1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012 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/dataset.h"
41 #include "data/dictionary.h"
42 #include "data/format.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-functions.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"
61 #include "gl/minmax.h"
62 #include "gl/xalloc.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=val:!avalue/dvalue,
79 tabl:!tables/notables,
82 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
84 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
90 /* Number of chi-square statistics. */
93 /* Number of symmetric statistics. */
96 /* Number of directional statistics. */
97 #define N_DIRECTIONAL 13
99 /* A single table entry for general mode. */
102 struct hmap_node node; /* Entry in hash table. */
103 double freq; /* Frequency count. */
104 union value values[1]; /* Values. */
108 table_entry_size (size_t n_values)
110 return (offsetof (struct table_entry, values)
111 + n_values * sizeof (union value));
114 /* Indexes into the 'vars' member of struct pivot_table and
115 struct crosstab member. */
118 ROW_VAR = 0, /* Row variable. */
119 COL_VAR = 1 /* Column variable. */
120 /* Higher indexes cause multiple tables to be output. */
123 /* A crosstabulation of 2 or more variables. */
126 struct crosstabs_proc *proc;
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 struct hmap_node hmap_node; /* In struct crosstabs_proc var_ranges map. */
167 const struct variable *var; /* The variable. */
168 int min; /* Minimum value. */
169 int max; /* Maximum value + 1. */
170 int count; /* max - min. */
173 struct crosstabs_proc
175 const struct dictionary *dict;
176 enum { INTEGER, GENERAL } mode;
177 enum mv_class exclude;
180 struct fmt_spec weight_format;
182 /* Variables specifies on VARIABLES. */
183 const struct variable **variables;
185 struct hmap var_ranges;
188 struct pivot_table *pivots;
192 int n_cells; /* Number of cells requested. */
193 unsigned int cells; /* Bit k is 1 if cell k is requested. */
194 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
197 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
199 bool descending; /* True if descending sort order is requested. */
202 const struct var_range *get_var_range (const struct crosstabs_proc *,
203 const struct variable *);
205 static bool should_tabulate_case (const struct pivot_table *,
206 const struct ccase *, enum mv_class exclude);
207 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
209 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
211 static void postcalc (struct crosstabs_proc *);
212 static void submit (struct pivot_table *, struct tab_table *);
214 /* Parses and executes the CROSSTABS procedure. */
216 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
218 const struct variable *wv = dict_get_weight (dataset_dict (ds));
219 struct var_range *range, *next_range;
220 struct crosstabs_proc proc;
221 struct casegrouper *grouper;
222 struct casereader *input, *group;
223 struct cmd_crosstabs cmd;
224 struct pivot_table *pt;
229 proc.dict = dataset_dict (ds);
230 proc.bad_warn = true;
231 proc.variables = NULL;
232 proc.n_variables = 0;
233 hmap_init (&proc.var_ranges);
236 proc.descending = false;
237 proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
239 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
241 result = CMD_FAILURE;
245 proc.mode = proc.n_variables ? INTEGER : GENERAL;
248 proc.descending = cmd.val == CRS_DVALUE;
252 proc.cells = 1u << CRS_CL_COUNT;
253 else if (cmd.a_cells[CRS_CL_ALL])
254 proc.cells = UINT_MAX;
258 for (i = 0; i < CRS_CL_count; i++)
260 proc.cells |= 1u << i;
262 proc.cells = ((1u << CRS_CL_COUNT)
264 | (1u << CRS_CL_COLUMN)
265 | (1u << CRS_CL_TOTAL));
267 proc.cells &= ((1u << CRS_CL_count) - 1);
268 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
270 for (i = 0; i < CRS_CL_count; i++)
271 if (proc.cells & (1u << i))
272 proc.a_cells[proc.n_cells++] = i;
275 if (cmd.a_statistics[CRS_ST_ALL])
276 proc.statistics = UINT_MAX;
277 else if (cmd.sbc_statistics)
282 for (i = 0; i < CRS_ST_count; i++)
283 if (cmd.a_statistics[i])
284 proc.statistics |= 1u << i;
285 if (proc.statistics == 0)
286 proc.statistics |= 1u << CRS_ST_CHISQ;
292 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
293 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
295 if (proc.mode == GENERAL && proc.exclude == MV_NEVER)
297 msg (SE, _("Missing mode REPORT not allowed in general mode. "
298 "Assuming MISSING=TABLE."));
299 proc.exclude = MV_ANY;
303 proc.pivot = cmd.pivot == CRS_PIVOT;
305 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
307 grouper = casegrouper_create_splits (input, dataset_dict (ds));
308 while (casegrouper_get_next_group (grouper, &group))
312 /* Output SPLIT FILE variables. */
313 c = casereader_peek (group, 0);
316 output_split_file_values (ds, c);
320 /* Initialize hash tables. */
321 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
322 hmap_init (&pt->data);
325 for (; (c = casereader_read (group)) != NULL; case_unref (c))
326 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
328 double weight = dict_get_case_weight (dataset_dict (ds), c,
330 if (should_tabulate_case (pt, c, proc.exclude))
332 if (proc.mode == GENERAL)
333 tabulate_general_case (pt, c, weight);
335 tabulate_integer_case (pt, c, weight);
338 pt->missing += weight;
340 casereader_destroy (group);
345 ok = casegrouper_destroy (grouper);
346 ok = proc_commit (ds) && ok;
348 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
351 free (proc.variables);
352 HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
355 hmap_delete (&proc.var_ranges, &range->hmap_node);
358 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
361 free (pt->const_vars);
362 /* We must not call value_destroy on const_values because
363 it is a wild pointer; it never pointed to anything owned
366 The rest of the data was allocated and destroyed at a
367 lower level already. */
374 /* Parses the TABLES subcommand. */
376 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
377 struct cmd_crosstabs *cmd UNUSED, void *proc_)
379 struct crosstabs_proc *proc = proc_;
380 struct const_var_set *var_set;
382 const struct variable ***by = NULL;
384 size_t *by_nvar = NULL;
389 /* Ensure that this is a TABLES subcommand. */
390 if (!lex_match_id (lexer, "TABLES")
391 && (lex_token (lexer) != T_ID ||
392 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
393 && lex_token (lexer) != T_ALL)
395 lex_match (lexer, T_EQUALS);
397 if (proc->variables != NULL)
398 var_set = const_var_set_create_from_array (proc->variables,
401 var_set = const_var_set_create_from_dict (dataset_dict (ds));
402 assert (var_set != NULL);
406 by = xnrealloc (by, n_by + 1, sizeof *by);
407 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
408 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
409 PV_NO_DUPLICATE | PV_NO_SCRATCH))
411 if (xalloc_oversized (nx, by_nvar[n_by]))
413 msg (SE, _("Too many cross-tabulation variables or dimensions."));
419 if (!lex_match (lexer, T_BY))
423 lex_force_match (lexer, T_BY);
431 by_iter = xcalloc (n_by, sizeof *by_iter);
432 proc->pivots = xnrealloc (proc->pivots,
433 proc->n_pivots + nx, sizeof *proc->pivots);
434 for (i = 0; i < nx; i++)
436 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;
448 for (j = 0; j < n_by; j++)
449 pt->vars[j] = by[j][by_iter[j]];
451 for (j = n_by - 1; j >= 0; j--)
453 if (++by_iter[j] < by_nvar[j])
462 /* All return paths lead here. */
463 for (i = 0; i < n_by; i++)
