1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010 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);
348 /* Initialize hash tables. */
349 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
350 hmap_init (&pt->data);
353 for (; (c = casereader_read (group)) != NULL; case_unref (c))
354 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
356 double weight = dict_get_case_weight (dataset_dict (ds), c,
358 if (should_tabulate_case (pt, c, proc->exclude))
360 if (proc->mode == GENERAL)
361 tabulate_general_case (pt, c, weight);
363 tabulate_integer_case (pt, c, weight);
366 pt->missing += weight;
368 casereader_destroy (group);
373 ok = casegrouper_destroy (grouper);
374 ok = proc_commit (ds) && ok;
376 return ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
379 /* Parses the TABLES subcommand. */
381 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
382 struct cmd_crosstabs *cmd UNUSED, void *proc_)
384 struct crosstabs_proc *proc = proc_;
385 struct const_var_set *var_set;
387 const struct variable ***by = NULL;
389 size_t *by_nvar = NULL;
394 /* Ensure that this is a TABLES subcommand. */
395 if (!lex_match_id (lexer, "TABLES")
396 && (lex_token (lexer) != T_ID ||
397 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
398 && lex_token (lexer) != T_ALL)
400 lex_match (lexer, '=');
402 if (proc->variables != NULL)
403 var_set = const_var_set_create_from_array (proc->variables,
406 var_set = const_var_set_create_from_dict (dataset_dict (ds));
407 assert (var_set != NULL);
411 by = xnrealloc (by, n_by + 1, sizeof *by);
412 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
413 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
414 PV_NO_DUPLICATE | PV_NO_SCRATCH))
416 if (xalloc_oversized (nx, by_nvar[n_by]))
418 msg (SE, _("Too many cross-tabulation variables or dimensions."));
424 if (!lex_match (lexer, T_BY))
428 lex_error (lexer, _("expecting BY"));
436 by_iter = xcalloc (n_by, sizeof *by_iter);
437 proc->pivots = xnrealloc (proc->pivots,
438 proc->n_pivots + nx, sizeof *proc->pivots);
439 for (i = 0; i < nx; i++)
441 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
444 pt->weight_format = proc->weight_format;
447 pt->vars = xmalloc (n_by * sizeof *pt->vars);
449 pt->const_vars = NULL;
450 pt->const_values = NULL;
452 for (j = 0; j < n_by; j++)
453 pt->vars[j] = by[j][by_iter[j]];
455 for (j = n_by - 1; j >= 0; j--)
457 if (++by_iter[j] < by_nvar[j])
466 /* All return paths lead here. */
467 for (i = 0; i < n_by; i++)
472 const_var_set_destroy (var_set);
477 /* Parses the VARIABLES subcommand. */
479 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
480 struct cmd_crosstabs *cmd UNUSED, void *proc_)
482 struct crosstabs_proc *proc = proc_;
485 msg (SE, _("VARIABLES must be specified before TABLES."));
489 lex_match (lexer, '=');
493 size_t orig_nv = proc->n_variables;
498 if (!parse_variables_const (lexer, dataset_dict (ds),
499 &proc->variables, &proc->n_variables,
500 (PV_APPEND | PV_NUMERIC
501 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
504 if (lex_token (lexer) != '(')
506 lex_error (lexer, "expecting `('");
511 if (!lex_force_int (lexer))
513 min = lex_integer (lexer);
516 lex_match (lexer, ',');
518 if (!lex_force_int (lexer))
520 max = lex_integer (lexer);
523 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
529 if (lex_token (lexer) != ')')
531 lex_error (lexer, "expecting `)'");
536 for (i = orig_nv; i < proc->n_variables; i++)
538 struct var_range *vr = xmalloc (sizeof *vr);
541 vr->count = max - min + 1;
542 var_attach_aux (proc->variables[i], vr, var_dtor_free);
545 if (lex_token (lexer) == '/')
552 free (proc->variables);
553 proc->variables = NULL;
554 proc->n_variables = 0;
558 /* Data file processing. */
561 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
562 enum mv_class exclude)
565 for (j = 0; j < pt->n_vars; j++)
567 const struct variable *var = pt->vars[j];
568 struct var_range *range = get_var_range (var);
570 if (var_is_value_missing (var, case_data (c, var), exclude))
575 double num = case_num (c, var);
576 if (num < range->min || num > range->max)
584 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
587 struct table_entry *te;
592 for (j = 0; j < pt->n_vars; j++)
594 /* Throw away fractional parts of values. */
595 hash = hash_int (case_num (c, pt->vars[j]), hash);
598 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
600 for (j = 0; j < pt->n_vars; j++)
601 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
604 /* Found an existing entry. */
611 /* No existing entry. Create a new one. */
612 te = xmalloc (table_entry_size (pt->n_vars));
614 for (j = 0; j < pt->n_vars; j++)
615 te->values[j].f = (int) case_num (c, pt->vars[j]);
616 hmap_insert (&pt->data, &te->node, hash);
620 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
623 struct table_entry *te;
628 for (j = 0; j < pt->n_vars; j++)
630 const struct variable *var = pt->vars[j];
631 hash = value_hash (case_data (c, var), var_get_width (var), hash);
634 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
636 for (j = 0; j < pt->n_vars; j++)
638 const struct variable *var = pt->vars[j];
639 if (!value_equal (case_data (c, var), &te->values[j],
640 var_get_width (var)))
644 /* Found an existing entry. */
651 /* No existing entry. Create a new one. */
652 te = xmalloc (table_entry_size (pt->n_vars));
654 for (j = 0; j < pt->n_vars; j++)
656 const struct variable *var = pt->vars[j];
657 int width = var_get_width (var);
658 value_init (&te->values[j], width);
659 value_copy (&te->values[j], case_data (c, var), width);
661 hmap_insert (&pt->data, &te->node, hash);
664 /* Post-data reading calculations. */
666 static int compare_table_entry_vars_3way (const struct table_entry *a,
667 const struct table_entry *b,
668 const struct pivot_table *pt,
670 static int compare_table_entry_3way (const void *ap_, const void *bp_,
672 static void enum_var_values (const struct pivot_table *, int var_idx,
673 union value **valuesp, int *n_values);
674 static void output_pivot_table (struct crosstabs_proc *,
675 struct pivot_table *);
676 static void make_pivot_table_subset (struct pivot_table *pt,
677 size_t row0, size_t row1,
678 struct pivot_table *subset);
679 static void make_summary_table (struct crosstabs_proc *);
680 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
683 postcalc (struct crosstabs_proc *proc)
685 struct pivot_table *pt;
687 /* Convert hash tables into sorted arrays of entries. */
688 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
690 struct table_entry *e;
693 pt->n_entries = hmap_count (&pt->data);
694 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
696 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
697 pt->entries[i++] = e;
698 hmap_destroy (&pt->data);
700 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
701 compare_table_entry_3way, pt);
704 make_summary_table (proc);
706 /* Output each pivot table. */
707 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
