1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009 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 - Pearson's R (but not Spearman!) is off a little.
20 - T values for Spearman's R and Pearson's R are wrong.
21 - How to calculate significance of symmetric and directional measures?
22 - Asymmetric ASEs and T values for lambda are wrong.
23 - ASE of Goodman and Kruskal's tau is not calculated.
24 - ASE of symmetric somers' d is wrong.
25 - Approx. T of uncertainty coefficient is wrong.
32 #include <gsl/gsl_cdf.h>
36 #include <data/case.h>
37 #include <data/casegrouper.h>
38 #include <data/casereader.h>
39 #include <data/data-out.h>
40 #include <data/dictionary.h>
41 #include <data/format.h>
42 #include <data/procedure.h>
43 #include <data/value-labels.h>
44 #include <data/variable.h>
45 #include <language/command.h>
46 #include <language/dictionary/split-file.h>
47 #include <language/lexer/lexer.h>
48 #include <language/lexer/variable-parser.h>
49 #include <libpspp/array.h>
50 #include <libpspp/assertion.h>
51 #include <libpspp/compiler.h>
52 #include <libpspp/hash.h>
53 #include <libpspp/hmap.h>
54 #include <libpspp/hmapx.h>
55 #include <libpspp/message.h>
56 #include <libpspp/misc.h>
57 #include <libpspp/pool.h>
58 #include <libpspp/str.h>
59 #include <output/tab.h>
66 #define _(msgid) gettext (msgid)
67 #define N_(msgid) msgid
75 missing=miss:!table/include/report;
76 +write[wr_]=none,cells,all;
77 +format=fmt:!labels/nolabels/novallabs,
80 tabl:!tables/notables,
83 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
85 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
91 /* Number of chi-square statistics. */
94 /* Number of symmetric statistics. */
97 /* Number of directional statistics. */
98 #define N_DIRECTIONAL 13
100 /* A single table entry for general mode. */
103 struct hmap_node node; /* Entry in hash table. */
104 double freq; /* Frequency count. */
105 union value values[1]; /* Values. */
109 table_entry_size (size_t n_values)
111 return (offsetof (struct table_entry, values)
112 + n_values * sizeof (union value));
115 /* Indexes into the 'vars' member of struct pivot_table and
116 struct crosstab member. */
119 ROW_VAR = 0, /* Row variable. */
120 COL_VAR = 1 /* Column variable. */
121 /* Higher indexes cause multiple tables to be output. */
124 /* A crosstabulation of 2 or more variables. */
127 struct fmt_spec weight_format; /* Format for weight variable. */
128 double missing; /* Weight of missing cases. */
130 /* Variables (2 or more). */
132 const struct variable **vars;
134 /* Constants (0 or more). */
136 const struct variable **const_vars;
137 union value *const_values;
141 struct table_entry **entries;
144 /* Column values, number of columns. */
148 /* Row values, number of rows. */
152 /* Number of statistically interesting columns/rows
153 (columns/rows with data in them). */
154 int ns_cols, ns_rows;
156 /* Matrix contents. */
157 double *mat; /* Matrix proper. */
158 double *row_tot; /* Row totals. */
159 double *col_tot; /* Column totals. */
160 double total; /* Grand total. */
163 /* Integer mode variable info. */
166 int min; /* Minimum value. */
167 int max; /* Maximum value + 1. */
168 int count; /* max - min. */
171 static inline struct var_range *
172 get_var_range (const struct variable *v)
174 return var_get_aux (v);
177 struct crosstabs_proc
179 const struct dictionary *dict;
180 enum { INTEGER, GENERAL } mode;
181 enum mv_class exclude;
184 struct fmt_spec weight_format;
186 /* Variables specifies on VARIABLES. */
187 const struct variable **variables;
191 struct pivot_table *pivots;
195 int n_cells; /* Number of cells requested. */
196 unsigned int cells; /* Bit k is 1 if cell k is requested. */
197 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
200 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
204 init_proc (struct crosstabs_proc *proc, struct dataset *ds)
206 const struct variable *wv = dict_get_weight (dataset_dict (ds));
207 proc->dict = dataset_dict (ds);
208 proc->bad_warn = true;
209 proc->variables = NULL;
210 proc->n_variables = 0;
213 proc->weight_format = wv ? *var_get_print_format (wv) : F_8_0;
217 free_proc (struct crosstabs_proc *proc)
219 struct pivot_table *pt;
221 free (proc->variables);
222 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
225 free (pt->const_vars);
226 /* We must not call value_destroy on const_values because
227 it is a wild pointer; it never pointed to anything owned
230 The rest of the data was allocated and destroyed at a
231 lower level already. */
236 static int internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
237 struct crosstabs_proc *);
238 static bool should_tabulate_case (const struct pivot_table *,
239 const struct ccase *, enum mv_class exclude);
240 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
242 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
244 static void postcalc (struct crosstabs_proc *);
245 static void submit (struct pivot_table *, struct tab_table *);
247 /* Parse and execute CROSSTABS, then clean up. */
249 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
251 struct crosstabs_proc proc;
254 init_proc (&proc, ds);
255 result = internal_cmd_crosstabs (lexer, ds, &proc);
261 /* Parses and executes the CROSSTABS procedure. */
263 internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
264 struct crosstabs_proc *proc)
266 struct casegrouper *grouper;
267 struct casereader *input, *group;
268 struct cmd_crosstabs cmd;
269 struct pivot_table *pt;
273 if (!parse_crosstabs (lexer, ds, &cmd, proc))
276 proc->mode = proc->n_variables ? INTEGER : GENERAL;
280 proc->cells = 1u << CRS_CL_COUNT;
281 else if (cmd.a_cells[CRS_CL_ALL])
282 proc->cells = UINT_MAX;
286 for (i = 0; i < CRS_CL_count; i++)
288 proc->cells |= 1u << i;
289 if (proc->cells == 0)
290 proc->cells = ((1u << CRS_CL_COUNT)
292 | (1u << CRS_CL_COLUMN)
293 | (1u << CRS_CL_TOTAL));
295 proc->cells &= ((1u << CRS_CL_count) - 1);
296 proc->cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
298 for (i = 0; i < CRS_CL_count; i++)
299 if (proc->cells & (1u << i))
300 proc->a_cells[proc->n_cells++] = i;
303 if (cmd.a_statistics[CRS_ST_ALL])
304 proc->statistics = UINT_MAX;
305 else if (cmd.sbc_statistics)
309 proc->statistics = 0;
310 for (i = 0; i < CRS_ST_count; i++)
311 if (cmd.a_statistics[i])
312 proc->statistics |= 1u << i;
313 if (proc->statistics == 0)
314 proc->statistics |= 1u << CRS_ST_CHISQ;
317 proc->statistics = 0;
320 proc->exclude = (cmd.miss == CRS_TABLE ? MV_ANY
321 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
323 if (proc->mode == GENERAL && proc->mode == MV_NEVER)
325 msg (SE, _("Missing mode REPORT not allowed in general mode. "
326 "Assuming MISSING=TABLE."));
331 proc->pivot = cmd.pivot == CRS_PIVOT;
333 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
335 grouper = casegrouper_create_splits (input, dataset_dict (ds));
336 while (casegrouper_get_next_group (grouper, &group))
340 /* Output SPLIT FILE variables. */
341 c = casereader_peek (group, 0);
344 output_split_file_values (ds, c);
349 for (; (c = casereader_read (group)) != NULL; case_unref (c))
350 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
352 double weight = dict_get_case_weight (dataset_dict (ds), c,
354 if (should_tabulate_case (pt, c, proc->exclude))
356 if (proc->mode == GENERAL)
357 tabulate_general_case (pt, c, weight);
359 tabulate_integer_case (pt, c, weight);
362 pt->missing += weight;
364 casereader_destroy (group);
369 ok = casegrouper_destroy (grouper);
370 ok = proc_commit (ds) && ok;
372 return ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
375 /* Parses the TABLES subcommand. */
377 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
378 struct cmd_crosstabs *cmd UNUSED, void *proc_)