468 const_var_set_destroy (var_set);
473 /* Parses the VARIABLES subcommand. */
475 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
476 struct cmd_crosstabs *cmd UNUSED, void *proc_)
478 struct crosstabs_proc *proc = proc_;
481 msg (SE, _("VARIABLES must be specified before TABLES."));
485 lex_match (lexer, T_EQUALS);
489 size_t orig_nv = proc->n_variables;
494 if (!parse_variables_const (lexer, dataset_dict (ds),
495 &proc->variables, &proc->n_variables,
496 (PV_APPEND | PV_NUMERIC
497 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
500 if (!lex_force_match (lexer, T_LPAREN))
503 if (!lex_force_int (lexer))
505 min = lex_integer (lexer);
508 lex_match (lexer, T_COMMA);
510 if (!lex_force_int (lexer))
512 max = lex_integer (lexer);
515 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
521 if (!lex_force_match (lexer, T_RPAREN))
524 for (i = orig_nv; i < proc->n_variables; i++)
526 const struct variable *var = proc->variables[i];
527 struct var_range *vr = xmalloc (sizeof *vr);
532 vr->count = max - min + 1;
533 hmap_insert (&proc->var_ranges, &vr->hmap_node,
534 hash_pointer (var, 0));
537 if (lex_token (lexer) == T_SLASH)
544 free (proc->variables);
545 proc->variables = NULL;
546 proc->n_variables = 0;
550 /* Data file processing. */
552 const struct var_range *
553 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
555 if (!hmap_is_empty (&proc->var_ranges))
557 const struct var_range *range;
559 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
560 hash_pointer (var, 0), &proc->var_ranges)
561 if (range->var == var)
569 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
570 enum mv_class exclude)
573 for (j = 0; j < pt->n_vars; j++)
575 const struct variable *var = pt->vars[j];
576 const struct var_range *range = get_var_range (pt->proc, var);
578 if (var_is_value_missing (var, case_data (c, var), exclude))
583 double num = case_num (c, var);
584 if (num < range->min || num > range->max)
592 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
595 struct table_entry *te;
600 for (j = 0; j < pt->n_vars; j++)
602 /* Throw away fractional parts of values. */
603 hash = hash_int (case_num (c, pt->vars[j]), hash);
606 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
608 for (j = 0; j < pt->n_vars; j++)
609 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
612 /* Found an existing entry. */
619 /* No existing entry. Create a new one. */
620 te = xmalloc (table_entry_size (pt->n_vars));
622 for (j = 0; j < pt->n_vars; j++)
623 te->values[j].f = (int) case_num (c, pt->vars[j]);
624 hmap_insert (&pt->data, &te->node, hash);
628 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
631 struct table_entry *te;
636 for (j = 0; j < pt->n_vars; j++)
638 const struct variable *var = pt->vars[j];
639 hash = value_hash (case_data (c, var), var_get_width (var), hash);
642 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
644 for (j = 0; j < pt->n_vars; j++)
646 const struct variable *var = pt->vars[j];
647 if (!value_equal (case_data (c, var), &te->values[j],
648 var_get_width (var)))
652 /* Found an existing entry. */
659 /* No existing entry. Create a new one. */
660 te = xmalloc (table_entry_size (pt->n_vars));
662 for (j = 0; j < pt->n_vars; j++)
664 const struct variable *var = pt->vars[j];
665 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
667 hmap_insert (&pt->data, &te->node, hash);
670 /* Post-data reading calculations. */
672 static int compare_table_entry_vars_3way (const struct table_entry *a,
673 const struct table_entry *b,
674 const struct pivot_table *pt,
676 static int compare_table_entry_3way (const void *ap_, const void *bp_,
678 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
681 static void enum_var_values (const struct pivot_table *, int var_idx,
682 union value **valuesp, int *n_values, bool descending);
683 static void output_pivot_table (struct crosstabs_proc *,
684 struct pivot_table *);
685 static void make_pivot_table_subset (struct pivot_table *pt,
686 size_t row0, size_t row1,
687 struct pivot_table *subset);
688 static void make_summary_table (struct crosstabs_proc *);
689 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
692 postcalc (struct crosstabs_proc *proc)
694 struct pivot_table *pt;
696 /* Convert hash tables into sorted arrays of entries. */
697 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
699 struct table_entry *e;
702 pt->n_entries = hmap_count (&pt->data);
703 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
705 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
706 pt->entries[i++] = e;
707 hmap_destroy (&pt->data);
709 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
710 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
714 make_summary_table (proc);
716 /* Output each pivot table. */
717 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
719 if (proc->pivot || pt->n_vars == 2)
720 output_pivot_table (proc, pt);
723 size_t row0 = 0, row1 = 0;
724 while (find_crosstab (pt, &row0, &row1))
726 struct pivot_table subset;
727 make_pivot_table_subset (pt, row0, row1, &subset);
728 output_pivot_table (proc, &subset);
733 /* Free output and prepare for next split file. */
734 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
740 /* Free only the members that were allocated in this
741 function. The other pointer members are either both
742 allocated and destroyed at a lower level (in
743 output_pivot_table), or both allocated and destroyed at
744 a higher level (in crs_custom_tables and free_proc,
746 for (i = 0; i < pt->n_entries; i++)
747 free (pt->entries[i]);
753 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
754 struct pivot_table *subset)
759 assert (pt->n_consts == 0);
760 subset->missing = pt->missing;
762 subset->vars = pt->vars;
763 subset->n_consts = pt->n_vars - 2;
764 subset->const_vars = pt->vars + 2;
765 subset->const_values = &pt->entries[row0]->values[2];
767 subset->entries = &pt->entries[row0];
768 subset->n_entries = row1 - row0;
772 compare_table_entry_var_3way (const struct table_entry *a,
773 const struct table_entry *b,
774 const struct pivot_table *pt,
777 return value_compare_3way (&a->values[idx], &b->values[idx],
778 var_get_width (pt->vars[idx]));
782 compare_table_entry_vars_3way (const struct table_entry *a,
783 const struct table_entry *b,
784 const struct pivot_table *pt,
789 for (i = idx1 - 1; i >= idx0; i--)
791 int cmp = compare_table_entry_var_3way (a, b, pt, i);
798 /* Compare the struct table_entry at *AP to the one at *BP and
799 return a strcmp()-type result. */
801 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
803 const struct table_entry *const *ap = ap_;
804 const struct table_entry *const *bp = bp_;
805 const struct table_entry *a = *ap;
806 const struct table_entry *b = *bp;
807 const struct pivot_table *pt = pt_;
810 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
814 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
818 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
821 /* Inverted version of compare_table_entry_3way */
823 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *pt_)
825 return -compare_table_entry_3way (ap_, bp_, pt_);
829 find_first_difference (const struct pivot_table *pt, size_t row)
832 return pt->n_vars - 1;
835 const struct table_entry *a = pt->entries[row];
836 const struct table_entry *b = pt->entries[row - 1];
839 for (col = pt->n_vars - 1; col >= 0; col--)
840 if (compare_table_entry_var_3way (a, b, pt, col))
846 /* Output a table summarizing the cases processed. */