709 if (proc->pivot || pt->n_vars == 2)
710 output_pivot_table (proc, pt);
713 size_t row0 = 0, row1 = 0;
714 while (find_crosstab (pt, &row0, &row1))
716 struct pivot_table subset;
717 make_pivot_table_subset (pt, row0, row1, &subset);
718 output_pivot_table (proc, &subset);
723 /* Free output and prepare for next split file. */
724 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
730 /* Free only the members that were allocated in this
731 function. The other pointer members are either both
732 allocated and destroyed at a lower level (in
733 output_pivot_table), or both allocated and destroyed at
734 a higher level (in crs_custom_tables and free_proc,
736 for (i = 0; i < pt->n_entries; i++)
737 free (pt->entries[i]);
743 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
744 struct pivot_table *subset)
749 assert (pt->n_consts == 0);
750 subset->missing = pt->missing;
752 subset->vars = pt->vars;
753 subset->n_consts = pt->n_vars - 2;
754 subset->const_vars = pt->vars + 2;
755 subset->const_values = &pt->entries[row0]->values[2];
757 subset->entries = &pt->entries[row0];
758 subset->n_entries = row1 - row0;
762 compare_table_entry_var_3way (const struct table_entry *a,
763 const struct table_entry *b,
764 const struct pivot_table *pt,
767 return value_compare_3way (&a->values[idx], &b->values[idx],
768 var_get_width (pt->vars[idx]));
772 compare_table_entry_vars_3way (const struct table_entry *a,
773 const struct table_entry *b,
774 const struct pivot_table *pt,
779 for (i = idx1 - 1; i >= idx0; i--)
781 int cmp = compare_table_entry_var_3way (a, b, pt, i);
788 /* Compare the struct table_entry at *AP to the one at *BP and
789 return a strcmp()-type result. */
791 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
793 const struct table_entry *const *ap = ap_;
794 const struct table_entry *const *bp = bp_;
795 const struct table_entry *a = *ap;
796 const struct table_entry *b = *bp;
797 const struct pivot_table *pt = pt_;
800 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
804 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
808 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
812 find_first_difference (const struct pivot_table *pt, size_t row)
815 return pt->n_vars - 1;
818 const struct table_entry *a = pt->entries[row];
819 const struct table_entry *b = pt->entries[row - 1];
822 for (col = pt->n_vars - 1; col >= 0; col--)
823 if (compare_table_entry_var_3way (a, b, pt, col))
829 /* Output a table summarizing the cases processed. */
831 make_summary_table (struct crosstabs_proc *proc)
833 struct tab_table *summary;
834 struct pivot_table *pt;
838 summary = tab_create (7, 3 + proc->n_pivots);
839 tab_title (summary, _("Summary."));
840 tab_headers (summary, 1, 0, 3, 0);
841 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
842 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
843 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
844 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
845 tab_hline (summary, TAL_1, 1, 6, 1);
846 tab_hline (summary, TAL_1, 1, 6, 2);
847 tab_vline (summary, TAL_1, 3, 1, 1);
848 tab_vline (summary, TAL_1, 5, 1, 1);
849 for (i = 0; i < 3; i++)
851 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
852 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
854 tab_offset (summary, 0, 3);
856 ds_init_empty (&name);
857 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
863 tab_hline (summary, TAL_1, 0, 6, 0);
866 for (i = 0; i < pt->n_vars; i++)
869 ds_put_cstr (&name, " * ");
870 ds_put_cstr (&name, var_to_string (pt->vars[i]));
872 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
875 for (i = 0; i < pt->n_entries; i++)
876 valid += pt->entries[i]->freq;
881 for (i = 0; i < 3; i++)
883 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
884 &proc->weight_format);
885 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
889 tab_next_row (summary);
893 submit (NULL, summary);
898 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
899 struct pivot_table *);
900 static struct tab_table *create_chisq_table (struct pivot_table *);
901 static struct tab_table *create_sym_table (struct pivot_table *);
902 static struct tab_table *create_risk_table (struct pivot_table *);
903 static struct tab_table *create_direct_table (struct pivot_table *);
904 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
905 struct tab_table *, int first_difference);
906 static void display_crosstabulation (struct crosstabs_proc *,
907 struct pivot_table *,
909 static void display_chisq (struct pivot_table *, struct tab_table *,
910 bool *showed_fisher);
911 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
913 static void display_risk (struct pivot_table *, struct tab_table *);
914 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
916 static void table_value_missing (struct crosstabs_proc *proc,
917 struct tab_table *table, int c, int r,
918 unsigned char opt, const union value *v,
919 const struct variable *var);
920 static void delete_missing (struct pivot_table *);
921 static void build_matrix (struct pivot_table *);
923 /* Output pivot table beginning at PB and continuing until PE,
924 exclusive. For efficiency, *MATP is a pointer to a matrix that can
925 hold *MAXROWS entries. */
927 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
929 struct tab_table *table = NULL; /* Crosstabulation table. */
930 struct tab_table *chisq = NULL; /* Chi-square table. */
931 bool showed_fisher = false;
932 struct tab_table *sym = NULL; /* Symmetric measures table. */
933 struct tab_table *risk = NULL; /* Risk estimate table. */
934 struct tab_table *direct = NULL; /* Directional measures table. */
937 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
940 table = create_crosstab_table (proc, pt);
941 if (proc->statistics & (1u << CRS_ST_CHISQ))
942 chisq = create_chisq_table (pt);
943 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
944 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
945 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
946 | (1u << CRS_ST_KAPPA)))
947 sym = create_sym_table (pt);
948 if (proc->statistics & (1u << CRS_ST_RISK))
949 risk = create_risk_table (pt);
950 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
951 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
952 direct = create_direct_table (pt);
955 while (find_crosstab (pt, &row0, &row1))
957 struct pivot_table x;
958 int first_difference;
960 make_pivot_table_subset (pt, row0, row1, &x);
962 /* Find all the row variable values. */
963 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
965 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
968 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
969 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
970 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
972 /* Allocate table space for the matrix. */
974 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
975 tab_realloc (table, -1,
976 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
