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;
1146 table = tab_create (pt->n_consts + 1 + pt->n_cols + 1,
1147 (pt->n_entries / pt->n_cols) * 3 / 2 * proc->n_cells + 10);
1148 tab_headers (table, pt->n_consts + 1, 0, 2, 0);
1150 /* First header line. */
1151 tab_joint_text (table, pt->n_consts + 1, 0,
1152 (pt->n_consts + 1) + (pt->n_cols - 1), 0,
1153 TAB_CENTER | TAT_TITLE, var_get_name (pt->vars[COL_VAR]));
1155 tab_hline (table, TAL_1, pt->n_consts + 1,
1156 pt->n_consts + 2 + pt->n_cols - 2, 1);
1158 /* Second header line. */
1159 for (i = 2; i < pt->n_consts + 2; i++)
1160 tab_joint_text (table, pt->n_consts + 2 - i - 1, 0,
1161 pt->n_consts + 2 - i - 1, 1,
1162 TAB_RIGHT | TAT_TITLE, var_to_string (pt->vars[i]));
1163 tab_text (table, pt->n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1164 var_get_name (pt->vars[ROW_VAR]));
1165 for (i = 0; i < pt->n_cols; i++)
1166 table_value_missing (proc, table, pt->n_consts + 2 + i - 1, 1, TAB_RIGHT,
1167 &pt->cols[i], pt->vars[COL_VAR]);
1168 tab_text (table, pt->n_consts + 2 + pt->n_cols - 1, 1, TAB_CENTER, _("Total"));
1170 tab_hline (table, TAL_1, 0, pt->n_consts + 2 + pt->n_cols - 1, 2);
1171 tab_vline (table, TAL_1, pt->n_consts + 2 + pt->n_cols - 1, 0, 1);
1174 ds_init_empty (&title);
1175 for (i = 0; i < pt->n_consts + 2; i++)
1178 ds_put_cstr (&title, " * ");
1179 ds_put_cstr (&title, var_get_name (pt->vars[i]));
1181 for (i = 0; i < pt->n_consts; i++)
1183 const struct variable *var = pt->const_vars[i];
1187 ds_put_format (&title, ", %s=", var_get_name (var));
1189 /* Insert the formatted value of the variable, then trim
1190 leading spaces in what was just inserted. */
1191 ofs = ds_length (&title);
1192 s = data_out (&pt->const_values[i], dict_get_encoding (proc->dict), var_get_print_format (var));
1193 ds_put_cstr (&title, s);
1195 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1199 ds_put_cstr (&title, " [");
1201 for (t = names; t < &names[n_names]; t++)
1202 if (proc->cells & (1u << t->value))
1205 ds_put_cstr (&title, ", ");
1206 ds_put_cstr (&title, gettext (t->name));
1208 ds_put_cstr (&title, "].");
1210 tab_title (table, "%s", ds_cstr (&title));
1211 ds_destroy (&title);
1213 tab_offset (table, 0, 2);
1217 static struct tab_table *
1218 create_chisq_table (struct pivot_table *pt)
1220 struct tab_table *chisq;
1222 chisq = tab_create (6 + (pt->n_vars - 2),
1223 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1224 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1226 tab_title (chisq, _("Chi-square tests."));
1228 tab_offset (chisq, pt->n_vars - 2, 0);
1229 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1230 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1231 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1232 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1233 _("Asymp. Sig. (2-sided)"));
1234 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1235 _("Exact Sig. (2-sided)"));
1236 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1237 _("Exact Sig. (1-sided)"));
1238 tab_offset (chisq, 0, 1);
1243 /* Symmetric measures. */
1244 static struct tab_table *
1245 create_sym_table (struct pivot_table *pt)
1247 struct tab_table *sym;
1249 sym = tab_create (6 + (pt->n_vars - 2),
1250 pt->n_entries / pt->n_cols * 7 + 10);
1251 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1252 tab_title (sym, _("Symmetric measures."));
1254 tab_offset (sym, pt->n_vars - 2, 0);
1255 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1256 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1257 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1258 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1259 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1260 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1261 tab_offset (sym, 0, 1);
1266 /* Risk estimate. */
1267 static struct tab_table *
1268 create_risk_table (struct pivot_table *pt)
1270 struct tab_table *risk;
1272 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1273 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1274 tab_title (risk, _("Risk estimate."));
1276 tab_offset (risk, pt->n_vars - 2, 0);
1277 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1278 _("95%% Confidence Interval"));
1279 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1280 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1281 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1282 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1283 tab_hline (risk, TAL_1, 2, 3, 1);
1284 tab_vline (risk, TAL_1, 2, 0, 1);
1285 tab_offset (risk, 0, 2);
1290 /* Directional measures. */
1291 static struct tab_table *
1292 create_direct_table (struct pivot_table *pt)
1294 struct tab_table *direct;
1296 direct = tab_create (7 + (pt->n_vars - 2),
1297 pt->n_entries / pt->n_cols * 7 + 10);
1298 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1299 tab_title (direct, _("Directional measures."));
1301 tab_offset (direct, pt->n_vars - 2, 0);
1302 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1303 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1304 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1305 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1306 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1307 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1308 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1309 tab_offset (direct, 0, 1);