848 make_summary_table (struct crosstabs_proc *proc)
850 struct tab_table *summary;
851 struct pivot_table *pt;
855 summary = tab_create (7, 3 + proc->n_pivots);
856 tab_title (summary, _("Summary."));
857 tab_headers (summary, 1, 0, 3, 0);
858 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
859 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
860 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
861 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
862 tab_hline (summary, TAL_1, 1, 6, 1);
863 tab_hline (summary, TAL_1, 1, 6, 2);
864 tab_vline (summary, TAL_1, 3, 1, 1);
865 tab_vline (summary, TAL_1, 5, 1, 1);
866 for (i = 0; i < 3; i++)
868 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
869 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
871 tab_offset (summary, 0, 3);
873 ds_init_empty (&name);
874 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
880 tab_hline (summary, TAL_1, 0, 6, 0);
883 for (i = 0; i < pt->n_vars; i++)
886 ds_put_cstr (&name, " * ");
887 ds_put_cstr (&name, var_to_string (pt->vars[i]));
889 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
892 for (i = 0; i < pt->n_entries; i++)
893 valid += pt->entries[i]->freq;
898 for (i = 0; i < 3; i++)
900 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
901 &proc->weight_format);
902 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
906 tab_next_row (summary);
910 submit (NULL, summary);
915 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
916 struct pivot_table *);
917 static struct tab_table *create_chisq_table (struct pivot_table *);
918 static struct tab_table *create_sym_table (struct pivot_table *);
919 static struct tab_table *create_risk_table (struct pivot_table *);
920 static struct tab_table *create_direct_table (struct pivot_table *);
921 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
922 struct tab_table *, int first_difference);
923 static void display_crosstabulation (struct crosstabs_proc *,
924 struct pivot_table *,
926 static void display_chisq (struct pivot_table *, struct tab_table *,
927 bool *showed_fisher);
928 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
930 static void display_risk (struct pivot_table *, struct tab_table *);
931 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
933 static void table_value_missing (struct crosstabs_proc *proc,
934 struct tab_table *table, int c, int r,
935 unsigned char opt, const union value *v,
936 const struct variable *var);
937 static void delete_missing (struct pivot_table *);
938 static void build_matrix (struct pivot_table *);
940 /* Output pivot table PT in the context of PROC. */
942 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
944 struct tab_table *table = NULL; /* Crosstabulation table. */
945 struct tab_table *chisq = NULL; /* Chi-square table. */
946 bool showed_fisher = false;
947 struct tab_table *sym = NULL; /* Symmetric measures table. */
948 struct tab_table *risk = NULL; /* Risk estimate table. */
949 struct tab_table *direct = NULL; /* Directional measures table. */
952 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols, proc->descending);
959 ds_init_cstr (&vars, var_to_string (pt->vars[0]));
960 for (i = 1; i < pt->n_vars; i++)
961 ds_put_format (&vars, " * %s", var_to_string (pt->vars[i]));
963 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
964 form "var1 * var2 * var3 * ...". */
965 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
973 table = create_crosstab_table (proc, pt);
974 if (proc->statistics & (1u << CRS_ST_CHISQ))
975 chisq = create_chisq_table (pt);
976 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
977 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
978 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
979 | (1u << CRS_ST_KAPPA)))
980 sym = create_sym_table (pt);
981 if (proc->statistics & (1u << CRS_ST_RISK))
982 risk = create_risk_table (pt);
983 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
984 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
985 direct = create_direct_table (pt);
988 while (find_crosstab (pt, &row0, &row1))
990 struct pivot_table x;
991 int first_difference;
993 make_pivot_table_subset (pt, row0, row1, &x);
995 /* Find all the row variable values. */
996 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows, proc->descending);
998 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
1001 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
1002 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
1003 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
1005 /* Allocate table space for the matrix. */
1007 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
1008 tab_realloc (table, -1,
1009 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
1010 tab_nr (table) * pt->n_entries / x.n_entries));
1014 /* Find the first variable that differs from the last subtable. */
1015 first_difference = find_first_difference (pt, row0);
1018 display_dimensions (proc, &x, table, first_difference);
1019 display_crosstabulation (proc, &x, table);
1022 if (proc->exclude == MV_NEVER)
1023 delete_missing (&x);
1027 display_dimensions (proc, &x, chisq, first_difference);
1028 display_chisq (&x, chisq, &showed_fisher);
1032 display_dimensions (proc, &x, sym, first_difference);
1033 display_symmetric (proc, &x, sym);
1037 display_dimensions (proc, &x, risk, first_difference);
1038 display_risk (&x, risk);
1042 display_dimensions (proc, &x, direct, first_difference);
1043 display_directional (proc, &x, direct);
1046 /* Free the parts of x that are not owned by pt. In
1047 particular we must not free x.cols, which is the same as
1048 pt->cols, which is freed at the end of this function. */
1056 submit (NULL, table);
1061 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1067 submit (pt, direct);
1073 build_matrix (struct pivot_table *x)
1075 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1076 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1079 struct table_entry **p;
1083 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1085 const struct table_entry *te = *p;
1087 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1089 for (; col < x->n_cols; col++)
1095 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1102 if (++col >= x->n_cols)
1108 while (mp < &x->mat[x->n_cols * x->n_rows])
1110 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1112 /* Column totals, row totals, ns_rows. */
1114 for (col = 0; col < x->n_cols; col++)
1115 x->col_tot[col] = 0.0;
1116 for (row = 0; row < x->n_rows; row++)
1117 x->row_tot[row] = 0.0;
1119 for (row = 0; row < x->n_rows; row++)
1121 bool row_is_empty = true;
1122 for (col = 0; col < x->n_cols; col++)
1126 row_is_empty = false;
1127 x->col_tot[col] += *mp;
1128 x->row_tot[row] += *mp;
1135 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1139 for (col = 0; col < x->n_cols; col++)
1140 for (row = 0; row < x->n_rows; row++)
1141 if (x->mat[col + row * x->n_cols] != 0.0)
1149 for (col = 0; col < x->n_cols; col++)
1150 x->total += x->col_tot[col];
1153 static struct tab_table *
1154 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1161 static const struct tuple names[] =
1163 {CRS_CL_COUNT, N_("count")},
1164 {CRS_CL_ROW, N_("row %")},
1165 {CRS_CL_COLUMN, N_("column %")},
1166 {CRS_CL_TOTAL, N_("total %")},
1167 {CRS_CL_EXPECTED, N_("expected")},
1168 {CRS_CL_RESIDUAL, N_("residual")},
1169 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1170 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1172 const int n_names = sizeof names / sizeof *names;