380 struct crosstabs_proc *proc = proc_;
381 struct const_var_set *var_set;
383 const struct variable ***by = NULL;
385 size_t *by_nvar = NULL;
390 /* Ensure that this is a TABLES subcommand. */
391 if (!lex_match_id (lexer, "TABLES")
392 && (lex_token (lexer) != T_ID ||
393 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
394 && lex_token (lexer) != T_ALL)
396 lex_match (lexer, '=');
398 if (proc->variables != NULL)
399 var_set = const_var_set_create_from_array (proc->variables,
402 var_set = const_var_set_create_from_dict (dataset_dict (ds));
403 assert (var_set != NULL);
407 by = xnrealloc (by, n_by + 1, sizeof *by);
408 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
409 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
410 PV_NO_DUPLICATE | PV_NO_SCRATCH))
412 if (xalloc_oversized (nx, by_nvar[n_by]))
414 msg (SE, _("Too many cross-tabulation variables or dimensions."));
420 if (!lex_match (lexer, T_BY))
424 lex_error (lexer, _("expecting BY"));
432 by_iter = xcalloc (n_by, sizeof *by_iter);
433 proc->pivots = xnrealloc (proc->pivots,
434 proc->n_pivots + nx, sizeof *proc->pivots);
435 for (i = 0; i < nx; i++)
437 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
440 pt->weight_format = proc->weight_format;
443 pt->vars = xmalloc (n_by * sizeof *pt->vars);
445 pt->const_vars = NULL;
446 pt->const_values = NULL;
447 hmap_init (&pt->data);
451 for (j = 0; j < n_by; j++)
452 pt->vars[j] = by[j][by_iter[j]];
454 for (j = n_by - 1; j >= 0; j--)
456 if (++by_iter[j] < by_nvar[j])
465 /* All return paths lead here. */
466 for (i = 0; i < n_by; i++)
471 const_var_set_destroy (var_set);
476 /* Parses the VARIABLES subcommand. */
478 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
479 struct cmd_crosstabs *cmd UNUSED, void *proc_)
481 struct crosstabs_proc *proc = proc_;
484 msg (SE, _("VARIABLES must be specified before TABLES."));
488 lex_match (lexer, '=');
492 size_t orig_nv = proc->n_variables;
497 if (!parse_variables_const (lexer, dataset_dict (ds),
498 &proc->variables, &proc->n_variables,
499 (PV_APPEND | PV_NUMERIC
500 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
503 if (lex_token (lexer) != '(')
505 lex_error (lexer, "expecting `('");
510 if (!lex_force_int (lexer))
512 min = lex_integer (lexer);
515 lex_match (lexer, ',');
517 if (!lex_force_int (lexer))
519 max = lex_integer (lexer);
522 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
528 if (lex_token (lexer) != ')')
530 lex_error (lexer, "expecting `)'");
535 for (i = orig_nv; i < proc->n_variables; i++)
537 struct var_range *vr = xmalloc (sizeof *vr);
540 vr->count = max - min + 1;
541 var_attach_aux (proc->variables[i], vr, var_dtor_free);
544 if (lex_token (lexer) == '/')
551 free (proc->variables);
552 proc->variables = NULL;
553 proc->n_variables = 0;
557 /* Data file processing. */
560 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
561 enum mv_class exclude)
564 for (j = 0; j < pt->n_vars; j++)
566 const struct variable *var = pt->vars[j];
567 struct var_range *range = get_var_range (var);
569 if (var_is_value_missing (var, case_data (c, var), exclude))
574 double num = case_num (c, var);
575 if (num < range->min || num > range->max)
583 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
586 struct table_entry *te;
591 for (j = 0; j < pt->n_vars; j++)
593 /* Throw away fractional parts of values. */
594 hash = hash_int (case_num (c, pt->vars[j]), hash);
597 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
599 for (j = 0; j < pt->n_vars; j++)
600 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
603 /* Found an existing entry. */
610 /* No existing entry. Create a new one. */
611 te = xmalloc (table_entry_size (pt->n_vars));
613 for (j = 0; j < pt->n_vars; j++)
614 te->values[j].f = (int) case_num (c, pt->vars[j]);
615 hmap_insert (&pt->data, &te->node, hash);
619 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
622 struct table_entry *te;
627 for (j = 0; j < pt->n_vars; j++)
629 const struct variable *var = pt->vars[j];
630 hash = value_hash (case_data (c, var), var_get_width (var), hash);
633 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
635 for (j = 0; j < pt->n_vars; j++)
637 const struct variable *var = pt->vars[j];
638 if (!value_equal (case_data (c, var), &te->values[j],
639 var_get_width (var)))
643 /* Found an existing entry. */
650 /* No existing entry. Create a new one. */
651 te = xmalloc (table_entry_size (pt->n_vars));
653 for (j = 0; j < pt->n_vars; j++)
655 const struct variable *var = pt->vars[j];
656 int width = var_get_width (var);
657 value_init (&te->values[j], width);
658 value_copy (&te->values[j], case_data (c, var), width);
660 hmap_insert (&pt->data, &te->node, hash);
663 /* Post-data reading calculations. */
665 static int compare_table_entry_vars_3way (const struct table_entry *a,
666 const struct table_entry *b,
667 const struct pivot_table *pt,
669 static int compare_table_entry_3way (const void *ap_, const void *bp_,
671 static void enum_var_values (const struct pivot_table *, int var_idx,
672 union value **valuesp, int *n_values);
673 static void output_pivot_table (struct crosstabs_proc *,
674 struct pivot_table *);
675 static void make_pivot_table_subset (struct pivot_table *pt,
676 size_t row0, size_t row1,
677 struct pivot_table *subset);
678 static void make_summary_table (struct crosstabs_proc *);
679 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
682 postcalc (struct crosstabs_proc *proc)
684 struct pivot_table *pt;
686 /* Convert hash tables into sorted arrays of entries. */
687 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
689 struct table_entry *e;
692 pt->n_entries = hmap_count (&pt->data);
693 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
695 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
696 pt->entries[i++] = e;
697 hmap_destroy (&pt->data);
699 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
700 compare_table_entry_3way, pt);
703 make_summary_table (proc);
705 /* Output each pivot table. */
706 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
708 if (proc->pivot || pt->n_vars == 2)
709 output_pivot_table (proc, pt);
712 size_t row0 = 0, row1 = 0;
713 while (find_crosstab (pt, &row0, &row1))
715 struct pivot_table subset;
716 make_pivot_table_subset (pt, row0, row1, &subset);
717 output_pivot_table (proc, &subset);
722 /* Free output and prepare for next split file. */
723 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
729 /* Free only the members that were allocated in this
730 function. The other pointer members are either both
731 allocated and destroyed at a lower level (in
732 output_pivot_table), or both allocated and destroyed at
733 a higher level (in crs_custom_tables and free_proc,
735 for (i = 0; i < pt->n_entries; i++)
736 free (pt->entries[i]);
742 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
743 struct pivot_table *subset)
748 assert (pt->n_consts == 0);
749 subset->missing = pt->missing;
751 subset->vars = pt->vars;
752 subset->n_consts = pt->n_vars - 2;
753 subset->const_vars = pt->vars + 2;
754 subset->const_values = &pt->entries[row0]->values[2];
756 subset->entries = &pt->entries[row0];
757 subset->n_entries = row1 - row0;
761 compare_table_entry_var_3way (const struct table_entry *a,
762 const struct table_entry *b,
763 const struct pivot_table *pt,
766 return value_compare_3way (&a->values[idx], &b->values[idx],
767 var_get_width (pt->vars[idx]));
771 compare_table_entry_vars_3way (const struct table_entry *a,
772 const struct table_entry *b,
773 const struct pivot_table *pt,
778 for (i = idx1 - 1; i >= idx0; i--)
780 int cmp = compare_table_entry_var_3way (a, b, pt, i);
787 /* Compare the struct table_entry at *AP to the one at *BP and
788 return a strcmp()-type result. */
