_text (t, 7, 1, TAB_CENTER | TAT_TITLE, _("Upper Bound"));
992 tab_text (t, 8, 1, TAB_CENTER | TAT_TITLE, _("Minimum"));
993 tab_text (t, 9, 1, TAB_CENTER | TAT_TITLE, _("Maximum"));
995 tab_title (t, _("Descriptives"));
998 for (v = 0; v < cmd->n_vars; ++v)
1000 const char *s = var_to_string (cmd->vars[v]);
1001 const struct fmt_spec *fmt = var_get_print_format (cmd->vars[v]);
1005 struct per_var_ws *pvw = &ws->vws[v];
1006 const struct categoricals *cats = covariance_get_categoricals (pvw->cov);
1008 tab_text (t, 0, row, TAB_LEFT | TAT_TITLE, s);
1010 tab_hline (t, TAL_1, 0, n_cols - 1, row);
1012 for (count = 0; count < categoricals_total (cats); ++count)
1015 double n, mean, variance;
1016 double std_dev, std_error ;
1020 const union value *gval = categoricals_get_value_by_category (cats, count);
1021 const struct descriptive_data *dd = categoricals_get_user_data_by_category (cats, count);
1023 moments1_calculate (dd->mom, &n, &mean, &variance, NULL, NULL);
1025 std_dev = sqrt (variance);
1026 std_error = std_dev / sqrt (n) ;
1028 ds_init_empty (&vstr);
1030 var_append_value_name (cmd->indep_var, gval, &vstr);
1032 tab_text (t, 1, row + count,
1033 TAB_LEFT | TAT_TITLE,
1038 /* Now fill in the numbers ... */
1040 tab_double (t, 2, row + count, 0, n, wfmt);
1042 tab_double (t, 3, row + count, 0, mean, NULL);
1044 tab_double (t, 4, row + count, 0, std_dev, NULL);
1047 tab_double (t, 5, row + count, 0, std_error, NULL);
1049 /* Now the confidence interval */
1051 T = gsl_cdf_tdist_Qinv (q, n - 1);
1053 tab_double (t, 6, row + count, 0,
1054 mean - T * std_error, NULL);
1056 tab_double (t, 7, row + count, 0,
1057 mean + T * std_error, NULL);
1061 tab_double (t, 8, row + count, 0, dd->minimum, fmt);
1062 tab_double (t, 9, row + count, 0, dd->maximum, fmt);
1067 double n, mean, variance;
1071 moments1_calculate (ws->dd_total[v]->mom, &n, &mean, &variance, NULL, NULL);
1073 std_dev = sqrt (variance);
1074 std_error = std_dev / sqrt (n) ;
1076 tab_text (t, 1, row + count,
1077 TAB_LEFT | TAT_TITLE, _("Total"));
1079 tab_double (t, 2, row + count, 0, n, wfmt);
1081 tab_double (t, 3, row + count, 0, mean, NULL);
1083 tab_double (t, 4, row + count, 0, std_dev, NULL);
1085 tab_double (t, 5, row + count, 0, std_error, NULL);
1087 /* Now the confidence interval */
1088 T = gsl_cdf_tdist_Qinv (q, n - 1);
1090 tab_double (t, 6, row + count, 0,
1091 mean - T * std_error, NULL);
1093 tab_double (t, 7, row + count, 0,
1094 mean + T * std_error, NULL);
1097 tab_double (t, 8, row + count, 0, ws->dd_total[v]->minimum, fmt);
1098 tab_double (t, 9, row + count, 0, ws->dd_total[v]->maximum, fmt);
1101 row += categoricals_total (cats) + 1;
1107 /* Show the homogeneity table */
1109 show_homogeneity (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
1113 size_t n_rows = cmd->n_vars + 1;
1115 struct tab_table *t = tab_create (n_cols, n_rows);
1116 tab_headers (t, 1, 0, 1, 0);
1118 /* Put a frame around the entire box, and vertical lines inside */
1123 n_cols - 1, n_rows - 1);
1126 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
1127 tab_vline (t, TAL_2, 1, 0, n_rows - 1);
1129 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("Levene Statistic"));
1130 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("df1"));
1131 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df2"));
1132 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
1134 tab_title (t, _("Test of Homogeneity of Variances"));
1136 for (v = 0; v < cmd->n_vars; ++v)
1139 const struct per_var_ws *pvw = &ws->vws[v];
1140 double F = levene_calculate (pvw->nl);
1142 const struct variable *var = cmd->vars[v];
1143 const char *s = var_to_string (var);
1146 moments1_calculate (ws->dd_total[v]->mom, &n, NULL, NULL, NULL, NULL);
1148 df1 = pvw->n_groups - 1;
1149 df2 = n - pvw->n_groups;