1173 const struct tuple *t;
1175 struct tab_table *table;
1176 struct string title;
1177 struct pivot_table x;
1181 make_pivot_table_subset (pt, 0, 0, &x);
1183 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1184 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1185 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1187 /* First header line. */
1188 tab_joint_text (table, x.n_consts + 1, 0,
1189 (x.n_consts + 1) + (x.n_cols - 1), 0,
1190 TAB_CENTER | TAT_TITLE, var_to_string (x.vars[COL_VAR]));
1192 tab_hline (table, TAL_1, x.n_consts + 1,
1193 x.n_consts + 2 + x.n_cols - 2, 1);
1195 /* Second header line. */
1196 for (i = 2; i < x.n_consts + 2; i++)
1197 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1198 x.n_consts + 2 - i - 1, 1,
1199 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1200 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1201 var_to_string (x.vars[ROW_VAR]));
1202 for (i = 0; i < x.n_cols; i++)
1203 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1204 &x.cols[i], x.vars[COL_VAR]);
1205 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1207 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1208 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1211 ds_init_empty (&title);
1212 for (i = 0; i < x.n_consts + 2; i++)
1215 ds_put_cstr (&title, " * ");
1216 ds_put_cstr (&title, var_to_string (x.vars[i]));
1218 for (i = 0; i < pt->n_consts; i++)
1220 const struct variable *var = pt->const_vars[i];
1223 ds_put_format (&title, ", %s=", var_to_string (var));
1225 /* Insert the formatted value of VAR without any leading spaces. */
1226 s = data_out (&pt->const_values[i], var_get_encoding (var),
1227 var_get_print_format (var));
1228 ds_put_cstr (&title, s + strspn (s, " "));
1232 ds_put_cstr (&title, " [");
1234 for (t = names; t < &names[n_names]; t++)
1235 if (proc->cells & (1u << t->value))
1238 ds_put_cstr (&title, ", ");
1239 ds_put_cstr (&title, gettext (t->name));
1241 ds_put_cstr (&title, "].");
1243 tab_title (table, "%s", ds_cstr (&title));
1244 ds_destroy (&title);
1246 tab_offset (table, 0, 2);
1250 static struct tab_table *
1251 create_chisq_table (struct pivot_table *pt)
1253 struct tab_table *chisq;
1255 chisq = tab_create (6 + (pt->n_vars - 2),
1256 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1257 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1259 tab_title (chisq, _("Chi-square tests."));
1261 tab_offset (chisq, pt->n_vars - 2, 0);
1262 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1263 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1264 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1265 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1266 _("Asymp. Sig. (2-tailed)"));
1267 tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1268 _("Exact Sig. (%d-tailed)"), 2);
1269 tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1270 _("Exact Sig. (%d-tailed)"), 1);
1271 tab_offset (chisq, 0, 1);
1276 /* Symmetric measures. */
1277 static struct tab_table *
1278 create_sym_table (struct pivot_table *pt)
1280 struct tab_table *sym;
1282 sym = tab_create (6 + (pt->n_vars - 2),
1283 pt->n_entries / pt->n_cols * 7 + 10);
1284 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1285 tab_title (sym, _("Symmetric measures."));
1287 tab_offset (sym, pt->n_vars - 2, 0);
1288 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1289 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1290 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1291 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1292 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1293 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1294 tab_offset (sym, 0, 1);
1299 /* Risk estimate. */
1300 static struct tab_table *
1301 create_risk_table (struct pivot_table *pt)
1303 struct tab_table *risk;
1305 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1306 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1307 tab_title (risk, _("Risk estimate."));
1309 tab_offset (risk, pt->n_vars - 2, 0);
1310 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1311 _("95%% Confidence Interval"));
1312 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1313 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1314 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1315 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1316 tab_hline (risk, TAL_1, 2, 3, 1);
1317 tab_vline (risk, TAL_1, 2, 0, 1);
1318 tab_offset (risk, 0, 2);
1323 /* Directional measures. */
1324 static struct tab_table *
1325 create_direct_table (struct pivot_table *pt)
1327 struct tab_table *direct;
1329 direct = tab_create (7 + (pt->n_vars - 2),
1330 pt->n_entries / pt->n_cols * 7 + 10);
1331 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1332 tab_title (direct, _("Directional measures."));
1334 tab_offset (direct, pt->n_vars - 2, 0);
1335 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1336 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1337 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1338 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1339 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1340 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1341 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1342 tab_offset (direct, 0, 1);
1348 /* Delete missing rows and columns for statistical analysis when
1351 delete_missing (struct pivot_table *pt)
1355 for (r = 0; r < pt->n_rows; r++)
1356 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1358 for (c = 0; c < pt->n_cols; c++)
1359 pt->mat[c + r * pt->n_cols] = 0.;
1364 for (c = 0; c < pt->n_cols; c++)
1365 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1367 for (r = 0; r < pt->n_rows; r++)
1368 pt->mat[c + r * pt->n_cols] = 0.;
1373 /* Prepare table T for submission, and submit it. */
1375 submit (struct pivot_table *pt, struct tab_table *t)
1382 tab_resize (t, -1, 0);
1383 if (tab_nr (t) == tab_t (t))
1385 table_unref (&t->table);
1388 tab_offset (t, 0, 0);
1390 for (i = 2; i < pt->n_vars; i++)
1391 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1392 var_to_string (pt->vars[i]));
1393 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1394 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1396 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1398 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1404 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1406 size_t row0 = *row1p;
1409 if (row0 >= pt->n_entries)
1412 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1414 struct table_entry *a = pt->entries[row0];
1415 struct table_entry *b = pt->entries[row1];
1416 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1424 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1425 result. WIDTH_ points to an int which is either 0 for a
1426 numeric value or a string width for a string value. */
1428 compare_value_3way (const void *a_, const void *b_, const void *width_)
1430 const union value *a = a_;
1431 const union value *b = b_;
1432 const int *width = width_;
1434 return value_compare_3way (a, b, *width);
1437 /* Inverted version of the above */
1439 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1441 return -compare_value_3way (a_, b_, width_);
1445 /* Given an array of ENTRY_CNT table_entry structures starting at
1446 ENTRIES, creates a sorted list of the values that the variable
1447 with index VAR_IDX takes on. The values are returned as a
1448 malloc()'d array stored in *VALUES, with the number of values
1449 stored in *VALUE_CNT.