977 tab_nr (table) * pt->n_entries / x.n_entries));
981 /* Find the first variable that differs from the last subtable. */
982 first_difference = find_first_difference (pt, row0);
985 display_dimensions (proc, &x, table, first_difference);
986 display_crosstabulation (proc, &x, table);
989 if (proc->exclude == MV_NEVER)
994 display_dimensions (proc, &x, chisq, first_difference);
995 display_chisq (&x, chisq, &showed_fisher);
999 display_dimensions (proc, &x, sym, first_difference);
1000 display_symmetric (proc, &x, sym);
1004 display_dimensions (proc, &x, risk, first_difference);
1005 display_risk (&x, risk);
1009 display_dimensions (proc, &x, direct, first_difference);
1010 display_directional (proc, &x, direct);
1013 /* Free the parts of x that are not owned by pt. In
1014 particular we must not free x.cols, which is the same as
1015 pt->cols, which is freed at the end of this function. */
1023 submit (NULL, table);
1028 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1034 submit (pt, direct);
1040 build_matrix (struct pivot_table *x)
1042 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1043 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1046 struct table_entry **p;
1050 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1052 const struct table_entry *te = *p;
1054 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1056 for (; col < x->n_cols; col++)
1062 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1069 if (++col >= x->n_cols)
1075 while (mp < &x->mat[x->n_cols * x->n_rows])
1077 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1079 /* Column totals, row totals, ns_rows. */
1081 for (col = 0; col < x->n_cols; col++)
1082 x->col_tot[col] = 0.0;
1083 for (row = 0; row < x->n_rows; row++)
1084 x->row_tot[row] = 0.0;
1086 for (row = 0; row < x->n_rows; row++)
1088 bool row_is_empty = true;
1089 for (col = 0; col < x->n_cols; col++)
1093 row_is_empty = false;
1094 x->col_tot[col] += *mp;
1095 x->row_tot[row] += *mp;
1102 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1106 for (col = 0; col < x->n_cols; col++)
1107 for (row = 0; row < x->n_rows; row++)
1108 if (x->mat[col + row * x->n_cols] != 0.0)
1116 for (col = 0; col < x->n_cols; col++)
1117 x->total += x->col_tot[col];
1120 static struct tab_table *
1121 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1128 static const struct tuple names[] =
1130 {CRS_CL_COUNT, N_("count")},
1131 {CRS_CL_ROW, N_("row %")},
1132 {CRS_CL_COLUMN, N_("column %")},
1133 {CRS_CL_TOTAL, N_("total %")},
1134 {CRS_CL_EXPECTED, N_("expected")},
1135 {CRS_CL_RESIDUAL, N_("residual")},
1136 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1137 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1139 const int n_names = sizeof names / sizeof *names;
1140 const struct tuple *t;
1142 struct tab_table *table;
1143 struct string title;
1144 struct pivot_table x;
1148 make_pivot_table_subset (pt, 0, 0, &x);
1150 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1151 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1152 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1154 /* First header line. */
1155 tab_joint_text (table, x.n_consts + 1, 0,
1156 (x.n_consts + 1) + (x.n_cols - 1), 0,
1157 TAB_CENTER | TAT_TITLE, var_get_name (x.vars[COL_VAR]));
1159 tab_hline (table, TAL_1, x.n_consts + 1,
1160 x.n_consts + 2 + x.n_cols - 2, 1);
1162 /* Second header line. */
1163 for (i = 2; i < x.n_consts + 2; i++)
1164 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1165 x.n_consts + 2 - i - 1, 1,
1166 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1167 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1168 var_get_name (x.vars[ROW_VAR]));
1169 for (i = 0; i < x.n_cols; i++)
1170 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1171 &x.cols[i], x.vars[COL_VAR]);
1172 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1174 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1175 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1178 ds_init_empty (&title);
1179 for (i = 0; i < x.n_consts + 2; i++)
1182 ds_put_cstr (&title, " * ");
1183 ds_put_cstr (&title, var_get_name (x.vars[i]));
1185 for (i = 0; i < pt->n_consts; i++)
1187 const struct variable *var = pt->const_vars[i];
1191 ds_put_format (&title, ", %s=", var_get_name (var));
1193 /* Insert the formatted value of the variable, then trim
1194 leading spaces in what was just inserted. */
1195 ofs = ds_length (&title);
1196 s = data_out (&pt->const_values[i], dict_get_encoding (proc->dict), var_get_print_format (var));
1197 ds_put_cstr (&title, s);
1199 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1203 ds_put_cstr (&title, " [");
1205 for (t = names; t < &names[n_names]; t++)
1206 if (proc->cells & (1u << t->value))
1209 ds_put_cstr (&title, ", ");
1210 ds_put_cstr (&title, gettext (t->name));
1212 ds_put_cstr (&title, "].");
1214 tab_title (table, "%s", ds_cstr (&title));
1215 ds_destroy (&title);
1217 tab_offset (table, 0, 2);
1221 static struct tab_table *
1222 create_chisq_table (struct pivot_table *pt)
1224 struct tab_table *chisq;
1226 chisq = tab_create (6 + (pt->n_vars - 2),
1227 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1228 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1230 tab_title (chisq, _("Chi-square tests."));
1232 tab_offset (chisq, pt->n_vars - 2, 0);
1233 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1234 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1235 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1236 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1237 _("Asymp. Sig. (2-sided)"));
1238 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1239 _("Exact Sig. (2-sided)"));
1240 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1241 _("Exact Sig. (1-sided)"));
1242 tab_offset (chisq, 0, 1);
1247 /* Symmetric measures. */
1248 static struct tab_table *
1249 create_sym_table (struct pivot_table *pt)
1251 struct tab_table *sym;
1253 sym = tab_create (6 + (pt->n_vars - 2),
1254 pt->n_entries / pt->n_cols * 7 + 10);
1255 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1256 tab_title (sym, _("Symmetric measures."));
1258 tab_offset (sym, pt->n_vars - 2, 0);
1259 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1260 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1261 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1262 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1263 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1264 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1265 tab_offset (sym, 0, 1);
1270 /* Risk estimate. */
1271 static struct tab_table *
1272 create_risk_table (struct pivot_table *pt)
1274 struct tab_table *risk;
1276 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1277 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1278 tab_title (risk, _("Risk estimate."));
1280 tab_offset (risk, pt->n_vars - 2, 0);
1281 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1282 _("95%% Confidence Interval"));