1151 tab_text (t, 0, v + 1, TAB_LEFT | TAT_TITLE, s);
1153 tab_double (t, 1, v + 1, TAB_RIGHT, F, NULL);
1154 tab_fixed (t, 2, v + 1, TAB_RIGHT, df1, 8, 0);
1155 tab_fixed (t, 3, v + 1, TAB_RIGHT, df2, 8, 0);
1157 /* Now the significance */
1158 tab_double (t, 4, v + 1, TAB_RIGHT, gsl_cdf_fdist_Q (F, df1, df2), NULL);
1165 /* Show the contrast coefficients table */
1167 show_contrast_coeffs (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
1172 int n_contrasts = ll_count (&cmd->contrast_list);
1173 int n_cols = 2 + ws->actual_number_of_groups;
1174 int n_rows = 2 + n_contrasts;
1176 struct tab_table *t;
1178 const struct covariance *cov = ws->vws[0].cov ;
1180 t = tab_create (n_cols, n_rows);
1181 tab_headers (t, 2, 0, 2, 0);
1183 /* Put a frame around the entire box, and vertical lines inside */
1188 n_cols - 1, n_rows - 1);
1202 tab_hline (t, TAL_1, 2, n_cols - 1, 1);
1203 tab_hline (t, TAL_2, 0, n_cols - 1, 2);
1205 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
1207 tab_title (t, _("Contrast Coefficients"));
1209 tab_text (t, 0, 2, TAB_LEFT | TAT_TITLE, _("Contrast"));
1212 tab_joint_text (t, 2, 0, n_cols - 1, 0, TAB_CENTER | TAT_TITLE,
1213 var_to_string (cmd->indep_var));
1215 for ( cli = ll_head (&cmd->contrast_list);
1216 cli != ll_null (&cmd->contrast_list);
1217 cli = ll_next (cli))
1220 struct contrasts_node *cn = ll_data (cli, struct contrasts_node, ll);
1223 tab_text_format (t, 1, c_num + 2, TAB_CENTER, "%d", c_num + 1);
1225 for (coeffi = ll_head (&cn->coefficient_list);
1226 coeffi != ll_null (&cn->coefficient_list);
1227 ++count, coeffi = ll_next (coeffi))
1229 const struct categoricals *cats = covariance_get_categoricals (cov);
1230 const union value *val = categoricals_get_value_by_category (cats, count);
1231 struct coeff_node *coeffn = ll_data (coeffi, struct coeff_node, ll);
1234 ds_init_empty (&vstr);
1236 var_append_value_name (cmd->indep_var, val, &vstr);
1238 tab_text (t, count + 2, 1, TAB_CENTER | TAT_TITLE, ds_cstr (&vstr));
1242 tab_text_format (t, count + 2, c_num + 2, TAB_RIGHT, "%g", coeffn->coeff);
1251 /* Show the results of the contrast tests */
1253 show_contrast_tests (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
1255 int n_contrasts = ll_count (&cmd->contrast_list);
1258 size_t n_rows = 1 + cmd->n_vars * 2 * n_contrasts;
1260 struct tab_table *t;
1262 t = tab_create (n_cols, n_rows);
1263 tab_headers (t, 3, 0, 1, 0);
1265 /* Put a frame around the entire box, and vertical lines inside */
1270 n_cols - 1, n_rows - 1);
1278 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
1279 tab_vline (t, TAL_2, 3, 0, n_rows - 1);
1281 tab_title (t, _("Contrast Tests"));
1283 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Contrast"));
1284 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Value of Contrast"));
1285 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Std. Error"));
1286 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("t"));
1287 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("df"));
1288 tab_text (t, 7, 0, TAB_CENTER | TAT_TITLE, _("Sig. (2-tailed)"));
1290 for (v = 0; v < cmd->n_vars; ++v)
1292 const struct per_var_ws *pvw = &ws->vws[v];
1293 const struct categoricals *cats = covariance_get_categoricals (pvw->cov);
1296 int lines_per_variable = 2 * n_contrasts;
1298 tab_text (t, 0, (v * lines_per_variable) + 1, TAB_LEFT | TAT_TITLE,
1299 var_to_string (cmd->vars[v]));
1301 for ( cli = ll_head (&cmd->contrast_list);
1302 cli != ll_null (&cmd->contrast_list);
1303 ++i, cli = ll_next (cli))
1305 struct contrasts_node *cn = ll_data (cli, struct contrasts_node, ll);
1308 double contrast_value = 0.0;
1309 double coef_msq = 0.0;
1312 double std_error_contrast;
1314 double sec_vneq = 0.0;
1316 /* Note: The calculation of the degrees of freedom in the
1317 "variances not equal" case is painfull!!