1452 enum_var_values (const struct pivot_table *pt, int var_idx,
1453 union value **valuesp, int *n_values, bool descending)
1455 const struct variable *var = pt->vars[var_idx];
1456 const struct var_range *range = get_var_range (pt->proc, var);
1457 union value *values;
1462 values = *valuesp = xnmalloc (range->count, sizeof *values);
1463 *n_values = range->count;
1464 for (i = 0; i < range->count; i++)
1465 values[i].f = range->min + i;
1469 int width = var_get_width (var);
1470 struct hmapx_node *node;
1471 const union value *iter;
1475 for (i = 0; i < pt->n_entries; i++)
1477 const struct table_entry *te = pt->entries[i];
1478 const union value *value = &te->values[var_idx];
1479 size_t hash = value_hash (value, width, 0);
1481 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1482 if (value_equal (iter, value, width))
1485 hmapx_insert (&set, (union value *) value, hash);
1490 *n_values = hmapx_count (&set);
1491 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1493 HMAPX_FOR_EACH (iter, node, &set)
1494 values[i++] = *iter;
1495 hmapx_destroy (&set);
1497 sort (values, *n_values, sizeof *values,
1498 descending ? compare_value_3way_inv : compare_value_3way,
1503 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1504 from V, displayed with print format spec from variable VAR. When
1505 in REPORT missing-value mode, missing values have an M appended. */
1507 table_value_missing (struct crosstabs_proc *proc,
1508 struct tab_table *table, int c, int r, unsigned char opt,
1509 const union value *v, const struct variable *var)
1511 const char *label = var_lookup_value_label (var, v);
1513 tab_text (table, c, r, TAB_LEFT, label);
1516 const struct fmt_spec *print = var_get_print_format (var);
1517 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1519 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1520 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1524 tab_value (table, c, r, opt, v, var, print);
1528 /* Draws a line across TABLE at the current row to indicate the most
1529 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1530 that changed, and puts the values that changed into the table. TB
1531 and PT must be the corresponding table_entry and crosstab,
1534 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1535 struct tab_table *table, int first_difference)
1537 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1539 for (; first_difference >= 2; first_difference--)
1540 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1541 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1542 pt->vars[first_difference]);
1545 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1546 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1547 additionally suffixed with a letter `M'. */
1549 format_cell_entry (struct tab_table *table, int c, int r, double value,
1550 char suffix, bool mark_missing, const struct dictionary *dict)
1558 s = data_out (&v, dict_get_encoding (dict), settings_get_format ());
1562 suffixes[suffix_len++] = suffix;
1564 suffixes[suffix_len++] = 'M';
1565 suffixes[suffix_len] = '\0';
1567 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1568 s + strspn (s, " "), suffixes);
1573 /* Displays the crosstabulation table. */
1575 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1576 struct tab_table *table)
1582 for (r = 0; r < pt->n_rows; r++)
1583 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1584 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1587 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1588 TAB_LEFT, _("Total"));
1590 /* Put in the actual cells. */
1592 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1593 for (r = 0; r < pt->n_rows; r++)
1595 if (proc->n_cells > 1)
1596 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1597 for (c = 0; c < pt->n_cols; c++)
1599 bool mark_missing = false;
1600 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1601 if (proc->exclude == MV_NEVER
1602 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1603 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1605 mark_missing = true;
1606 for (i = 0; i < proc->n_cells; i++)
1611 switch (proc->a_cells[i])
1617 v = *mp / pt->row_tot[r] * 100.;
1621 v = *mp / pt->col_tot[c] * 100.;
1625 v = *mp / pt->total * 100.;
1628 case CRS_CL_EXPECTED:
1631 case CRS_CL_RESIDUAL:
1632 v = *mp - expected_value;
1634 case CRS_CL_SRESIDUAL:
1635 v = (*mp - expected_value) / sqrt (expected_value);
1637 case CRS_CL_ASRESIDUAL:
1638 v = ((*mp - expected_value)
1639 / sqrt (expected_value
1640 * (1. - pt->row_tot[r] / pt->total)
1641 * (1. - pt->col_tot[c] / pt->total)));
1646 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1652 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1656 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1657 for (r = 0; r < pt->n_rows; r++)
1659 bool mark_missing = false;
1661 if (proc->exclude == MV_NEVER
1662 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1663 mark_missing = true;
1665 for (i = 0; i < proc->n_cells; i++)
1670 switch (proc->a_cells[i])
1680 v = pt->row_tot[r] / pt->total * 100.;
1684 v = pt->row_tot[r] / pt->total * 100.;
1687 case CRS_CL_EXPECTED:
1688 case CRS_CL_RESIDUAL:
1689 case CRS_CL_SRESIDUAL:
1690 case CRS_CL_ASRESIDUAL:
1697 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1698 tab_next_row (table);
1702 /* Column totals, grand total. */
1704 if (proc->n_cells > 1)
1705 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1706 for (c = 0; c <= pt->n_cols; c++)
1708 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1709 bool mark_missing = false;
1712 if (proc->exclude == MV_NEVER && c < pt->n_cols
1713 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1714 mark_missing = true;
1716 for (i = 0; i < proc->n_cells; i++)
1721 switch (proc->a_cells[i])
1727 v = ct / pt->total * 100.;
1735 v = ct / pt->total * 100.;
1738 case CRS_CL_EXPECTED:
1739 case CRS_CL_RESIDUAL:
1740 case CRS_CL_SRESIDUAL:
1741 case CRS_CL_ASRESIDUAL:
1747 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1752 tab_offset (table, -1, tab_row (table) + last_row);
1753 tab_offset (table, 0, -1);
1756 static void calc_r (struct pivot_table *,
1757 double *PT, double *Y, double *, double *, double *);
1758 static void calc_chisq (struct pivot_table *,
1759 double[N_CHISQ], int[N_CHISQ], double *, double *);
1761 /* Display chi-square statistics. */
1763 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1764 bool *showed_fisher)
1766 static const char *chisq_stats[N_CHISQ] =
1768 N_("Pearson Chi-Square"),
1769 N_("Likelihood Ratio"),
1770 N_("Fisher's Exact Test"),
1771 N_("Continuity Correction"),
1772 N_("Linear-by-Linear Association"),
1774 double chisq_v[N_CHISQ];
1775 double fisher1, fisher2;
1780 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1782 tab_offset (chisq, pt->n_consts + pt->n_vars - 2, -1);
1784 for (i = 0; i < N_CHISQ; i++)
1786 if ((i != 2 && chisq_v[i] == SYSMIS)
1787 || (i == 2 && fisher1 == SYSMIS))
1790 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1793 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1794 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1795 tab_double (chisq, 3, 0, TAB_RIGHT,
1796 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1800 *showed_fisher = true;
1801 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1802 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1804 tab_next_row (chisq);
1807 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1808 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1809 tab_next_row (chisq);