790 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
792 const struct table_entry *const *ap = ap_;
793 const struct table_entry *const *bp = bp_;
794 const struct table_entry *a = *ap;
795 const struct table_entry *b = *bp;
796 const struct pivot_table *pt = pt_;
799 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
803 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
807 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
811 find_first_difference (const struct pivot_table *pt, size_t row)
814 return pt->n_vars - 1;
817 const struct table_entry *a = pt->entries[row];
818 const struct table_entry *b = pt->entries[row - 1];
821 for (col = pt->n_vars - 1; col >= 0; col--)
822 if (compare_table_entry_var_3way (a, b, pt, col))
828 /* Output a table summarizing the cases processed. */
830 make_summary_table (struct crosstabs_proc *proc)
832 struct tab_table *summary;
833 struct pivot_table *pt;
837 summary = tab_create (7, 3 + proc->n_pivots);
838 tab_title (summary, _("Summary."));
839 tab_headers (summary, 1, 0, 3, 0);
840 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
841 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
842 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
843 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
844 tab_hline (summary, TAL_1, 1, 6, 1);
845 tab_hline (summary, TAL_1, 1, 6, 2);
846 tab_vline (summary, TAL_1, 3, 1, 1);
847 tab_vline (summary, TAL_1, 5, 1, 1);
848 for (i = 0; i < 3; i++)
850 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
851 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
853 tab_offset (summary, 0, 3);
855 ds_init_empty (&name);
856 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
862 tab_hline (summary, TAL_1, 0, 6, 0);
865 for (i = 0; i < pt->n_vars; i++)
868 ds_put_cstr (&name, " * ");
869 ds_put_cstr (&name, var_to_string (pt->vars[i]));
871 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
874 for (i = 0; i < pt->n_entries; i++)
875 valid += pt->entries[i]->freq;
880 for (i = 0; i < 3; i++)
882 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
883 &proc->weight_format);
884 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
888 tab_next_row (summary);
892 submit (NULL, summary);
897 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
898 struct pivot_table *);
899 static struct tab_table *create_chisq_table (struct pivot_table *);
900 static struct tab_table *create_sym_table (struct pivot_table *);
901 static struct tab_table *create_risk_table (struct pivot_table *);
902 static struct tab_table *create_direct_table (struct pivot_table *);
903 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
904 struct tab_table *, int first_difference);
905 static void display_crosstabulation (struct crosstabs_proc *,
906 struct pivot_table *,
908 static void display_chisq (struct pivot_table *, struct tab_table *,
909 bool *showed_fisher);
910 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
912 static void display_risk (struct pivot_table *, struct tab_table *);
913 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
915 static void table_value_missing (struct crosstabs_proc *proc,
916 struct tab_table *table, int c, int r,
917 unsigned char opt, const union value *v,
918 const struct variable *var);
919 static void delete_missing (struct pivot_table *);
920 static void build_matrix (struct pivot_table *);
922 /* Output pivot table beginning at PB and continuing until PE,
923 exclusive. For efficiency, *MATP is a pointer to a matrix that can
924 hold *MAXROWS entries. */
926 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
928 struct tab_table *table = NULL; /* Crosstabulation table. */
929 struct tab_table *chisq = NULL; /* Chi-square table. */
930 bool showed_fisher = false;
931 struct tab_table *sym = NULL; /* Symmetric measures table. */
932 struct tab_table *risk = NULL; /* Risk estimate table. */
933 struct tab_table *direct = NULL; /* Directional measures table. */
936 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
939 table = create_crosstab_table (proc, pt);
940 if (proc->statistics & (1u << CRS_ST_CHISQ))
941 chisq = create_chisq_table (pt);
942 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
943 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
944 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
945 | (1u << CRS_ST_KAPPA)))
946 sym = create_sym_table (pt);
947 if (proc->statistics & (1u << CRS_ST_RISK))
948 risk = create_risk_table (pt);
949 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
950 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
951 direct = create_direct_table (pt);
954 while (find_crosstab (pt, &row0, &row1))
956 struct pivot_table x;
957 int first_difference;
959 make_pivot_table_subset (pt, row0, row1, &x);
961 /* Find all the row variable values. */
962 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
964 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
967 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
968 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
969 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
971 /* Allocate table space for the matrix. */
973 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
974 tab_realloc (table, -1,
975 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
976 tab_nr (table) * pt->n_entries / x.n_entries));
980 /* Find the first variable that differs from the last subtable. */
981 first_difference = find_first_difference (pt, row0);
984 display_dimensions (proc, &x, table, first_difference);
985 display_crosstabulation (proc, &x, table);
988 if (proc->exclude == MV_NEVER)
993 display_dimensions (proc, &x, chisq, first_difference);
994 display_chisq (&x, chisq, &showed_fisher);
998 display_dimensions (proc, &x, sym, first_difference);
999 display_symmetric (proc, &x, sym);
1003 display_dimensions (proc, &x, risk, first_difference);
1004 display_risk (&x, risk);
1008 display_dimensions (proc, &x, direct, first_difference);
1009 display_directional (proc, &x, direct);
1012 /* Free the parts of x that are not owned by pt. In
1013 particular we must not free x.cols, which is the same as
1014 pt->cols, which is freed at the end of this function. */
1022 submit (NULL, table);
1027 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1033 submit (pt, direct);
1039 build_matrix (struct pivot_table *x)
1041 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1042 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1045 struct table_entry **p;
1049 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1051 const struct table_entry *te = *p;
1053 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1055 for (; col < x->n_cols; col++)
1061 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1068 if (++col >= x->n_cols)
1074 while (mp < &x->mat[x->n_cols * x->n_rows])
1076 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1078 /* Column totals, row totals, ns_rows. */
1080 for (col = 0; col < x->n_cols; col++)
1081 x->col_tot[col] = 0.0;
1082 for (row = 0; row < x->n_rows; row++)
1083 x->row_tot[row] = 0.0;
1085 for (row = 0; row < x->n_rows; row++)
1087 bool row_is_empty = true;
1088 for (col = 0; col < x->n_cols; col++)
1092 row_is_empty = false;
1093 x->col_tot[col] += *mp;
1094 x->row_tot[row] += *mp;
1101 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1105 for (col = 0; col < x->n_cols; col++)
1106 for (row = 0; row < x->n_rows; row++)
1107 if (x->mat[col + row * x->n_cols] != 0.0)
1115 for (col = 0; col < x->n_cols; col++)
1116 x->total += x->col_tot[col];
1119 static struct tab_table *
1120 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1127 static const struct tuple names[] =
1129 {CRS_CL_COUNT, N_("count")},
1130 {CRS_CL_ROW, N_("row %")},
1131 {CRS_CL_COLUMN, N_("column %")},
1132 {CRS_CL_TOTAL, N_("total %")},