1315 /* Delete missing rows and columns for statistical analysis when
1318 delete_missing (struct pivot_table *pt)
1322 for (r = 0; r < pt->n_rows; r++)
1323 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1325 for (c = 0; c < pt->n_cols; c++)
1326 pt->mat[c + r * pt->n_cols] = 0.;
1331 for (c = 0; c < pt->n_cols; c++)
1332 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1334 for (r = 0; r < pt->n_rows; r++)
1335 pt->mat[c + r * pt->n_cols] = 0.;
1340 /* Prepare table T for submission, and submit it. */
1342 submit (struct pivot_table *pt, struct tab_table *t)
1349 tab_resize (t, -1, 0);
1350 if (tab_nr (t) == tab_t (t))
1352 table_unref (&t->table);
1355 tab_offset (t, 0, 0);
1357 for (i = 2; i < pt->n_vars; i++)
1358 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1359 var_to_string (pt->vars[i]));
1360 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1361 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1363 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1365 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1371 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1373 size_t row0 = *row1p;
1376 if (row0 >= pt->n_entries)
1379 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1381 struct table_entry *a = pt->entries[row0];
1382 struct table_entry *b = pt->entries[row1];
1383 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1391 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1392 result. WIDTH_ points to an int which is either 0 for a
1393 numeric value or a string width for a string value. */
1395 compare_value_3way (const void *a_, const void *b_, const void *width_)
1397 const union value *a = a_;
1398 const union value *b = b_;
1399 const int *width = width_;
1401 return value_compare_3way (a, b, *width);
1404 /* Given an array of ENTRY_CNT table_entry structures starting at
1405 ENTRIES, creates a sorted list of the values that the variable
1406 with index VAR_IDX takes on. The values are returned as a
1407 malloc()'d array stored in *VALUES, with the number of values
1408 stored in *VALUE_CNT.
1411 enum_var_values (const struct pivot_table *pt, int var_idx,
1412 union value **valuesp, int *n_values)
1414 const struct variable *var = pt->vars[var_idx];
1415 struct var_range *range = get_var_range (var);
1416 union value *values;
1421 values = *valuesp = xnmalloc (range->count, sizeof *values);
1422 *n_values = range->count;
1423 for (i = 0; i < range->count; i++)
1424 values[i].f = range->min + i;
1428 int width = var_get_width (var);
1429 struct hmapx_node *node;
1430 const union value *iter;
1434 for (i = 0; i < pt->n_entries; i++)
1436 const struct table_entry *te = pt->entries[i];
1437 const union value *value = &te->values[var_idx];
1438 size_t hash = value_hash (value, width, 0);
1440 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1441 if (value_equal (iter, value, width))
1444 hmapx_insert (&set, (union value *) value, hash);
1449 *n_values = hmapx_count (&set);
1450 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1452 HMAPX_FOR_EACH (iter, node, &set)
1453 values[i++] = *iter;
1454 hmapx_destroy (&set);
1456 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1460 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1461 from V, displayed with print format spec from variable VAR. When
1462 in REPORT missing-value mode, missing values have an M appended. */
1464 table_value_missing (struct crosstabs_proc *proc,
1465 struct tab_table *table, int c, int r, unsigned char opt,
1466 const union value *v, const struct variable *var)
1468 const char *label = var_lookup_value_label (var, v);
1470 tab_text (table, c, r, TAB_LEFT, label);
1473 const struct fmt_spec *print = var_get_print_format (var);
1474 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1476 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1477 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1481 tab_value (table, c, r, opt, v, proc->dict, print);
1485 /* Draws a line across TABLE at the current row to indicate the most
1486 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1487 that changed, and puts the values that changed into the table. TB
1488 and PT must be the corresponding table_entry and crosstab,
1491 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1492 struct tab_table *table, int first_difference)
1494 tab_hline (table, TAL_1, pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1496 for (; first_difference >= 2; first_difference--)
1497 table_value_missing (proc, table, pt->n_vars - first_difference - 1, 0,
1498 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1499 pt->vars[first_difference]);
1502 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1503 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1504 additionally suffixed with a letter `M'. */
1506 format_cell_entry (struct tab_table *table, int c, int r, double value,
1507 char suffix, bool mark_missing, const struct dictionary *dict)
1509 const struct fmt_spec f = {FMT_F, 10, 1};
1516 s = data_out (&v, dict_get_encoding (dict), &f);
1520 suffixes[suffix_len++] = suffix;
1522 suffixes[suffix_len++] = 'M';
1523 suffixes[suffix_len] = '\0';
1525 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1526 s + strspn (s, " "), suffixes);
1529 /* Displays the crosstabulation table. */