1811 tab_offset (chisq, 0, -1);
1814 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1815 double[N_SYMMETRIC], double[N_SYMMETRIC],
1816 double[N_SYMMETRIC],
1817 double[3], double[3], double[3]);
1819 /* Display symmetric measures. */
1821 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1822 struct tab_table *sym)
1824 static const char *categories[] =
1826 N_("Nominal by Nominal"),
1827 N_("Ordinal by Ordinal"),
1828 N_("Interval by Interval"),
1829 N_("Measure of Agreement"),
1832 static const char *stats[N_SYMMETRIC] =
1836 N_("Contingency Coefficient"),
1837 N_("Kendall's tau-b"),
1838 N_("Kendall's tau-c"),
1840 N_("Spearman Correlation"),
1845 static const int stats_categories[N_SYMMETRIC] =
1847 0, 0, 0, 1, 1, 1, 1, 2, 3,
1851 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1852 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1855 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1856 somers_d_v, somers_d_ase, somers_d_t))
1859 tab_offset (sym, pt->n_consts + pt->n_vars - 2, -1);
1861 for (i = 0; i < N_SYMMETRIC; i++)
1863 if (sym_v[i] == SYSMIS)
1866 if (stats_categories[i] != last_cat)
1868 last_cat = stats_categories[i];
1869 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1872 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1873 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1874 if (sym_ase[i] != SYSMIS)
1875 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1876 if (sym_t[i] != SYSMIS)
1877 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1878 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1882 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1883 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1886 tab_offset (sym, 0, -1);
1889 static int calc_risk (struct pivot_table *,
1890 double[], double[], double[], union value *);
1892 /* Display risk estimate. */
1894 display_risk (struct pivot_table *pt, struct tab_table *risk)
1897 double risk_v[3], lower[3], upper[3];
1901 if (!calc_risk (pt, risk_v, upper, lower, c))
1904 tab_offset (risk, pt->n_consts + pt->n_vars - 2, -1);
1906 for (i = 0; i < 3; i++)
1908 const struct variable *cv = pt->vars[COL_VAR];
1909 const struct variable *rv = pt->vars[ROW_VAR];
1910 int cvw = var_get_width (cv);
1911 int rvw = var_get_width (rv);
1913 if (risk_v[i] == SYSMIS)
1919 if (var_is_numeric (cv))
1920 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1921 var_to_string (cv), c[0].f, c[1].f);
1923 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1925 cvw, value_str (&c[0], cvw),
1926 cvw, value_str (&c[1], cvw));
1930 if (var_is_numeric (rv))
1931 sprintf (buf, _("For cohort %s = %g"),
1932 var_to_string (rv), pt->rows[i - 1].f);
1934 sprintf (buf, _("For cohort %s = %.*s"),
1936 rvw, value_str (&pt->rows[i - 1], rvw));
1940 tab_text (risk, 0, 0, TAB_LEFT, buf);
1941 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1942 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1943 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1944 tab_next_row (risk);
1947 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1948 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1949 tab_next_row (risk);
1951 tab_offset (risk, 0, -1);
1954 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1955 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1956 double[N_DIRECTIONAL]);
1958 /* Display directional measures. */
1960 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1961 struct tab_table *direct)
1963 static const char *categories[] =
1965 N_("Nominal by Nominal"),
1966 N_("Ordinal by Ordinal"),
1967 N_("Nominal by Interval"),
1970 static const char *stats[] =
1973 N_("Goodman and Kruskal tau"),
1974 N_("Uncertainty Coefficient"),
1979 static const char *types[] =
1986 static const int stats_categories[N_DIRECTIONAL] =
1988 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1991 static const int stats_stats[N_DIRECTIONAL] =
1993 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1996 static const int stats_types[N_DIRECTIONAL] =
1998 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2001 static const int *stats_lookup[] =
2008 static const char **stats_names[] =
2020 double direct_v[N_DIRECTIONAL];
2021 double direct_ase[N_DIRECTIONAL];
2022 double direct_t[N_DIRECTIONAL];
2026 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2029 tab_offset (direct, pt->n_consts + pt->n_vars - 2, -1);
2031 for (i = 0; i < N_DIRECTIONAL; i++)
2033 if (direct_v[i] == SYSMIS)
2039 for (j = 0; j < 3; j++)
2040 if (last[j] != stats_lookup[j][i])
2043 tab_hline (direct, TAL_1, j, 6, 0);
2048 int k = last[j] = stats_lookup[j][i];
2053 string = var_to_string (pt->vars[0]);
2055 string = var_to_string (pt->vars[1]);
2057 tab_text_format (direct, j, 0, TAB_LEFT,
2058 gettext (stats_names[j][k]), string);
2063 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2064 if (direct_ase[i] != SYSMIS)
2065 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2066 if (direct_t[i] != SYSMIS)
2067 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2068 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2069 tab_next_row (direct);
2072 tab_offset (direct, 0, -1);
2075 /* Statistical calculations. */
2077 /* Returns the value of the gamma (factorial) function for an integer
2080 gamma_int (double pt)
2085 for (i = 2; i < pt; i++)
2090 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2092 static inline double
2093 Pr (int a, int b, int c, int d)
2095 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2096 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2097 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2098 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2099 / gamma_int (a + b + c + d + 1.));
2102 /* Swap the contents of A and B. */
2104 swap (int *a, int *b)
2111 /* Calculate significance for Fisher's exact test as specified in
2112 _SPSS Statistical Algorithms_, Appendix 5. */
2114 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2118 if (MIN (c, d) < MIN (a, b))
2119 swap (&a, &c), swap (&b, &d);
2120 if (MIN (b, d) < MIN (a, c))
2121 swap (&a, &b), swap (&c, &d);
2125 swap (&a, &b), swap (&c, &d);
2127 swap (&a, &c), swap (&b, &d);
2131 for (pt = 0; pt <= a; pt++)
2132 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2134 *fisher2 = *fisher1;
2135 for (pt = 1; pt <= b; pt++)
2136 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2139 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2140 columns with values COLS and N_ROWS rows with values ROWS. Values
2141 in the matrix sum to pt->total. */
2143 calc_chisq (struct pivot_table *pt,
2144 double chisq[N_CHISQ], int df[N_CHISQ],
2145 double *fisher1, double *fisher2)
2149 chisq[0] = chisq[1] = 0.;
2150 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2151 *fisher1 = *fisher2 = SYSMIS;
2153 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2155 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2157 chisq[0] = chisq[1] = SYSMIS;
2161 for (r = 0; r < pt->n_rows; r++)
2162 for (c = 0; c < pt->n_cols; c++)
2164 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2165 const double freq = pt->mat[pt->n_cols * r + c];
2166 const double residual = freq - expected;
2168 chisq[0] += residual * residual / expected;
2170 chisq[1] += freq * log (expected / freq);
2181 /* Calculate Yates and Fisher exact test. */
2182 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2184 double f11, f12, f21, f22;
2190 for (i = j = 0; i < pt->n_cols; i++)
2191 if (pt->col_tot[i] != 0.)