1133 {CRS_CL_EXPECTED, N_("expected")},
1134 {CRS_CL_RESIDUAL, N_("residual")},
1135 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1136 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1138 const int n_names = sizeof names / sizeof *names;
1139 const struct tuple *t;
1141 struct tab_table *table;
1142 struct string title;
1145 table = tab_create (pt->n_consts + 1 + pt->n_cols + 1,
1146 (pt->n_entries / pt->n_cols) * 3 / 2 * proc->n_cells + 10);
1147 tab_headers (table, pt->n_consts + 1, 0, 2, 0);
1149 /* First header line. */
1150 tab_joint_text (table, pt->n_consts + 1, 0,
1151 (pt->n_consts + 1) + (pt->n_cols - 1), 0,
1152 TAB_CENTER | TAT_TITLE, var_get_name (pt->vars[COL_VAR]));
1154 tab_hline (table, TAL_1, pt->n_consts + 1,
1155 pt->n_consts + 2 + pt->n_cols - 2, 1);
1157 /* Second header line. */
1158 for (i = 2; i < pt->n_consts + 2; i++)
1159 tab_joint_text (table, pt->n_consts + 2 - i - 1, 0,
1160 pt->n_consts + 2 - i - 1, 1,
1161 TAB_RIGHT | TAT_TITLE, var_to_string (pt->vars[i]));
1162 tab_text (table, pt->n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1163 var_get_name (pt->vars[ROW_VAR]));
1164 for (i = 0; i < pt->n_cols; i++)
1165 table_value_missing (proc, table, pt->n_consts + 2 + i - 1, 1, TAB_RIGHT,
1166 &pt->cols[i], pt->vars[COL_VAR]);
1167 tab_text (table, pt->n_consts + 2 + pt->n_cols - 1, 1, TAB_CENTER, _("Total"));
1169 tab_hline (table, TAL_1, 0, pt->n_consts + 2 + pt->n_cols - 1, 2);
1170 tab_vline (table, TAL_1, pt->n_consts + 2 + pt->n_cols - 1, 0, 1);
1173 ds_init_empty (&title);
1174 for (i = 0; i < pt->n_consts + 2; i++)
1177 ds_put_cstr (&title, " * ");
1178 ds_put_cstr (&title, var_get_name (pt->vars[i]));
1180 for (i = 0; i < pt->n_consts; i++)
1182 const struct variable *var = pt->const_vars[i];
1186 ds_put_format (&title, ", %s=", var_get_name (var));
1188 /* Insert the formatted value of the variable, then trim
1189 leading spaces in what was just inserted. */
1190 ofs = ds_length (&title);
1191 s = data_out (&pt->const_values[i], dict_get_encoding (proc->dict), var_get_print_format (var));
1192 ds_put_cstr (&title, s);
1194 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1198 ds_put_cstr (&title, " [");
1200 for (t = names; t < &names[n_names]; t++)
1201 if (proc->cells & (1u << t->value))
1204 ds_put_cstr (&title, ", ");
1205 ds_put_cstr (&title, gettext (t->name));
1207 ds_put_cstr (&title, "].");
1209 tab_title (table, "%s", ds_cstr (&title));
1210 ds_destroy (&title);
1212 tab_offset (table, 0, 2);
1216 static struct tab_table *
1217 create_chisq_table (struct pivot_table *pt)
1219 struct tab_table *chisq;
1221 chisq = tab_create (6 + (pt->n_vars - 2),
1222 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1223 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1225 tab_title (chisq, _("Chi-square tests."));
1227 tab_offset (chisq, pt->n_vars - 2, 0);
1228 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1229 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1230 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1231 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1232 _("Asymp. Sig. (2-sided)"));
1233 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1234 _("Exact Sig. (2-sided)"));
1235 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1236 _("Exact Sig. (1-sided)"));
1237 tab_offset (chisq, 0, 1);
1242 /* Symmetric measures. */
1243 static struct tab_table *
1244 create_sym_table (struct pivot_table *pt)
1246 struct tab_table *sym;
1248 sym = tab_create (6 + (pt->n_vars - 2),
1249 pt->n_entries / pt->n_cols * 7 + 10);
1250 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1251 tab_title (sym, _("Symmetric measures."));
1253 tab_offset (sym, pt->n_vars - 2, 0);
1254 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1255 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1256 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1257 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1258 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1259 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1260 tab_offset (sym, 0, 1);
1265 /* Risk estimate. */
1266 static struct tab_table *
1267 create_risk_table (struct pivot_table *pt)
1269 struct tab_table *risk;
1271 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1272 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1273 tab_title (risk, _("Risk estimate."));
1275 tab_offset (risk, pt->n_vars - 2, 0);
1276 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1277 _("95%% Confidence Interval"));
1278 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1279 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1280 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1281 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1282 tab_hline (risk, TAL_1, 2, 3, 1);
1283 tab_vline (risk, TAL_1, 2, 0, 1);
1284 tab_offset (risk, 0, 2);
1289 /* Directional measures. */
1290 static struct tab_table *
1291 create_direct_table (struct pivot_table *pt)
1293 struct tab_table *direct;
1295 direct = tab_create (7 + (pt->n_vars - 2),
1296 pt->n_entries / pt->n_cols * 7 + 10);
1297 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1298 tab_title (direct, _("Directional measures."));
1300 tab_offset (direct, pt->n_vars - 2, 0);
1301 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1302 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1303 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1304 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1305 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1306 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1307 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1308 tab_offset (direct, 0, 1);
1314 /* Delete missing rows and columns for statistical analysis when
1317 delete_missing (struct pivot_table *pt)
1321 for (r = 0; r < pt->n_rows; r++)
1322 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1324 for (c = 0; c < pt->n_cols; c++)
1325 pt->mat[c + r * pt->n_cols] = 0.;
1330 for (c = 0; c < pt->n_cols; c++)
1331 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1333 for (r = 0; r < pt->n_rows; r++)
1334 pt->mat[c + r * pt->n_cols] = 0.;
1339 /* Prepare table T for submission, and submit it. */
1341 submit (struct pivot_table *pt, struct tab_table *t)
1348 tab_resize (t, -1, 0);
1349 if (tab_nr (t) == tab_t (t))
1351 table_unref (&t->table);
1354 tab_offset (t, 0, 0);
1356 for (i = 2; i < pt->n_vars; i++)
1357 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1358 var_to_string (pt->vars[i]));
1359 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1360 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1362 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1364 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1370 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1372 size_t row0 = *row1p;
1375 if (row0 >= pt->n_entries)
1378 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1380 struct table_entry *a = pt->entries[row0];
1381 struct table_entry *b = pt->entries[row1];
1382 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1390 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1391 result. WIDTH_ points to an int which is either 0 for a
1392 numeric value or a string width for a string value. */
1394 compare_value_3way (const void *a_, const void *b_, const void *width_)
1396 const union value *a = a_;
1397 const union value *b = b_;
1398 const int *width = width_;
1400 return value_compare_3way (a, b, *width);
1403 /* Given an array of ENTRY_CNT table_entry structures starting at
1404 ENTRIES, creates a sorted list of the values that the variable
1405 with index VAR_IDX takes on. The values are returned as a
1406 malloc()'d array stored in *VALUES, with the number of values
1407 stored in *VALUE_CNT.