1283 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1284 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1285 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1286 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1287 tab_hline (risk, TAL_1, 2, 3, 1);
1288 tab_vline (risk, TAL_1, 2, 0, 1);
1289 tab_offset (risk, 0, 2);
1294 /* Directional measures. */
1295 static struct tab_table *
1296 create_direct_table (struct pivot_table *pt)
1298 struct tab_table *direct;
1300 direct = tab_create (7 + (pt->n_vars - 2),
1301 pt->n_entries / pt->n_cols * 7 + 10);
1302 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1303 tab_title (direct, _("Directional measures."));
1305 tab_offset (direct, pt->n_vars - 2, 0);
1306 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1307 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1308 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1309 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1310 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1311 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1312 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1313 tab_offset (direct, 0, 1);
1319 /* Delete missing rows and columns for statistical analysis when
1322 delete_missing (struct pivot_table *pt)
1326 for (r = 0; r < pt->n_rows; r++)
1327 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1329 for (c = 0; c < pt->n_cols; c++)
1330 pt->mat[c + r * pt->n_cols] = 0.;
1335 for (c = 0; c < pt->n_cols; c++)
1336 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1338 for (r = 0; r < pt->n_rows; r++)
1339 pt->mat[c + r * pt->n_cols] = 0.;
1344 /* Prepare table T for submission, and submit it. */
1346 submit (struct pivot_table *pt, struct tab_table *t)
1353 tab_resize (t, -1, 0);
1354 if (tab_nr (t) == tab_t (t))
1356 table_unref (&t->table);
1359 tab_offset (t, 0, 0);
1361 for (i = 2; i < pt->n_vars; i++)
1362 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1363 var_to_string (pt->vars[i]));
1364 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1365 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1367 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1369 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1375 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1377 size_t row0 = *row1p;
1380 if (row0 >= pt->n_entries)
1383 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1385 struct table_entry *a = pt->entries[row0];
1386 struct table_entry *b = pt->entries[row1];
1387 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1395 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1396 result. WIDTH_ points to an int which is either 0 for a
1397 numeric value or a string width for a string value. */
1399 compare_value_3way (const void *a_, const void *b_, const void *width_)
1401 const union value *a = a_;
1402 const union value *b = b_;
1403 const int *width = width_;
1405 return value_compare_3way (a, b, *width);
1408 /* Given an array of ENTRY_CNT table_entry structures starting at
1409 ENTRIES, creates a sorted list of the values that the variable
1410 with index VAR_IDX takes on. The values are returned as a
1411 malloc()'d array stored in *VALUES, with the number of values
1412 stored in *VALUE_CNT.
1415 enum_var_values (const struct pivot_table *pt, int var_idx,
1416 union value **valuesp, int *n_values)
1418 const struct variable *var = pt->vars[var_idx];
1419 struct var_range *range = get_var_range (var);
1420 union value *values;
1425 values = *valuesp = xnmalloc (range->count, sizeof *values);
1426 *n_values = range->count;
1427 for (i = 0; i < range->count; i++)
1428 values[i].f = range->min + i;
1432 int width = var_get_width (var);
1433 struct hmapx_node *node;
1434 const union value *iter;
1438 for (i = 0; i < pt->n_entries; i++)
1440 const struct table_entry *te = pt->entries[i];
1441 const union value *value = &te->values[var_idx];
1442 size_t hash = value_hash (value, width, 0);
1444 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1445 if (value_equal (iter, value, width))
1448 hmapx_insert (&set, (union value *) value, hash);
1453 *n_values = hmapx_count (&set);
1454 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1456 HMAPX_FOR_EACH (iter, node, &set)
1457 values[i++] = *iter;
1458 hmapx_destroy (&set);
1460 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1464 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1465 from V, displayed with print format spec from variable VAR. When
1466 in REPORT missing-value mode, missing values have an M appended. */
1468 table_value_missing (struct crosstabs_proc *proc,
1469 struct tab_table *table, int c, int r, unsigned char opt,
1470 const union value *v, const struct variable *var)
1472 const char *label = var_lookup_value_label (var, v);
1474 tab_text (table, c, r, TAB_LEFT, label);
1477 const struct fmt_spec *print = var_get_print_format (var);
1478 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1480 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1481 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1485 tab_value (table, c, r, opt, v, proc->dict, print);
1489 /* Draws a line across TABLE at the current row to indicate the most
1490 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1491 that changed, and puts the values that changed into the table. TB
1492 and PT must be the corresponding table_entry and crosstab,
1495 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1496 struct tab_table *table, int first_difference)
1498 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1500 for (; first_difference >= 2; first_difference--)
1501 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1502 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1503 pt->vars[first_difference]);
1506 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1507 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1508 additionally suffixed with a letter `M'. */
1510 format_cell_entry (struct tab_table *table, int c, int r, double value,
1511 char suffix, bool mark_missing, const struct dictionary *dict)
1513 const struct fmt_spec f = {FMT_F, 10, 1};
1520 s = data_out (&v, dict_get_encoding (dict), &f);
1524 suffixes[suffix_len++] = suffix;
1526 suffixes[suffix_len++] = 'M';
1527 suffixes[suffix_len] = '\0';
1529 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1530 s + strspn (s, " "), suffixes);
1533 /* Displays the crosstabulation table. */
1535 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1536 struct tab_table *table)
1542 for (r = 0; r < pt->n_rows; r++)
1543 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1544 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1547 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1548 TAB_LEFT, _("Total"));
1550 /* Put in the actual cells. */
1552 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1553 for (r = 0; r < pt->n_rows; r++)
1555 if (proc->n_cells > 1)
1556 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1557 for (c = 0; c < pt->n_cols; c++)