2200 f11 = pt->mat[nz_cols[0]];
2201 f12 = pt->mat[nz_cols[1]];
2202 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2203 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2208 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2211 chisq[3] = (pt->total * pow2 (pt_)
2212 / (f11 + f12) / (f21 + f22)
2213 / (f11 + f21) / (f12 + f22));
2221 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2222 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2225 /* Calculate Mantel-Haenszel. */
2226 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2228 double r, ase_0, ase_1;
2229 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2231 chisq[4] = (pt->total - 1.) * r * r;
2236 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2237 ASE_1, and ase_0 into ASE_0. The row and column values must be
2238 passed in PT and Y. */
2240 calc_r (struct pivot_table *pt,
2241 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2243 double SX, SY, S, T;
2245 double sum_XYf, sum_X2Y2f;
2246 double sum_Xr, sum_X2r;
2247 double sum_Yc, sum_Y2c;
2250 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2251 for (j = 0; j < pt->n_cols; j++)
2253 double fij = pt->mat[j + i * pt->n_cols];
2254 double product = PT[i] * Y[j];
2255 double temp = fij * product;
2257 sum_X2Y2f += temp * product;
2260 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2262 sum_Xr += PT[i] * pt->row_tot[i];
2263 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2265 Xbar = sum_Xr / pt->total;
2267 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2269 sum_Yc += Y[i] * pt->col_tot[i];
2270 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2272 Ybar = sum_Yc / pt->total;
2274 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2275 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2276 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2279 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2284 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2285 for (j = 0; j < pt->n_cols; j++)
2287 double Xresid, Yresid;
2290 Xresid = PT[i] - Xbar;
2291 Yresid = Y[j] - Ybar;
2292 temp = (T * Xresid * Yresid
2294 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2295 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2300 *ase_1 = sqrt (s) / (T * T);
2304 /* Calculate symmetric statistics and their asymptotic standard
2305 errors. Returns 0 if none could be calculated. */
2307 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2308 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2309 double t[N_SYMMETRIC],
2310 double somers_d_v[3], double somers_d_ase[3],
2311 double somers_d_t[3])
2315 q = MIN (pt->ns_rows, pt->ns_cols);
2319 for (i = 0; i < N_SYMMETRIC; i++)
2320 v[i] = ase[i] = t[i] = SYSMIS;
2322 /* Phi, Cramer's V, contingency coefficient. */
2323 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2325 double Xp = 0.; /* Pearson chi-square. */
2328 for (r = 0; r < pt->n_rows; r++)
2329 for (c = 0; c < pt->n_cols; c++)
2331 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2332 const double freq = pt->mat[pt->n_cols * r + c];
2333 const double residual = freq - expected;
2335 Xp += residual * residual / expected;
2338 if (proc->statistics & (1u << CRS_ST_PHI))
2340 v[0] = sqrt (Xp / pt->total);
2341 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2343 if (proc->statistics & (1u << CRS_ST_CC))
2344 v[2] = sqrt (Xp / (Xp + pt->total));
2347 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2348 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2353 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2357 Dr = Dc = pow2 (pt->total);
2358 for (r = 0; r < pt->n_rows; r++)
2359 Dr -= pow2 (pt->row_tot[r]);
2360 for (c = 0; c < pt->n_cols; c++)
2361 Dc -= pow2 (pt->col_tot[c]);
2363 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2364 for (c = 0; c < pt->n_cols; c++)
2368 for (r = 0; r < pt->n_rows; r++)
2369 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2378 for (i = 0; i < pt->n_rows; i++)
2382 for (j = 1; j < pt->n_cols; j++)
2383 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2386 for (j = 1; j < pt->n_cols; j++)
2387 Dij += cum[j + (i - 1) * pt->n_cols];
2391 double fij = pt->mat[j + i * pt->n_cols];
2395 if (++j == pt->n_cols)
2397 assert (j < pt->n_cols);
2399 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2400 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2404 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2405 Dij -= cum[j + (i - 1) * pt->n_cols];
2411 if (proc->statistics & (1u << CRS_ST_BTAU))
2412 v[3] = (P - Q) / sqrt (Dr * Dc);
2413 if (proc->statistics & (1u << CRS_ST_CTAU))
2414 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2415 if (proc->statistics & (1u << CRS_ST_GAMMA))
2416 v[5] = (P - Q) / (P + Q);
2418 /* ASE for tau-b, tau-c, gamma. Calculations could be
2419 eliminated here, at expense of memory. */
2424 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2425 for (i = 0; i < pt->n_rows; i++)
2429 for (j = 1; j < pt->n_cols; j++)
2430 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2433 for (j = 1; j < pt->n_cols; j++)
2434 Dij += cum[j + (i - 1) * pt->n_cols];
2438 double fij = pt->mat[j + i * pt->n_cols];
2440 if (proc->statistics & (1u << CRS_ST_BTAU))
2442 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2443 + v[3] * (pt->row_tot[i] * Dc
2444 + pt->col_tot[j] * Dr));
2445 btau_cum += fij * temp * temp;
2449 const double temp = Cij - Dij;
2450 ctau_cum += fij * temp * temp;
2453 if (proc->statistics & (1u << CRS_ST_GAMMA))
2455 const double temp = Q * Cij - P * Dij;
2456 gamma_cum += fij * temp * temp;
2459 if (proc->statistics & (1u << CRS_ST_D))
2461 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2462 - (P - Q) * (pt->total - pt->row_tot[i]));
2463 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2464 - (Q - P) * (pt->total - pt->col_tot[j]));
2467 if (++j == pt->n_cols)
2469 assert (j < pt->n_cols);
2471 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2472 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2476 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2477 Dij -= cum[j + (i - 1) * pt->n_cols];
2483 btau_var = ((btau_cum
2484 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2486 if (proc->statistics & (1u << CRS_ST_BTAU))
2488 ase[3] = sqrt (btau_var);
2489 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2492 if (proc->statistics & (1u << CRS_ST_CTAU))
2494 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2495 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2496 t[4] = v[4] / ase[4];
2498 if (proc->statistics & (1u << CRS_ST_GAMMA))
2500 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2501 t[5] = v[5] / (2. / (P + Q)
2502 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2504 if (proc->statistics & (1u << CRS_ST_D))
2506 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2507 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2508 somers_d_t[0] = (somers_d_v[0]
2510 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2511 somers_d_v[1] = (P - Q) / Dc;
2512 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2513 somers_d_t[1] = (somers_d_v[1]
2515 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2516 somers_d_v[2] = (P - Q) / Dr;
2517 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2518 somers_d_t[2] = (somers_d_v[2]
2520 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2526 /* Spearman correlation, Pearson's r. */
2527 if (proc->statistics & (1u << CRS_ST_CORR))
2529 double *R = xmalloc (sizeof *R * pt->n_rows);
2530 double *C = xmalloc (sizeof *C * pt->n_cols);
2533 double y, t, c = 0., s = 0.;
2538 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2539 y = pt->row_tot[i] - c;
2543 if (++i == pt->n_rows)
2545 assert (i < pt->n_rows);
2550 double y, t, c = 0., s = 0.;
2555 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2556 y = pt->col_tot[j] - c;
2560 if (++j == pt->n_cols)
2562 assert (j < pt->n_cols);
2566 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2572 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2576 /* Cohen's kappa. */
2577 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2579 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2582 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2583 i < pt->ns_rows; i++, j++)
2587 while (pt->col_tot[j] == 0.)
2590 prod = pt->row_tot[i] * pt->col_tot[j];
2591 sum = pt->row_tot[i] + pt->col_tot[j];
2593 sum_fii += pt->mat[j + i * pt->n_cols];
2595 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2596 sum_riciri_ci += prod * sum;
2598 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2599 for (j = 0; j < pt->ns_cols; j++)
2601 double sum = pt->row_tot[i] + pt->col_tot[j];
2602 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2605 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2607 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2608 + sum_rici * sum_rici
2609 - pt->total * sum_riciri_ci)
2610 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2612 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2613 / pow2 (pow2 (pt->total) - sum_rici))
2614 + ((2. * (pt->total - sum_fii)
2615 * (2. * sum_fii * sum_rici
2616 - pt->total * sum_fiiri_ci))
2617 / cube (pow2 (pt->total) - sum_rici))
2618 + (pow2 (pt->total - sum_fii)
2619 * (pt->total * sum_fijri_ci2 - 4.
2620 * sum_rici * sum_rici)
2621 / pow4 (pow2 (pt->total) - sum_rici))));
2623 t[8] = v[8] / ase[8];
2630 /* Calculate risk estimate. */
2632 calc_risk (struct pivot_table *pt,
2633 double *value, double *upper, double *lower, union value *c)
2635 double f11, f12, f21, f22;
2641 for (i = 0; i < 3; i++)
2642 value[i] = upper[i] = lower[i] = SYSMIS;
2645 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2652 for (i = j = 0; i < pt->n_cols; i++)
2653 if (pt->col_tot[i] != 0.)