1410 enum_var_values (const struct pivot_table *pt, int var_idx,
1411 union value **valuesp, int *n_values)
1413 const struct variable *var = pt->vars[var_idx];
1414 struct var_range *range = get_var_range (var);
1415 union value *values;
1420 values = *valuesp = xnmalloc (range->count, sizeof *values);
1421 *n_values = range->count;
1422 for (i = 0; i < range->count; i++)
1423 values[i].f = range->min + i;
1427 int width = var_get_width (var);
1428 struct hmapx_node *node;
1429 const union value *iter;
1433 for (i = 0; i < pt->n_entries; i++)
1435 const struct table_entry *te = pt->entries[i];
1436 const union value *value = &te->values[var_idx];
1437 size_t hash = value_hash (value, width, 0);
1439 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1440 if (value_equal (iter, value, width))
1443 hmapx_insert (&set, (union value *) value, hash);
1448 *n_values = hmapx_count (&set);
1449 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1451 HMAPX_FOR_EACH (iter, node, &set)
1452 values[i++] = *iter;
1453 hmapx_destroy (&set);
1455 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1459 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1460 from V, displayed with print format spec from variable VAR. When
1461 in REPORT missing-value mode, missing values have an M appended. */
1463 table_value_missing (struct crosstabs_proc *proc,
1464 struct tab_table *table, int c, int r, unsigned char opt,
1465 const union value *v, const struct variable *var)
1467 const char *label = var_lookup_value_label (var, v);
1469 tab_text (table, c, r, TAB_LEFT, label);
1472 const struct fmt_spec *print = var_get_print_format (var);
1473 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1475 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1476 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1480 tab_value (table, c, r, opt, v, proc->dict, print);
1484 /* Draws a line across TABLE at the current row to indicate the most
1485 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1486 that changed, and puts the values that changed into the table. TB
1487 and PT must be the corresponding table_entry and crosstab,
1490 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1491 struct tab_table *table, int first_difference)
1493 tab_hline (table, TAL_1, pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1495 for (; first_difference >= 2; first_difference--)
1496 table_value_missing (proc, table, pt->n_vars - first_difference - 1, 0,
1497 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1498 pt->vars[first_difference]);
1501 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1502 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1503 additionally suffixed with a letter `M'. */
1505 format_cell_entry (struct tab_table *table, int c, int r, double value,
1506 char suffix, bool mark_missing, const struct dictionary *dict)
1508 const struct fmt_spec f = {FMT_F, 10, 1};
1515 s = data_out (&v, dict_get_encoding (dict), &f);
1519 suffixes[suffix_len++] = suffix;
1521 suffixes[suffix_len++] = 'M';
1522 suffixes[suffix_len] = '\0';
1524 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1525 s + strspn (s, " "), suffixes);
1528 /* Displays the crosstabulation table. */
1530 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1531 struct tab_table *table)
1537 for (r = 0; r < pt->n_rows; r++)
1538 table_value_missing (proc, table, pt->n_vars - 2, r * proc->n_cells,
1539 TAB_RIGHT, &pt->rows[r], pt->vars[ROW_VAR]);
1541 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1542 TAB_LEFT, _("Total"));
1544 /* Put in the actual cells. */
1546 tab_offset (table, pt->n_vars - 1, -1);
1547 for (r = 0; r < pt->n_rows; r++)
1549 if (proc->n_cells > 1)
1550 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1551 for (c = 0; c < pt->n_cols; c++)
1553 bool mark_missing = false;
1554 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1555 if (proc->exclude == MV_NEVER
1556 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1557 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1559 mark_missing = true;
1560 for (i = 0; i < proc->n_cells; i++)
1565 switch (proc->a_cells[i])
1571 v = *mp / pt->row_tot[r] * 100.;
1575 v = *mp / pt->col_tot[c] * 100.;
1579 v = *mp / pt->total * 100.;
1582 case CRS_CL_EXPECTED:
1585 case CRS_CL_RESIDUAL:
1586 v = *mp - expected_value;
1588 case CRS_CL_SRESIDUAL:
1589 v = (*mp - expected_value) / sqrt (expected_value);
1591 case CRS_CL_ASRESIDUAL:
1592 v = ((*mp - expected_value)
1593 / sqrt (expected_value
1594 * (1. - pt->row_tot[r] / pt->total)
1595 * (1. - pt->col_tot[c] / pt->total)));
1600 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1606 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1610 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1611 for (r = 0; r < pt->n_rows; r++)
1613 bool mark_missing = false;
1615 if (proc->exclude == MV_NEVER
1616 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1617 mark_missing = true;
1619 for (i = 0; i < proc->n_cells; i++)
1624 switch (proc->a_cells[i])
1634 v = pt->row_tot[r] / pt->total * 100.;
1638 v = pt->row_tot[r] / pt->total * 100.;
1641 case CRS_CL_EXPECTED:
1642 case CRS_CL_RESIDUAL:
1643 case CRS_CL_SRESIDUAL:
1644 case CRS_CL_ASRESIDUAL:
1651 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1652 tab_next_row (table);
1656 /* Column totals, grand total. */
1658 if (proc->n_cells > 1)
1659 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1660 for (c = 0; c <= pt->n_cols; c++)
1662 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1663 bool mark_missing = false;
1666 if (proc->exclude == MV_NEVER && c < pt->n_cols
1667 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1668 mark_missing = true;
1670 for (i = 0; i < proc->n_cells; i++)
1675 switch (proc->a_cells[i])
1681 v = ct / pt->total * 100.;
1689 v = ct / pt->total * 100.;
1692 case CRS_CL_EXPECTED:
1693 case CRS_CL_RESIDUAL:
1694 case CRS_CL_SRESIDUAL:
1695 case CRS_CL_ASRESIDUAL:
1701 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1706 tab_offset (table, -1, tab_row (table) + last_row);
1707 tab_offset (table, 0, -1);
1710 static void calc_r (struct pivot_table *,
1711 double *PT, double *Y, double *, double *, double *);
1712 static void calc_chisq (struct pivot_table *,
1713 double[N_CHISQ], int[N_CHISQ], double *, double *);
1715 /* Display chi-square statistics. */
1717 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1718 bool *showed_fisher)
1720 static const char *chisq_stats[N_CHISQ] =
1722 N_("Pearson Chi-Square"),
1723 N_("Likelihood Ratio"),
1724 N_("Fisher's Exact Test"),
1725 N_("Continuity Correction"),
1726 N_("Linear-by-Linear Association"),
1728 double chisq_v[N_CHISQ];
1729 double fisher1, fisher2;
1734 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1736 tab_offset (chisq, pt->n_vars - 2, -1);
1738 for (i = 0; i < N_CHISQ; i++)
1740 if ((i != 2 && chisq_v[i] == SYSMIS)
1741 || (i == 2 && fisher1 == SYSMIS))
1744 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1747 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1748 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1749 tab_double (chisq, 3, 0, TAB_RIGHT,
1750 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1754 *showed_fisher = true;
1755 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1756 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1758 tab_next_row (chisq);
1761 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1762 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1763 tab_next_row (chisq);