1559 bool mark_missing = false;
1560 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1561 if (proc->exclude == MV_NEVER
1562 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1563 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1565 mark_missing = true;
1566 for (i = 0; i < proc->n_cells; i++)
1571 switch (proc->a_cells[i])
1577 v = *mp / pt->row_tot[r] * 100.;
1581 v = *mp / pt->col_tot[c] * 100.;
1585 v = *mp / pt->total * 100.;
1588 case CRS_CL_EXPECTED:
1591 case CRS_CL_RESIDUAL:
1592 v = *mp - expected_value;
1594 case CRS_CL_SRESIDUAL:
1595 v = (*mp - expected_value) / sqrt (expected_value);
1597 case CRS_CL_ASRESIDUAL:
1598 v = ((*mp - expected_value)
1599 / sqrt (expected_value
1600 * (1. - pt->row_tot[r] / pt->total)
1601 * (1. - pt->col_tot[c] / pt->total)));
1606 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1612 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1616 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1617 for (r = 0; r < pt->n_rows; r++)
1619 bool mark_missing = false;
1621 if (proc->exclude == MV_NEVER
1622 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1623 mark_missing = true;
1625 for (i = 0; i < proc->n_cells; i++)
1630 switch (proc->a_cells[i])
1640 v = pt->row_tot[r] / pt->total * 100.;
1644 v = pt->row_tot[r] / pt->total * 100.;
1647 case CRS_CL_EXPECTED:
1648 case CRS_CL_RESIDUAL:
1649 case CRS_CL_SRESIDUAL:
1650 case CRS_CL_ASRESIDUAL:
1657 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1658 tab_next_row (table);
1662 /* Column totals, grand total. */
1664 if (proc->n_cells > 1)
1665 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1666 for (c = 0; c <= pt->n_cols; c++)
1668 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1669 bool mark_missing = false;
1672 if (proc->exclude == MV_NEVER && c < pt->n_cols
1673 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1674 mark_missing = true;
1676 for (i = 0; i < proc->n_cells; i++)
1681 switch (proc->a_cells[i])
1687 v = ct / pt->total * 100.;
1695 v = ct / pt->total * 100.;
1698 case CRS_CL_EXPECTED:
1699 case CRS_CL_RESIDUAL:
1700 case CRS_CL_SRESIDUAL:
1701 case CRS_CL_ASRESIDUAL:
1707 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1712 tab_offset (table, -1, tab_row (table) + last_row);
1713 tab_offset (table, 0, -1);
1716 static void calc_r (struct pivot_table *,
1717 double *PT, double *Y, double *, double *, double *);
1718 static void calc_chisq (struct pivot_table *,
1719 double[N_CHISQ], int[N_CHISQ], double *, double *);
1721 /* Display chi-square statistics. */
1723 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1724 bool *showed_fisher)
1726 static const char *chisq_stats[N_CHISQ] =
1728 N_("Pearson Chi-Square"),
1729 N_("Likelihood Ratio"),
1730 N_("Fisher's Exact Test"),
1731 N_("Continuity Correction"),
1732 N_("Linear-by-Linear Association"),
1734 double chisq_v[N_CHISQ];
1735 double fisher1, fisher2;
1740 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1742 tab_offset (chisq, pt->n_vars - 2, -1);
1744 for (i = 0; i < N_CHISQ; i++)
1746 if ((i != 2 && chisq_v[i] == SYSMIS)
1747 || (i == 2 && fisher1 == SYSMIS))
1750 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1753 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1754 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1755 tab_double (chisq, 3, 0, TAB_RIGHT,
1756 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1760 *showed_fisher = true;
1761 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1762 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1764 tab_next_row (chisq);
1767 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1768 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1769 tab_next_row (chisq);
1771 tab_offset (chisq, 0, -1);
1774 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1775 double[N_SYMMETRIC], double[N_SYMMETRIC],
1776 double[N_SYMMETRIC],
1777 double[3], double[3], double[3]);
1779 /* Display symmetric measures. */
1781 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1782 struct tab_table *sym)
1784 static const char *categories[] =
1786 N_("Nominal by Nominal"),
1787 N_("Ordinal by Ordinal"),
1788 N_("Interval by Interval"),
1789 N_("Measure of Agreement"),
1792 static const char *stats[N_SYMMETRIC] =
1796 N_("Contingency Coefficient"),
1797 N_("Kendall's tau-b"),
1798 N_("Kendall's tau-c"),
1800 N_("Spearman Correlation"),
1805 static const int stats_categories[N_SYMMETRIC] =
1807 0, 0, 0, 1, 1, 1, 1, 2, 3,
1811 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1812 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1815 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1816 somers_d_v, somers_d_ase, somers_d_t))
1819 tab_offset (sym, pt->n_vars - 2, -1);
1821 for (i = 0; i < N_SYMMETRIC; i++)
1823 if (sym_v[i] == SYSMIS)
1826 if (stats_categories[i] != last_cat)
1828 last_cat = stats_categories[i];
1829 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1832 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1833 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1834 if (sym_ase[i] != SYSMIS)
1835 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1836 if (sym_t[i] != SYSMIS)
1837 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1838 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1842 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1843 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1846 tab_offset (sym, 0, -1);
1849 static int calc_risk (struct pivot_table *,
1850 double[], double[], double[], union value *);
1852 /* Display risk estimate. */
1854 display_risk (struct pivot_table *pt, struct tab_table *risk)
1857 double risk_v[3], lower[3], upper[3];
1861 if (!calc_risk (pt, risk_v, upper, lower, c))
1864 tab_offset (risk, pt->n_vars - 2, -1);
1866 for (i = 0; i < 3; i++)
1868 const struct variable *cv = pt->vars[COL_VAR];
1869 const struct variable *rv = pt->vars[ROW_VAR];
1870 int cvw = var_get_width (cv);
1871 int rvw = var_get_width (rv);
1873 if (risk_v[i] == SYSMIS)
1879 if (var_is_numeric (cv))
1880 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1881 var_get_name (cv), c[0].f, c[1].f);
1883 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1885 cvw, value_str (&c[0], cvw),
1886 cvw, value_str (&c[1], cvw));
1890 if (var_is_numeric (rv))
1891 sprintf (buf, _("For cohort %s = %g"),
1892 var_get_name (rv), pt->rows[i - 1].f);
1894 sprintf (buf, _("For cohort %s = %.*s"),
1896 rvw, value_str (&pt->rows[i - 1], rvw));
1900 tab_text (risk, 0, 0, TAB_LEFT, buf);
1901 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1902 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1903 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1904 tab_next_row (risk);
1907 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1908 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1909 tab_next_row (risk);
1911 tab_offset (risk, 0, -1);