2662 f11 = pt->mat[nz_cols[0]];
2663 f12 = pt->mat[nz_cols[1]];
2664 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2665 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2667 c[0] = pt->cols[nz_cols[0]];
2668 c[1] = pt->cols[nz_cols[1]];
2671 value[0] = (f11 * f22) / (f12 * f21);
2672 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2673 lower[0] = value[0] * exp (-1.960 * v);
2674 upper[0] = value[0] * exp (1.960 * v);
2676 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2677 v = sqrt ((f12 / (f11 * (f11 + f12)))
2678 + (f22 / (f21 * (f21 + f22))));
2679 lower[1] = value[1] * exp (-1.960 * v);
2680 upper[1] = value[1] * exp (1.960 * v);
2682 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2683 v = sqrt ((f11 / (f12 * (f11 + f12)))
2684 + (f21 / (f22 * (f21 + f22))));
2685 lower[2] = value[2] * exp (-1.960 * v);
2686 upper[2] = value[2] * exp (1.960 * v);
2691 /* Calculate directional measures. */
2693 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2694 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2695 double t[N_DIRECTIONAL])
2700 for (i = 0; i < N_DIRECTIONAL; i++)
2701 v[i] = ase[i] = t[i] = SYSMIS;
2705 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2707 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2708 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2709 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2710 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2711 double sum_fim, sum_fmj;
2713 int rm_index, cm_index;
2716 /* Find maximum for each row and their sum. */
2717 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2719 double max = pt->mat[i * pt->n_cols];
2722 for (j = 1; j < pt->n_cols; j++)
2723 if (pt->mat[j + i * pt->n_cols] > max)
2725 max = pt->mat[j + i * pt->n_cols];
2729 sum_fim += fim[i] = max;
2730 fim_index[i] = index;
2733 /* Find maximum for each column. */
2734 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2736 double max = pt->mat[j];
2739 for (i = 1; i < pt->n_rows; i++)
2740 if (pt->mat[j + i * pt->n_cols] > max)
2742 max = pt->mat[j + i * pt->n_cols];
2746 sum_fmj += fmj[j] = max;
2747 fmj_index[j] = index;
2750 /* Find maximum row total. */
2751 rm = pt->row_tot[0];
2753 for (i = 1; i < pt->n_rows; i++)
2754 if (pt->row_tot[i] > rm)
2756 rm = pt->row_tot[i];
2760 /* Find maximum column total. */
2761 cm = pt->col_tot[0];
2763 for (j = 1; j < pt->n_cols; j++)
2764 if (pt->col_tot[j] > cm)
2766 cm = pt->col_tot[j];
2770 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2771 v[1] = (sum_fmj - rm) / (pt->total - rm);
2772 v[2] = (sum_fim - cm) / (pt->total - cm);
2774 /* ASE1 for Y given PT. */
2778 for (accum = 0., i = 0; i < pt->n_rows; i++)
2779 for (j = 0; j < pt->n_cols; j++)
2781 const int deltaj = j == cm_index;
2782 accum += (pt->mat[j + i * pt->n_cols]
2783 * pow2 ((j == fim_index[i])
2788 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2791 /* ASE0 for Y given PT. */
2795 for (accum = 0., i = 0; i < pt->n_rows; i++)
2796 if (cm_index != fim_index[i])
2797 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2798 + pt->mat[i * pt->n_cols + cm_index]);
2799 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2802 /* ASE1 for PT given Y. */
2806 for (accum = 0., i = 0; i < pt->n_rows; i++)
2807 for (j = 0; j < pt->n_cols; j++)
2809 const int deltaj = i == rm_index;
2810 accum += (pt->mat[j + i * pt->n_cols]
2811 * pow2 ((i == fmj_index[j])
2816 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2819 /* ASE0 for PT given Y. */
2823 for (accum = 0., j = 0; j < pt->n_cols; j++)
2824 if (rm_index != fmj_index[j])
2825 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2826 + pt->mat[j + pt->n_cols * rm_index]);
2827 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2830 /* Symmetric ASE0 and ASE1. */
2835 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2836 for (j = 0; j < pt->n_cols; j++)
2838 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2839 int temp1 = (i == rm_index) + (j == cm_index);
2840 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2841 accum1 += (pt->mat[j + i * pt->n_cols]
2842 * pow2 (temp0 + (v[0] - 1.) * temp1));
2844 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2845 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2846 / (2. * pt->total - rm - cm));
2855 double sum_fij2_ri, sum_fij2_ci;
2856 double sum_ri2, sum_cj2;
2858 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2859 for (j = 0; j < pt->n_cols; j++)
2861 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2862 sum_fij2_ri += temp / pt->row_tot[i];
2863 sum_fij2_ci += temp / pt->col_tot[j];
2866 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2867 sum_ri2 += pow2 (pt->row_tot[i]);
2869 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2870 sum_cj2 += pow2 (pt->col_tot[j]);
2872 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2873 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2877 if (proc->statistics & (1u << CRS_ST_UC))
2879 double UX, UY, UXY, P;
2880 double ase1_yx, ase1_xy, ase1_sym;
2883 for (UX = 0., i = 0; i < pt->n_rows; i++)
2884 if (pt->row_tot[i] > 0.)
2885 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2887 for (UY = 0., j = 0; j < pt->n_cols; j++)
2888 if (pt->col_tot[j] > 0.)
2889 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2891 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2892 for (j = 0; j < pt->n_cols; j++)
2894 double entry = pt->mat[j + i * pt->n_cols];
2899 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2900 UXY -= entry / pt->total * log (entry / pt->total);
2903 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2904 for (j = 0; j < pt->n_cols; j++)
2906 double entry = pt->mat[j + i * pt->n_cols];
2911 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2912 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2913 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2914 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2915 ase1_sym += entry * pow2 ((UXY
2916 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2917 - (UX + UY) * log (entry / pt->total));
2920 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2921 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2922 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2923 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2925 v[6] = (UX + UY - UXY) / UX;
2926 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2927 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2929 v[7] = (UX + UY - UXY) / UY;
2930 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2931 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2935 if (proc->statistics & (1u << CRS_ST_D))
2937 double v_dummy[N_SYMMETRIC];
2938 double ase_dummy[N_SYMMETRIC];
2939 double t_dummy[N_SYMMETRIC];
2940 double somers_d_v[3];
2941 double somers_d_ase[3];
2942 double somers_d_t[3];
2944 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2945 somers_d_v, somers_d_ase, somers_d_t))
2948 for (i = 0; i < 3; i++)
2950 v[8 + i] = somers_d_v[i];
2951 ase[8 + i] = somers_d_ase[i];
2952 t[8 + i] = somers_d_t[i];
2958 if (proc->statistics & (1u << CRS_ST_ETA))
2961 double sum_Xr, sum_X2r;
2965 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2967 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2968 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2970 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2972 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2976 for (cum = 0., i = 0; i < pt->n_rows; i++)
2978 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2979 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2982 SXW -= cum * cum / pt->col_tot[j];
2984 v[11] = sqrt (1. - SXW / SX);
2988 double sum_Yc, sum_Y2c;
2992 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2994 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2995 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2997 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
2999 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3003 for (cum = 0., j = 0; j < pt->n_cols; j++)
3005 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3006 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3009 SYW -= cum * cum / pt->row_tot[i];
3011 v[12] = sqrt (1. - SYW / SY);