1765 tab_offset (chisq, 0, -1);
1768 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1769 double[N_SYMMETRIC], double[N_SYMMETRIC],
1770 double[N_SYMMETRIC],
1771 double[3], double[3], double[3]);
1773 /* Display symmetric measures. */
1775 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1776 struct tab_table *sym)
1778 static const char *categories[] =
1780 N_("Nominal by Nominal"),
1781 N_("Ordinal by Ordinal"),
1782 N_("Interval by Interval"),
1783 N_("Measure of Agreement"),
1786 static const char *stats[N_SYMMETRIC] =
1790 N_("Contingency Coefficient"),
1791 N_("Kendall's tau-b"),
1792 N_("Kendall's tau-c"),
1794 N_("Spearman Correlation"),
1799 static const int stats_categories[N_SYMMETRIC] =
1801 0, 0, 0, 1, 1, 1, 1, 2, 3,
1805 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1806 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1809 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1810 somers_d_v, somers_d_ase, somers_d_t))
1813 tab_offset (sym, pt->n_vars - 2, -1);
1815 for (i = 0; i < N_SYMMETRIC; i++)
1817 if (sym_v[i] == SYSMIS)
1820 if (stats_categories[i] != last_cat)
1822 last_cat = stats_categories[i];
1823 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1826 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1827 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1828 if (sym_ase[i] != SYSMIS)
1829 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1830 if (sym_t[i] != SYSMIS)
1831 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1832 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1836 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1837 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1840 tab_offset (sym, 0, -1);
1843 static int calc_risk (struct pivot_table *,
1844 double[], double[], double[], union value *);
1846 /* Display risk estimate. */
1848 display_risk (struct pivot_table *pt, struct tab_table *risk)
1851 double risk_v[3], lower[3], upper[3];
1855 if (!calc_risk (pt, risk_v, upper, lower, c))
1858 tab_offset (risk, pt->n_vars - 2, -1);
1860 for (i = 0; i < 3; i++)
1862 const struct variable *cv = pt->vars[COL_VAR];
1863 const struct variable *rv = pt->vars[ROW_VAR];
1864 int cvw = var_get_width (cv);
1865 int rvw = var_get_width (rv);
1867 if (risk_v[i] == SYSMIS)
1873 if (var_is_numeric (cv))
1874 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1875 var_get_name (cv), c[0].f, c[1].f);
1877 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1879 cvw, value_str (&c[0], cvw),
1880 cvw, value_str (&c[1], cvw));
1884 if (var_is_numeric (rv))
1885 sprintf (buf, _("For cohort %s = %g"),
1886 var_get_name (rv), pt->rows[i - 1].f);
1888 sprintf (buf, _("For cohort %s = %.*s"),
1890 rvw, value_str (&pt->rows[i - 1], rvw));
1894 tab_text (risk, 0, 0, TAB_LEFT, buf);
1895 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1896 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1897 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1898 tab_next_row (risk);
1901 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1902 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1903 tab_next_row (risk);
1905 tab_offset (risk, 0, -1);
1908 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1909 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1910 double[N_DIRECTIONAL]);
1912 /* Display directional measures. */
1914 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1915 struct tab_table *direct)
1917 static const char *categories[] =
1919 N_("Nominal by Nominal"),
1920 N_("Ordinal by Ordinal"),
1921 N_("Nominal by Interval"),
1924 static const char *stats[] =
1927 N_("Goodman and Kruskal tau"),
1928 N_("Uncertainty Coefficient"),
1933 static const char *types[] =
1940 static const int stats_categories[N_DIRECTIONAL] =
1942 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1945 static const int stats_stats[N_DIRECTIONAL] =
1947 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1950 static const int stats_types[N_DIRECTIONAL] =
1952 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
1955 static const int *stats_lookup[] =
1962 static const char **stats_names[] =
1974 double direct_v[N_DIRECTIONAL];
1975 double direct_ase[N_DIRECTIONAL];
1976 double direct_t[N_DIRECTIONAL];
1980 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
1983 tab_offset (direct, pt->n_vars - 2, -1);
1985 for (i = 0; i < N_DIRECTIONAL; i++)
1987 if (direct_v[i] == SYSMIS)
1993 for (j = 0; j < 3; j++)
1994 if (last[j] != stats_lookup[j][i])
1997 tab_hline (direct, TAL_1, j, 6, 0);
2002 int k = last[j] = stats_lookup[j][i];
2007 string = var_get_name (pt->vars[0]);
2009 string = var_get_name (pt->vars[1]);
2011 tab_text_format (direct, j, 0, TAB_LEFT,
2012 gettext (stats_names[j][k]), string);
2017 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2018 if (direct_ase[i] != SYSMIS)
2019 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2020 if (direct_t[i] != SYSMIS)
2021 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2022 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2023 tab_next_row (direct);
2026 tab_offset (direct, 0, -1);
2029 /* Statistical calculations. */
2031 /* Returns the value of the gamma (factorial) function for an integer
2034 gamma_int (double pt)
2039 for (i = 2; i < pt; i++)
2044 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2046 static inline double
2047 Pr (int a, int b, int c, int d)
2049 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2050 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2051 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2052 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2053 / gamma_int (a + b + c + d + 1.));
2056 /* Swap the contents of A and B. */
2058 swap (int *a, int *b)
2065 /* Calculate significance for Fisher's exact test as specified in
2066 _SPSS Statistical Algorithms_, Appendix 5. */
2068 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2072 if (MIN (c, d) < MIN (a, b))
2073 swap (&a, &c), swap (&b, &d);
2074 if (MIN (b, d) < MIN (a, c))
2075 swap (&a, &b), swap (&c, &d);
2079 swap (&a, &b), swap (&c, &d);
2081 swap (&a, &c), swap (&b, &d);
2085 for (pt = 0; pt <= a; pt++)
2086 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2088 *fisher2 = *fisher1;
2089 for (pt = 1; pt <= b; pt++)
2090 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2093 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2094 columns with values COLS and N_ROWS rows with values ROWS. Values
2095 in the matrix sum to pt->total. */
2097 calc_chisq (struct pivot_table *pt,
2098 double chisq[N_CHISQ], int df[N_CHISQ],
2099 double *fisher1, double *fisher2)
2103 chisq[0] = chisq[1] = 0.;
2104 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2105 *fisher1 = *fisher2 = SYSMIS;
2107 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2109 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2111 chisq[0] = chisq[1] = SYSMIS;
2115 for (r = 0; r < pt->n_rows; r++)
2116 for (c = 0; c < pt->n_cols; c++)
2118 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2119 const double freq = pt->mat[pt->n_cols * r + c];
2120 const double residual = freq - expected;
2122 chisq[0] += residual * residual / expected;
2124 chisq[1] += freq * log (expected / freq);
2135 /* Calculate Yates and Fisher exact test. */
2136 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2138 double f11, f12, f21, f22;
2144 for (i = j = 0; i < pt->n_cols; i++)
2145 if (pt->col_tot[i] != 0.)