1914 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1915 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1916 double[N_DIRECTIONAL]);
1918 /* Display directional measures. */
1920 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1921 struct tab_table *direct)
1923 static const char *categories[] =
1925 N_("Nominal by Nominal"),
1926 N_("Ordinal by Ordinal"),
1927 N_("Nominal by Interval"),
1930 static const char *stats[] =
1933 N_("Goodman and Kruskal tau"),
1934 N_("Uncertainty Coefficient"),
1939 static const char *types[] =
1946 static const int stats_categories[N_DIRECTIONAL] =
1948 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1951 static const int stats_stats[N_DIRECTIONAL] =
1953 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1956 static const int stats_types[N_DIRECTIONAL] =
1958 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
1961 static const int *stats_lookup[] =
1968 static const char **stats_names[] =
1980 double direct_v[N_DIRECTIONAL];
1981 double direct_ase[N_DIRECTIONAL];
1982 double direct_t[N_DIRECTIONAL];
1986 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
1989 tab_offset (direct, pt->n_vars - 2, -1);
1991 for (i = 0; i < N_DIRECTIONAL; i++)
1993 if (direct_v[i] == SYSMIS)
1999 for (j = 0; j < 3; j++)
2000 if (last[j] != stats_lookup[j][i])
2003 tab_hline (direct, TAL_1, j, 6, 0);
2008 int k = last[j] = stats_lookup[j][i];
2013 string = var_get_name (pt->vars[0]);
2015 string = var_get_name (pt->vars[1]);
2017 tab_text_format (direct, j, 0, TAB_LEFT,
2018 gettext (stats_names[j][k]), string);
2023 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2024 if (direct_ase[i] != SYSMIS)
2025 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2026 if (direct_t[i] != SYSMIS)
2027 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2028 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2029 tab_next_row (direct);
2032 tab_offset (direct, 0, -1);
2035 /* Statistical calculations. */
2037 /* Returns the value of the gamma (factorial) function for an integer
2040 gamma_int (double pt)
2045 for (i = 2; i < pt; i++)
2050 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2052 static inline double
2053 Pr (int a, int b, int c, int d)
2055 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2056 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2057 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2058 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2059 / gamma_int (a + b + c + d + 1.));
2062 /* Swap the contents of A and B. */
2064 swap (int *a, int *b)
2071 /* Calculate significance for Fisher's exact test as specified in
2072 _SPSS Statistical Algorithms_, Appendix 5. */
2074 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2078 if (MIN (c, d) < MIN (a, b))
2079 swap (&a, &c), swap (&b, &d);
2080 if (MIN (b, d) < MIN (a, c))
2081 swap (&a, &b), swap (&c, &d);
2085 swap (&a, &b), swap (&c, &d);
2087 swap (&a, &c), swap (&b, &d);
2091 for (pt = 0; pt <= a; pt++)
2092 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2094 *fisher2 = *fisher1;
2095 for (pt = 1; pt <= b; pt++)
2096 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2099 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2100 columns with values COLS and N_ROWS rows with values ROWS. Values
2101 in the matrix sum to pt->total. */
2103 calc_chisq (struct pivot_table *pt,
2104 double chisq[N_CHISQ], int df[N_CHISQ],
2105 double *fisher1, double *fisher2)
2109 chisq[0] = chisq[1] = 0.;
2110 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2111 *fisher1 = *fisher2 = SYSMIS;
2113 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2115 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2117 chisq[0] = chisq[1] = SYSMIS;
2121 for (r = 0; r < pt->n_rows; r++)
2122 for (c = 0; c < pt->n_cols; c++)
2124 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2125 const double freq = pt->mat[pt->n_cols * r + c];
2126 const double residual = freq - expected;
2128 chisq[0] += residual * residual / expected;
2130 chisq[1] += freq * log (expected / freq);
2141 /* Calculate Yates and Fisher exact test. */
2142 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2144 double f11, f12, f21, f22;
2150 for (i = j = 0; i < pt->n_cols; i++)
2151 if (pt->col_tot[i] != 0.)
2160 f11 = pt->mat[nz_cols[0]];
2161 f12 = pt->mat[nz_cols[1]];
2162 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2163 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2168 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2171 chisq[3] = (pt->total * pow2 (pt_)
2172 / (f11 + f12) / (f21 + f22)
2173 / (f11 + f21) / (f12 + f22));
2181 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2182 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2185 /* Calculate Mantel-Haenszel. */
2186 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2188 double r, ase_0, ase_1;
2189 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2191 chisq[4] = (pt->total - 1.) * r * r;
2196 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2197 ASE_1, and ase_0 into ASE_0. The row and column values must be
2198 passed in PT and Y. */
2200 calc_r (struct pivot_table *pt,
2201 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2203 double SX, SY, S, T;
2205 double sum_XYf, sum_X2Y2f;
2206 double sum_Xr, sum_X2r;
2207 double sum_Yc, sum_Y2c;
2210 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2211 for (j = 0; j < pt->n_cols; j++)
2213 double fij = pt->mat[j + i * pt->n_cols];
2214 double product = PT[i] * Y[j];
2215 double temp = fij * product;
2217 sum_X2Y2f += temp * product;
2220 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2222 sum_Xr += PT[i] * pt->row_tot[i];
2223 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2225 Xbar = sum_Xr / pt->total;
2227 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2229 sum_Yc += Y[i] * pt->col_tot[i];
2230 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2232 Ybar = sum_Yc / pt->total;
2234 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2235 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2236 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2239 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2244 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2245 for (j = 0; j < pt->n_cols; j++)
2247 double Xresid, Yresid;
2250 Xresid = PT[i] - Xbar;
2251 Yresid = Y[j] - Ybar;
2252 temp = (T * Xresid * Yresid
2254 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2255 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2260 *ase_1 = sqrt (s) / (T * T);
2264 /* Calculate symmetric statistics and their asymptotic standard
2265 errors. Returns 0 if none could be calculated. */
2267 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2268 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2269 double t[N_SYMMETRIC],
2270 double somers_d_v[3], double somers_d_ase[3],
2271 double somers_d_t[3])
2275 q = MIN (pt->ns_rows, pt->ns_cols);
2279 for (i = 0; i < N_SYMMETRIC; i++)
2280 v[i] = ase[i] = t[i] = SYSMIS;
2282 /* Phi, Cramer's V, contingency coefficient. */