1318 The following formula may help to understand it:
1319 \frac{\left (\sum_{i=1}^k{c_i^2\frac{s_i^2}{n_i}}\right)^2}
1322 \frac{\left (c_i^2\frac{s_i^2}{n_i}\right)^2} {n_i-1}
1327 double df_denominator = 0.0;
1328 double df_numerator = 0.0;
1331 moments1_calculate (ws->dd_total[v]->mom, &grand_n, NULL, NULL, NULL, NULL);
1332 df = grand_n - pvw->n_groups;
1336 tab_text (t, 1, (v * lines_per_variable) + i + 1,
1337 TAB_LEFT | TAT_TITLE,
1338 _("Assume equal variances"));
1340 tab_text (t, 1, (v * lines_per_variable) + i + 1 + n_contrasts,
1341 TAB_LEFT | TAT_TITLE,
1342 _("Does not assume equal"));
1345 tab_text_format (t, 2, (v * lines_per_variable) + i + 1,
1346 TAB_CENTER | TAT_TITLE, "%d", i + 1);
1349 tab_text_format (t, 2,
1350 (v * lines_per_variable) + i + 1 + n_contrasts,
1351 TAB_CENTER | TAT_TITLE, "%d", i + 1);
1353 for (coeffi = ll_head (&cn->coefficient_list);
1354 coeffi != ll_null (&cn->coefficient_list);
1355 ++ci, coeffi = ll_next (coeffi))
1357 double n, mean, variance;
1358 const struct descriptive_data *dd = categoricals_get_user_data_by_category (cats, ci);
1359 struct coeff_node *cn = ll_data (coeffi, struct coeff_node, ll);
1360 const double coef = cn->coeff;
1363 moments1_calculate (dd->mom, &n, &mean, &variance, NULL, NULL);
1365 winv = variance / n;
1367 contrast_value += coef * mean;
1369 coef_msq += (pow2 (coef)) / n;
1371 sec_vneq += (pow2 (coef)) * variance / n;
1373 df_numerator += (pow2 (coef)) * winv;
1374 df_denominator += pow2((pow2 (coef)) * winv) / (n - 1);
1377 sec_vneq = sqrt (sec_vneq);
1379 df_numerator = pow2 (df_numerator);
1381 tab_double (t, 3, (v * lines_per_variable) + i + 1,
1382 TAB_RIGHT, contrast_value, NULL);
1384 tab_double (t, 3, (v * lines_per_variable) + i + 1 +
1386 TAB_RIGHT, contrast_value, NULL);
1388 std_error_contrast = sqrt (pvw->mse * coef_msq);
1391 tab_double (t, 4, (v * lines_per_variable) + i + 1,
1392 TAB_RIGHT, std_error_contrast,
1395 T = fabs (contrast_value / std_error_contrast);
1399 tab_double (t, 5, (v * lines_per_variable) + i + 1,
1404 /* Degrees of Freedom */
1405 tab_fixed (t, 6, (v * lines_per_variable) + i + 1,
1410 /* Significance TWO TAILED !!*/
1411 tab_double (t, 7, (v * lines_per_variable) + i + 1,
1412 TAB_RIGHT, 2 * gsl_cdf_tdist_Q (T, df),
1415 /* Now for the Variances NOT Equal case */
1419 (v * lines_per_variable) + i + 1 + n_contrasts,
1420 TAB_RIGHT, sec_vneq,
1423 T = contrast_value / sec_vneq;
1425 (v * lines_per_variable) + i + 1 + n_contrasts,
1429 df = df_numerator / df_denominator;
1432 (v * lines_per_variable) + i + 1 + n_contrasts,
1436 /* The Significance */
1437 tab_double (t, 7, (v * lines_per_variable) + i + 1 + n_contrasts,
1438 TAB_RIGHT, 2 * gsl_cdf_tdist_Q (T,df),
1443 tab_hline (t, TAL_1, 0, n_cols - 1, (v * lines_per_variable) + 1);
1452 show_comparisons (const struct oneway_spec *cmd, const struct oneway_workspace *ws, int v)
1454 const int n_cols = 8;
1455 const int heading_rows = 2;
1456 const int heading_cols = 3;
1459 int r = heading_rows ;