2154 f11 = pt->mat[nz_cols[0]];
2155 f12 = pt->mat[nz_cols[1]];
2156 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2157 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2162 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2165 chisq[3] = (pt->total * pow2 (pt_)
2166 / (f11 + f12) / (f21 + f22)
2167 / (f11 + f21) / (f12 + f22));
2175 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2176 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2179 /* Calculate Mantel-Haenszel. */
2180 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2182 double r, ase_0, ase_1;
2183 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2185 chisq[4] = (pt->total - 1.) * r * r;
2190 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2191 ASE_1, and ase_0 into ASE_0. The row and column values must be
2192 passed in PT and Y. */
2194 calc_r (struct pivot_table *pt,
2195 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2197 double SX, SY, S, T;
2199 double sum_XYf, sum_X2Y2f;
2200 double sum_Xr, sum_X2r;
2201 double sum_Yc, sum_Y2c;
2204 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2205 for (j = 0; j < pt->n_cols; j++)
2207 double fij = pt->mat[j + i * pt->n_cols];
2208 double product = PT[i] * Y[j];
2209 double temp = fij * product;
2211 sum_X2Y2f += temp * product;
2214 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2216 sum_Xr += PT[i] * pt->row_tot[i];
2217 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2219 Xbar = sum_Xr / pt->total;
2221 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2223 sum_Yc += Y[i] * pt->col_tot[i];
2224 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2226 Ybar = sum_Yc / pt->total;
2228 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2229 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2230 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2233 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2238 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2239 for (j = 0; j < pt->n_cols; j++)
2241 double Xresid, Yresid;
2244 Xresid = PT[i] - Xbar;
2245 Yresid = Y[j] - Ybar;
2246 temp = (T * Xresid * Yresid
2248 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2249 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2254 *ase_1 = sqrt (s) / (T * T);
2258 /* Calculate symmetric statistics and their asymptotic standard
2259 errors. Returns 0 if none could be calculated. */
2261 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2262 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2263 double t[N_SYMMETRIC],
2264 double somers_d_v[3], double somers_d_ase[3],
2265 double somers_d_t[3])
2269 q = MIN (pt->ns_rows, pt->ns_cols);
2273 for (i = 0; i < N_SYMMETRIC; i++)
2274 v[i] = ase[i] = t[i] = SYSMIS;
2276 /* Phi, Cramer's V, contingency coefficient. */
2277 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2279 double Xp = 0.; /* Pearson chi-square. */
2282 for (r = 0; r < pt->n_rows; r++)
2283 for (c = 0; c < pt->n_cols; c++)
2285 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2286 const double freq = pt->mat[pt->n_cols * r + c];
2287 const double residual = freq - expected;
2289 Xp += residual * residual / expected;
2292 if (proc->statistics & (1u << CRS_ST_PHI))
2294 v[0] = sqrt (Xp / pt->total);
2295 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2297 if (proc->statistics & (1u << CRS_ST_CC))
2298 v[2] = sqrt (Xp / (Xp + pt->total));
2301 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2302 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2307 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2311 Dr = Dc = pow2 (pt->total);
2312 for (r = 0; r < pt->n_rows; r++)
2313 Dr -= pow2 (pt->row_tot[r]);
2314 for (c = 0; c < pt->n_cols; c++)
2315 Dc -= pow2 (pt->col_tot[c]);
2317 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2318 for (c = 0; c < pt->n_cols; c++)
2322 for (r = 0; r < pt->n_rows; r++)
2323 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2332 for (i = 0; i < pt->n_rows; i++)
2336 for (j = 1; j < pt->n_cols; j++)
2337 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2340 for (j = 1; j < pt->n_cols; j++)
2341 Dij += cum[j + (i - 1) * pt->n_cols];
2345 double fij = pt->mat[j + i * pt->n_cols];
2349 if (++j == pt->n_cols)
2351 assert (j < pt->n_cols);
2353 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2354 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2358 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2359 Dij -= cum[j + (i - 1) * pt->n_cols];
2365 if (proc->statistics & (1u << CRS_ST_BTAU))
2366 v[3] = (P - Q) / sqrt (Dr * Dc);
2367 if (proc->statistics & (1u << CRS_ST_CTAU))
2368 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2369 if (proc->statistics & (1u << CRS_ST_GAMMA))
2370 v[5] = (P - Q) / (P + Q);
2372 /* ASE for tau-b, tau-c, gamma. Calculations could be
2373 eliminated here, at expense of memory. */
2378 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2379 for (i = 0; i < pt->n_rows; i++)
2383 for (j = 1; j < pt->n_cols; j++)
2384 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2387 for (j = 1; j < pt->n_cols; j++)
2388 Dij += cum[j + (i - 1) * pt->n_cols];
2392 double fij = pt->mat[j + i * pt->n_cols];
2394 if (proc->statistics & (1u << CRS_ST_BTAU))
2396 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2397 + v[3] * (pt->row_tot[i] * Dc
2398 + pt->col_tot[j] * Dr));
2399 btau_cum += fij * temp * temp;
2403 const double temp = Cij - Dij;
2404 ctau_cum += fij * temp * temp;
2407 if (proc->statistics & (1u << CRS_ST_GAMMA))
2409 const double temp = Q * Cij - P * Dij;
2410 gamma_cum += fij * temp * temp;
2413 if (proc->statistics & (1u << CRS_ST_D))
2415 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2416 - (P - Q) * (pt->total - pt->row_tot[i]));
2417 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2418 - (Q - P) * (pt->total - pt->col_tot[j]));
2421 if (++j == pt->n_cols)
2423 assert (j < pt->n_cols);
2425 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2426 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2430 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2431 Dij -= cum[j + (i - 1) * pt->n_cols];
2437 btau_var = ((btau_cum
2438 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2440 if (proc->statistics & (1u << CRS_ST_BTAU))
2442 ase[3] = sqrt (btau_var);
2443 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2446 if (proc->statistics & (1u << CRS_ST_CTAU))
2448 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2449 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2450 t[4] = v[4] / ase[4];
2452 if (proc->statistics & (1u << CRS_ST_GAMMA))
2454 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2455 t[5] = v[5] / (2. / (P + Q)
2456 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2458 if (proc->statistics & (1u << CRS_ST_D))
2460 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2461 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2462 somers_d_t[0] = (somers_d_v[0]
2464 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2465 somers_d_v[1] = (P - Q) / Dc;
2466 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2467 somers_d_t[1] = (somers_d_v[1]
2469 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2470 somers_d_v[2] = (P - Q) / Dr;
2471 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2472 somers_d_t[2] = (somers_d_v[2]
2474 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2480 /* Spearman correlation, Pearson's r. */
2481 if (proc->statistics & (1u << CRS_ST_CORR))
2483 double *R = xmalloc (sizeof *R * pt->n_rows);
2484 double *C = xmalloc (sizeof *C * pt->n_cols);
2487 double y, t, c = 0., s = 0.;
2492 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2493 y = pt->row_tot[i] - c;
2497 if (++i == pt->n_rows)
2499 assert (i < pt->n_rows);
2504 double y, t, c = 0., s = 0.;
2509 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2510 y = pt->col_tot[j] - c;
2514 if (++j == pt->n_cols)
2516 assert (j < pt->n_cols);
2520 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2526 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2530 /* Cohen's kappa. */
2531 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2533 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2536 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2537 i < pt->ns_rows; i++, j++)
2541 while (pt->col_tot[j] == 0.)
2544 prod = pt->row_tot[i] * pt->col_tot[j];
2545 sum = pt->row_tot[i] + pt->col_tot[j];
2547 sum_fii += pt->mat[j + i * pt->n_cols];
2549 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2550 sum_riciri_ci += prod * sum;
2552 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2553 for (j = 0; j < pt->ns_cols; j++)
2555 double sum = pt->row_tot[i] + pt->col_tot[j];
2556 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2559 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2561 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2562 + sum_rici * sum_rici
2563 - pt->total * sum_riciri_ci)
2564 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2566 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2567 / pow2 (pow2 (pt->total) - sum_rici))
2568 + ((2. * (pt->total - sum_fii)
2569 * (2. * sum_fii * sum_rici
2570 - pt->total * sum_fiiri_ci))
2571 / cube (pow2 (pt->total) - sum_rici))
2572 + (pow2 (pt->total - sum_fii)
2573 * (pt->total * sum_fijri_ci2 - 4.
2574 * sum_rici * sum_rici)
2575 / pow4 (pow2 (pt->total) - sum_rici))));
2577 t[8] = v[8] / ase[8];
2584 /* Calculate risk estimate. */
2586 calc_risk (struct pivot_table *pt,
2587 double *value, double *upper, double *lower, union value *c)
2589 double f11, f12, f21, f22;
2595 for (i = 0; i < 3; i++)
2596 value[i] = upper[i] = lower[i] = SYSMIS;
2599 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2606 for (i = j = 0; i < pt->n_cols; i++)
2607 if (pt->col_tot[i] != 0.)