2283 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2285 double Xp = 0.; /* Pearson chi-square. */
2288 for (r = 0; r < pt->n_rows; r++)
2289 for (c = 0; c < pt->n_cols; c++)
2291 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2292 const double freq = pt->mat[pt->n_cols * r + c];
2293 const double residual = freq - expected;
2295 Xp += residual * residual / expected;
2298 if (proc->statistics & (1u << CRS_ST_PHI))
2300 v[0] = sqrt (Xp / pt->total);
2301 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2303 if (proc->statistics & (1u << CRS_ST_CC))
2304 v[2] = sqrt (Xp / (Xp + pt->total));
2307 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2308 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2313 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2317 Dr = Dc = pow2 (pt->total);
2318 for (r = 0; r < pt->n_rows; r++)
2319 Dr -= pow2 (pt->row_tot[r]);
2320 for (c = 0; c < pt->n_cols; c++)
2321 Dc -= pow2 (pt->col_tot[c]);
2323 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2324 for (c = 0; c < pt->n_cols; c++)
2328 for (r = 0; r < pt->n_rows; r++)
2329 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2338 for (i = 0; i < pt->n_rows; i++)
2342 for (j = 1; j < pt->n_cols; j++)
2343 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2346 for (j = 1; j < pt->n_cols; j++)
2347 Dij += cum[j + (i - 1) * pt->n_cols];
2351 double fij = pt->mat[j + i * pt->n_cols];
2355 if (++j == pt->n_cols)
2357 assert (j < pt->n_cols);
2359 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2360 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2364 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2365 Dij -= cum[j + (i - 1) * pt->n_cols];
2371 if (proc->statistics & (1u << CRS_ST_BTAU))
2372 v[3] = (P - Q) / sqrt (Dr * Dc);
2373 if (proc->statistics & (1u << CRS_ST_CTAU))
2374 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2375 if (proc->statistics & (1u << CRS_ST_GAMMA))
2376 v[5] = (P - Q) / (P + Q);
2378 /* ASE for tau-b, tau-c, gamma. Calculations could be
2379 eliminated here, at expense of memory. */
2384 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2385 for (i = 0; i < pt->n_rows; i++)
2389 for (j = 1; j < pt->n_cols; j++)
2390 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2393 for (j = 1; j < pt->n_cols; j++)
2394 Dij += cum[j + (i - 1) * pt->n_cols];
2398 double fij = pt->mat[j + i * pt->n_cols];
2400 if (proc->statistics & (1u << CRS_ST_BTAU))
2402 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2403 + v[3] * (pt->row_tot[i] * Dc
2404 + pt->col_tot[j] * Dr));
2405 btau_cum += fij * temp * temp;
2409 const double temp = Cij - Dij;
2410 ctau_cum += fij * temp * temp;
2413 if (proc->statistics & (1u << CRS_ST_GAMMA))
2415 const double temp = Q * Cij - P * Dij;
2416 gamma_cum += fij * temp * temp;
2419 if (proc->statistics & (1u << CRS_ST_D))
2421 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2422 - (P - Q) * (pt->total - pt->row_tot[i]));
2423 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2424 - (Q - P) * (pt->total - pt->col_tot[j]));
2427 if (++j == pt->n_cols)
2429 assert (j < pt->n_cols);
2431 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2432 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2436 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2437 Dij -= cum[j + (i - 1) * pt->n_cols];
2443 btau_var = ((btau_cum
2444 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2446 if (proc->statistics & (1u << CRS_ST_BTAU))
2448 ase[3] = sqrt (btau_var);
2449 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2452 if (proc->statistics & (1u << CRS_ST_CTAU))
2454 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2455 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2456 t[4] = v[4] / ase[4];
2458 if (proc->statistics & (1u << CRS_ST_GAMMA))
2460 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2461 t[5] = v[5] / (2. / (P + Q)
2462 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2464 if (proc->statistics & (1u << CRS_ST_D))
2466 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2467 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2468 somers_d_t[0] = (somers_d_v[0]
2470 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2471 somers_d_v[1] = (P - Q) / Dc;
2472 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2473 somers_d_t[1] = (somers_d_v[1]
2475 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2476 somers_d_v[2] = (P - Q) / Dr;
2477 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2478 somers_d_t[2] = (somers_d_v[2]
2480 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2486 /* Spearman correlation, Pearson's r. */
2487 if (proc->statistics & (1u << CRS_ST_CORR))
2489 double *R = xmalloc (sizeof *R * pt->n_rows);
2490 double *C = xmalloc (sizeof *C * pt->n_cols);
2493 double y, t, c = 0., s = 0.;
2498 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2499 y = pt->row_tot[i] - c;
2503 if (++i == pt->n_rows)
2505 assert (i < pt->n_rows);
2510 double y, t, c = 0., s = 0.;
2515 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2516 y = pt->col_tot[j] - c;
2520 if (++j == pt->n_cols)
2522 assert (j < pt->n_cols);
2526 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2532 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2536 /* Cohen's kappa. */
2537 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2539 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2542 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2543 i < pt->ns_rows; i++, j++)
2547 while (pt->col_tot[j] == 0.)
2550 prod = pt->row_tot[i] * pt->col_tot[j];
2551 sum = pt->row_tot[i] + pt->col_tot[j];
2553 sum_fii += pt->mat[j + i * pt->n_cols];
2555 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2556 sum_riciri_ci += prod * sum;
2558 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2559 for (j = 0; j < pt->ns_cols; j++)
2561 double sum = pt->row_tot[i] + pt->col_tot[j];
2562 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2565 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2567 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2568 + sum_rici * sum_rici
2569 - pt->total * sum_riciri_ci)
2570 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2572 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2573 / pow2 (pow2 (pt->total) - sum_rici))
2574 + ((2. * (pt->total - sum_fii)
2575 * (2. * sum_fii * sum_rici
2576 - pt->total * sum_fiiri_ci))
2577 / cube (pow2 (pt->total) - sum_rici))
2578 + (pow2 (pt->total - sum_fii)
2579 * (pt->total * sum_fijri_ci2 - 4.
2580 * sum_rici * sum_rici)
2581 / pow4 (pow2 (pt->total) - sum_rici))));
2583 t[8] = v[8] / ase[8];
2590 /* Calculate risk estimate. */
2592 calc_risk (struct pivot_table *pt,
2593 double *value, double *upper, double *lower, union value *c)
2595 double f11, f12, f21, f22;
2601 for (i = 0; i < 3; i++)
2602 value[i] = upper[i] = lower[i] = SYSMIS;
2605 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2612 for (i = j = 0; i < pt->n_cols; i++)
2613 if (pt->col_tot[i] != 0.)