1461 const struct per_var_ws *pvw = &ws->vws[v];
1462 const struct categoricals *cat = pvw->cat;
1463 const int n_rows = heading_rows + cmd->n_posthoc * pvw->n_groups * (pvw->n_groups - 1);
1465 struct tab_table *t = tab_create (n_cols, n_rows);
1467 tab_headers (t, heading_cols, 0, heading_rows, 0);
1469 /* Put a frame around the entire box, and vertical lines inside */
1474 n_cols - 1, n_rows - 1);
1480 n_cols - 1, n_rows - 1);
1482 tab_vline (t, TAL_2, heading_cols, 0, n_rows - 1);
1484 tab_title (t, _("Multiple Comparisons"));
1486 tab_text_format (t, 1, 1, TAB_LEFT | TAT_TITLE, _("(I) %s"), var_to_string (cmd->indep_var));
1487 tab_text_format (t, 2, 1, TAB_LEFT | TAT_TITLE, _("(J) %s"), var_to_string (cmd->indep_var));
1488 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Mean Difference"));
1489 tab_text (t, 3, 1, TAB_CENTER | TAT_TITLE, _("(I - J)"));
1490 tab_text (t, 4, 1, TAB_CENTER | TAT_TITLE, _("Std. Error"));
1491 tab_text (t, 5, 1, TAB_CENTER | TAT_TITLE, _("Sig."));
1493 tab_joint_text_format (t, 6, 0, 7, 0, TAB_CENTER | TAT_TITLE,
1494 _("%g%% Confidence Interval"),
1495 (1 - cmd->alpha) * 100.0);
1497 tab_text (t, 6, 1, TAB_CENTER | TAT_TITLE, _("Lower Bound"));
1498 tab_text (t, 7, 1, TAB_CENTER | TAT_TITLE, _("Upper Bound"));
1501 for (p = 0; p < cmd->n_posthoc; ++p)
1504 const struct posthoc *ph = &ph_tests[cmd->posthoc[p]];
1506 tab_hline (t, TAL_2, 0, n_cols - 1, r);
1508 tab_text (t, 0, r, TAB_LEFT | TAT_TITLE, gettext (ph->label));
1510 for (i = 0; i < pvw->n_groups ; ++i)
1512 double weight_i, mean_i, var_i;
1516 struct descriptive_data *dd_i = categoricals_get_user_data_by_category (cat, i);
1517 const union value *gval = categoricals_get_value_by_category (cat, i);
1519 ds_init_empty (&vstr);
1520 var_append_value_name (cmd->indep_var, gval, &vstr);
1523 tab_hline (t, TAL_1, 1, n_cols - 1, r);
1524 tab_text (t, 1, r, TAB_LEFT | TAT_TITLE, ds_cstr (&vstr));
1526 moments1_calculate (dd_i->mom, &weight_i, &mean_i, &var_i, 0, 0);
1528 for (j = 0 ; j < pvw->n_groups; ++j)
1530 double weight_j, mean_j, var_j;
1532 struct descriptive_data *dd_j = categoricals_get_user_data_by_category (cat, j);
1537 gval = categoricals_get_value_by_category (cat, j);
1538 var_append_value_name (cmd->indep_var, gval, &vstr);
1539 tab_text (t, 2, r + rx, TAB_LEFT | TAT_TITLE, ds_cstr (&vstr));
1541 moments1_calculate (dd_j->mom, &weight_j, &mean_j, &var_j, 0, 0);
1543 tab_double (t, 3, r + rx, 0, mean_i - mean_j, 0);
1545 double std_err = pvw->mse;
1546 std_err *= weight_i + weight_j;
1547 std_err /= weight_i * weight_j;
1548 std_err = sqrt (std_err);
1550 tab_double (t, 4, r + rx, 0, std_err, 0);
1552 tab_double (t, 5, r + rx, 0, 2 * multiple_comparison_sig (std_err, pvw, dd_i, dd_j, ph), 0);
1554 half_range = mc_half_range (cmd, pvw, std_err, dd_i, dd_j, ph);
1556 tab_double (t, 6, r + rx, 0,
1557 (mean_i - mean_j) - half_range, 0 );
1559 tab_double (t, 7, r + rx, 0,
1560 (mean_i - mean_j) + half_range, 0 );
1565 r += pvw->n_groups - 1;