2616 f11 = pt->mat[nz_cols[0]];
2617 f12 = pt->mat[nz_cols[1]];
2618 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2619 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2621 c[0] = pt->cols[nz_cols[0]];
2622 c[1] = pt->cols[nz_cols[1]];
2625 value[0] = (f11 * f22) / (f12 * f21);
2626 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2627 lower[0] = value[0] * exp (-1.960 * v);
2628 upper[0] = value[0] * exp (1.960 * v);
2630 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2631 v = sqrt ((f12 / (f11 * (f11 + f12)))
2632 + (f22 / (f21 * (f21 + f22))));
2633 lower[1] = value[1] * exp (-1.960 * v);
2634 upper[1] = value[1] * exp (1.960 * v);
2636 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2637 v = sqrt ((f11 / (f12 * (f11 + f12)))
2638 + (f21 / (f22 * (f21 + f22))));
2639 lower[2] = value[2] * exp (-1.960 * v);
2640 upper[2] = value[2] * exp (1.960 * v);
2645 /* Calculate directional measures. */
2647 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2648 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2649 double t[N_DIRECTIONAL])
2654 for (i = 0; i < N_DIRECTIONAL; i++)
2655 v[i] = ase[i] = t[i] = SYSMIS;
2659 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2661 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2662 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2663 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2664 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2665 double sum_fim, sum_fmj;
2667 int rm_index, cm_index;
2670 /* Find maximum for each row and their sum. */
2671 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2673 double max = pt->mat[i * pt->n_cols];
2676 for (j = 1; j < pt->n_cols; j++)
2677 if (pt->mat[j + i * pt->n_cols] > max)
2679 max = pt->mat[j + i * pt->n_cols];
2683 sum_fim += fim[i] = max;
2684 fim_index[i] = index;
2687 /* Find maximum for each column. */
2688 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2690 double max = pt->mat[j];
2693 for (i = 1; i < pt->n_rows; i++)
2694 if (pt->mat[j + i * pt->n_cols] > max)
2696 max = pt->mat[j + i * pt->n_cols];
2700 sum_fmj += fmj[j] = max;
2701 fmj_index[j] = index;
2704 /* Find maximum row total. */
2705 rm = pt->row_tot[0];
2707 for (i = 1; i < pt->n_rows; i++)
2708 if (pt->row_tot[i] > rm)
2710 rm = pt->row_tot[i];
2714 /* Find maximum column total. */
2715 cm = pt->col_tot[0];
2717 for (j = 1; j < pt->n_cols; j++)
2718 if (pt->col_tot[j] > cm)
2720 cm = pt->col_tot[j];
2724 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2725 v[1] = (sum_fmj - rm) / (pt->total - rm);
2726 v[2] = (sum_fim - cm) / (pt->total - cm);
2728 /* ASE1 for Y given PT. */
2732 for (accum = 0., i = 0; i < pt->n_rows; i++)
2733 for (j = 0; j < pt->n_cols; j++)
2735 const int deltaj = j == cm_index;
2736 accum += (pt->mat[j + i * pt->n_cols]
2737 * pow2 ((j == fim_index[i])
2742 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2745 /* ASE0 for Y given PT. */
2749 for (accum = 0., i = 0; i < pt->n_rows; i++)
2750 if (cm_index != fim_index[i])
2751 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2752 + pt->mat[i * pt->n_cols + cm_index]);
2753 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2756 /* ASE1 for PT given Y. */
2760 for (accum = 0., i = 0; i < pt->n_rows; i++)
2761 for (j = 0; j < pt->n_cols; j++)
2763 const int deltaj = i == rm_index;
2764 accum += (pt->mat[j + i * pt->n_cols]
2765 * pow2 ((i == fmj_index[j])
2770 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2773 /* ASE0 for PT given Y. */
2777 for (accum = 0., j = 0; j < pt->n_cols; j++)
2778 if (rm_index != fmj_index[j])
2779 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2780 + pt->mat[j + pt->n_cols * rm_index]);
2781 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2784 /* Symmetric ASE0 and ASE1. */
2789 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2790 for (j = 0; j < pt->n_cols; j++)
2792 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2793 int temp1 = (i == rm_index) + (j == cm_index);
2794 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2795 accum1 += (pt->mat[j + i * pt->n_cols]
2796 * pow2 (temp0 + (v[0] - 1.) * temp1));
2798 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2799 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2800 / (2. * pt->total - rm - cm));
2809 double sum_fij2_ri, sum_fij2_ci;
2810 double sum_ri2, sum_cj2;
2812 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2813 for (j = 0; j < pt->n_cols; j++)
2815 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2816 sum_fij2_ri += temp / pt->row_tot[i];
2817 sum_fij2_ci += temp / pt->col_tot[j];
2820 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2821 sum_ri2 += pow2 (pt->row_tot[i]);
2823 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2824 sum_cj2 += pow2 (pt->col_tot[j]);
2826 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2827 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2831 if (proc->statistics & (1u << CRS_ST_UC))
2833 double UX, UY, UXY, P;
2834 double ase1_yx, ase1_xy, ase1_sym;
2837 for (UX = 0., i = 0; i < pt->n_rows; i++)
2838 if (pt->row_tot[i] > 0.)
2839 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2841 for (UY = 0., j = 0; j < pt->n_cols; j++)
2842 if (pt->col_tot[j] > 0.)
2843 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2845 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2846 for (j = 0; j < pt->n_cols; j++)
2848 double entry = pt->mat[j + i * pt->n_cols];
2853 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2854 UXY -= entry / pt->total * log (entry / pt->total);
2857 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2858 for (j = 0; j < pt->n_cols; j++)
2860 double entry = pt->mat[j + i * pt->n_cols];
2865 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2866 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2867 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2868 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2869 ase1_sym += entry * pow2 ((UXY
2870 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2871 - (UX + UY) * log (entry / pt->total));
2874 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2875 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2876 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2877 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2879 v[6] = (UX + UY - UXY) / UX;
2880 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2881 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2883 v[7] = (UX + UY - UXY) / UY;
2884 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2885 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2889 if (proc->statistics & (1u << CRS_ST_D))
2891 double v_dummy[N_SYMMETRIC];
2892 double ase_dummy[N_SYMMETRIC];
2893 double t_dummy[N_SYMMETRIC];
2894 double somers_d_v[3];
2895 double somers_d_ase[3];
2896 double somers_d_t[3];
2898 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2899 somers_d_v, somers_d_ase, somers_d_t))
2902 for (i = 0; i < 3; i++)
2904 v[8 + i] = somers_d_v[i];
2905 ase[8 + i] = somers_d_ase[i];
2906 t[8 + i] = somers_d_t[i];
2912 if (proc->statistics & (1u << CRS_ST_ETA))
2915 double sum_Xr, sum_X2r;
2919 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2921 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2922 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2924 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2926 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2930 for (cum = 0., i = 0; i < pt->n_rows; i++)
2932 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2933 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2936 SXW -= cum * cum / pt->col_tot[j];
2938 v[11] = sqrt (1. - SXW / SX);
2942 double sum_Yc, sum_Y2c;
2946 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2948 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2949 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2951 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
2953 for (SYW = 0., i = 0; i < pt->n_rows; i++)
2957 for (cum = 0., j = 0; j < pt->n_cols; j++)
2959 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
2960 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
2963 SYW -= cum * cum / pt->row_tot[i];
2965 v[12] = sqrt (1. - SYW / SY);