2622 f11 = pt->mat[nz_cols[0]];
2623 f12 = pt->mat[nz_cols[1]];
2624 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2625 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2627 c[0] = pt->cols[nz_cols[0]];
2628 c[1] = pt->cols[nz_cols[1]];
2631 value[0] = (f11 * f22) / (f12 * f21);
2632 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2633 lower[0] = value[0] * exp (-1.960 * v);
2634 upper[0] = value[0] * exp (1.960 * v);
2636 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2637 v = sqrt ((f12 / (f11 * (f11 + f12)))
2638 + (f22 / (f21 * (f21 + f22))));
2639 lower[1] = value[1] * exp (-1.960 * v);
2640 upper[1] = value[1] * exp (1.960 * v);
2642 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2643 v = sqrt ((f11 / (f12 * (f11 + f12)))
2644 + (f21 / (f22 * (f21 + f22))));
2645 lower[2] = value[2] * exp (-1.960 * v);
2646 upper[2] = value[2] * exp (1.960 * v);
2651 /* Calculate directional measures. */
2653 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2654 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2655 double t[N_DIRECTIONAL])
2660 for (i = 0; i < N_DIRECTIONAL; i++)
2661 v[i] = ase[i] = t[i] = SYSMIS;
2665 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2667 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2668 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2669 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2670 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2671 double sum_fim, sum_fmj;
2673 int rm_index, cm_index;
2676 /* Find maximum for each row and their sum. */
2677 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2679 double max = pt->mat[i * pt->n_cols];
2682 for (j = 1; j < pt->n_cols; j++)
2683 if (pt->mat[j + i * pt->n_cols] > max)
2685 max = pt->mat[j + i * pt->n_cols];
2689 sum_fim += fim[i] = max;
2690 fim_index[i] = index;
2693 /* Find maximum for each column. */
2694 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2696 double max = pt->mat[j];
2699 for (i = 1; i < pt->n_rows; i++)
2700 if (pt->mat[j + i * pt->n_cols] > max)
2702 max = pt->mat[j + i * pt->n_cols];
2706 sum_fmj += fmj[j] = max;
2707 fmj_index[j] = index;
2710 /* Find maximum row total. */
2711 rm = pt->row_tot[0];
2713 for (i = 1; i < pt->n_rows; i++)
2714 if (pt->row_tot[i] > rm)
2716 rm = pt->row_tot[i];
2720 /* Find maximum column total. */
2721 cm = pt->col_tot[0];
2723 for (j = 1; j < pt->n_cols; j++)
2724 if (pt->col_tot[j] > cm)
2726 cm = pt->col_tot[j];
2730 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2731 v[1] = (sum_fmj - rm) / (pt->total - rm);
2732 v[2] = (sum_fim - cm) / (pt->total - cm);
2734 /* ASE1 for Y given PT. */
2738 for (accum = 0., i = 0; i < pt->n_rows; i++)
2739 for (j = 0; j < pt->n_cols; j++)
2741 const int deltaj = j == cm_index;
2742 accum += (pt->mat[j + i * pt->n_cols]
2743 * pow2 ((j == fim_index[i])
2748 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2751 /* ASE0 for Y given PT. */
2755 for (accum = 0., i = 0; i < pt->n_rows; i++)
2756 if (cm_index != fim_index[i])
2757 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2758 + pt->mat[i * pt->n_cols + cm_index]);
2759 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2762 /* ASE1 for PT given Y. */
2766 for (accum = 0., i = 0; i < pt->n_rows; i++)
2767 for (j = 0; j < pt->n_cols; j++)
2769 const int deltaj = i == rm_index;
2770 accum += (pt->mat[j + i * pt->n_cols]
2771 * pow2 ((i == fmj_index[j])
2776 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2779 /* ASE0 for PT given Y. */
2783 for (accum = 0., j = 0; j < pt->n_cols; j++)
2784 if (rm_index != fmj_index[j])
2785 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2786 + pt->mat[j + pt->n_cols * rm_index]);
2787 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2790 /* Symmetric ASE0 and ASE1. */
2795 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2796 for (j = 0; j < pt->n_cols; j++)
2798 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2799 int temp1 = (i == rm_index) + (j == cm_index);
2800 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2801 accum1 += (pt->mat[j + i * pt->n_cols]
2802 * pow2 (temp0 + (v[0] - 1.) * temp1));
2804 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2805 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2806 / (2. * pt->total - rm - cm));
2815 double sum_fij2_ri, sum_fij2_ci;
2816 double sum_ri2, sum_cj2;
2818 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2819 for (j = 0; j < pt->n_cols; j++)
2821 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2822 sum_fij2_ri += temp / pt->row_tot[i];
2823 sum_fij2_ci += temp / pt->col_tot[j];
2826 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2827 sum_ri2 += pow2 (pt->row_tot[i]);
2829 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2830 sum_cj2 += pow2 (pt->col_tot[j]);
2832 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2833 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2837 if (proc->statistics & (1u << CRS_ST_UC))
2839 double UX, UY, UXY, P;
2840 double ase1_yx, ase1_xy, ase1_sym;
2843 for (UX = 0., i = 0; i < pt->n_rows; i++)
2844 if (pt->row_tot[i] > 0.)
2845 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2847 for (UY = 0., j = 0; j < pt->n_cols; j++)
2848 if (pt->col_tot[j] > 0.)
2849 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2851 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2852 for (j = 0; j < pt->n_cols; j++)
2854 double entry = pt->mat[j + i * pt->n_cols];
2859 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2860 UXY -= entry / pt->total * log (entry / pt->total);
2863 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2864 for (j = 0; j < pt->n_cols; j++)
2866 double entry = pt->mat[j + i * pt->n_cols];
2871 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2872 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2873 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2874 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2875 ase1_sym += entry * pow2 ((UXY
2876 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2877 - (UX + UY) * log (entry / pt->total));
2880 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2881 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2882 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2883 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2885 v[6] = (UX + UY - UXY) / UX;
2886 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2887 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2889 v[7] = (UX + UY - UXY) / UY;
2890 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2891 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2895 if (proc->statistics & (1u << CRS_ST_D))
2897 double v_dummy[N_SYMMETRIC];
2898 double ase_dummy[N_SYMMETRIC];
2899 double t_dummy[N_SYMMETRIC];
2900 double somers_d_v[3];
2901 double somers_d_ase[3];
2902 double somers_d_t[3];
2904 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2905 somers_d_v, somers_d_ase, somers_d_t))
2908 for (i = 0; i < 3; i++)
2910 v[8 + i] = somers_d_v[i];
2911 ase[8 + i] = somers_d_ase[i];
2912 t[8 + i] = somers_d_t[i];
2918 if (proc->statistics & (1u << CRS_ST_ETA))
2921 double sum_Xr, sum_X2r;
2925 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2927 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2928 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2930 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2932 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2936 for (cum = 0., i = 0; i < pt->n_rows; i++)
2938 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2939 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2942 SXW -= cum * cum / pt->col_tot[j];
2944 v[11] = sqrt (1. - SXW / SX);
2948 double sum_Yc, sum_Y2c;
2952 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2954 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2955 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2957 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
2959 for (SYW = 0., i = 0; i < pt->n_rows; i++)
2963 for (cum = 0., j = 0; j < pt->n_cols; j++)
2965 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
2966 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
2969 SYW -= cum * cum / pt->row_tot[i];
2971 v[12] = sqrt (1. - SYW / SY);