1531 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1532 struct tab_table *table)
1538 for (r = 0; r < pt->n_rows; r++)
1539 table_value_missing (proc, table, pt->n_vars - 2, r * proc->n_cells,
1540 TAB_RIGHT, &pt->rows[r], pt->vars[ROW_VAR]);
1542 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1543 TAB_LEFT, _("Total"));
1545 /* Put in the actual cells. */
1547 tab_offset (table, pt->n_vars - 1, -1);
1548 for (r = 0; r < pt->n_rows; r++)
1550 if (proc->n_cells > 1)
1551 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1552 for (c = 0; c < pt->n_cols; c++)
1554 bool mark_missing = false;
1555 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1556 if (proc->exclude == MV_NEVER
1557 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1558 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1560 mark_missing = true;
1561 for (i = 0; i < proc->n_cells; i++)
1566 switch (proc->a_cells[i])
1572 v = *mp / pt->row_tot[r] * 100.;
1576 v = *mp / pt->col_tot[c] * 100.;
1580 v = *mp / pt->total * 100.;
1583 case CRS_CL_EXPECTED:
1586 case CRS_CL_RESIDUAL:
1587 v = *mp - expected_value;
1589 case CRS_CL_SRESIDUAL:
1590 v = (*mp - expected_value) / sqrt (expected_value);
1592 case CRS_CL_ASRESIDUAL:
1593 v = ((*mp - expected_value)
1594 / sqrt (expected_value
1595 * (1. - pt->row_tot[r] / pt->total)
1596 * (1. - pt->col_tot[c] / pt->total)));
1601 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1607 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1611 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1612 for (r = 0; r < pt->n_rows; r++)
1614 bool mark_missing = false;
1616 if (proc->exclude == MV_NEVER
1617 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1618 mark_missing = true;
1620 for (i = 0; i < proc->n_cells; i++)
1625 switch (proc->a_cells[i])
1635 v = pt->row_tot[r] / pt->total * 100.;
1639 v = pt->row_tot[r] / pt->total * 100.;
1642 case CRS_CL_EXPECTED:
1643 case CRS_CL_RESIDUAL:
1644 case CRS_CL_SRESIDUAL:
1645 case CRS_CL_ASRESIDUAL:
1652 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1653 tab_next_row (table);
1657 /* Column totals, grand total. */
1659 if (proc->n_cells > 1)
1660 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1661 for (c = 0; c <= pt->n_cols; c++)
1663 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1664 bool mark_missing = false;
1667 if (proc->exclude == MV_NEVER && c < pt->n_cols
1668 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1669 mark_missing = true;
1671 for (i = 0; i < proc->n_cells; i++)
1676 switch (proc->a_cells[i])
1682 v = ct / pt->total * 100.;
1690 v = ct / pt->total * 100.;
1693 case CRS_CL_EXPECTED:
1694 case CRS_CL_RESIDUAL:
1695 case CRS_CL_SRESIDUAL:
1696 case CRS_CL_ASRESIDUAL:
1702 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1707 tab_offset (table, -1, tab_row (table) + last_row);
1708 tab_offset (table, 0, -1);
1711 static void calc_r (struct pivot_table *,
1712 double *PT, double *Y, double *, double *, double *);
1713 static void calc_chisq (struct pivot_table *,
1714 double[N_CHISQ], int[N_CHISQ], double *, double *);
1716 /* Display chi-square statistics. */
1718 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1719 bool *showed_fisher)
1721 static const char *chisq_stats[N_CHISQ] =
1723 N_("Pearson Chi-Square"),
1724 N_("Likelihood Ratio"),
1725 N_("Fisher's Exact Test"),
1726 N_("Continuity Correction"),
1727 N_("Linear-by-Linear Association"),
1729 double chisq_v[N_CHISQ];
1730 double fisher1, fisher2;
1735 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1737 tab_offset (chisq, pt->n_vars - 2, -1);
1739 for (i = 0; i < N_CHISQ; i++)
1741 if ((i != 2 && chisq_v[i] == SYSMIS)
1742 || (i == 2 && fisher1 == SYSMIS))
1745 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1748 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1749 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1750 tab_double (chisq, 3, 0, TAB_RIGHT,
1751 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1755 *showed_fisher = true;
1756 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1757 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1759 tab_next_row (chisq);
1762 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1763 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1764 tab_next_row (chisq);
1766 tab_offset (chisq, 0, -1);
1769 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1770 double[N_SYMMETRIC], double[N_SYMMETRIC],
1771 double[N_SYMMETRIC],
1772 double[3], double[3], double[3]);
1774 /* Display symmetric measures. */
1776 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1777 struct tab_table *sym)
1779 static const char *categories[] =
1781 N_("Nominal by Nominal"),
1782 N_("Ordinal by Ordinal"),
1783 N_("Interval by Interval"),
1784 N_("Measure of Agreement"),
1787 static const char *stats[N_SYMMETRIC] =
1791 N_("Contingency Coefficient"),
1792 N_("Kendall's tau-b"),
1793 N_("Kendall's tau-c"),
1795 N_("Spearman Correlation"),
1800 static const int stats_categories[N_SYMMETRIC] =
1802 0, 0, 0, 1, 1, 1, 1, 2, 3,
1806 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1807 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1810 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1811 somers_d_v, somers_d_ase, somers_d_t))
1814 tab_offset (sym, pt->n_vars - 2, -1);
1816 for (i = 0; i < N_SYMMETRIC; i++)
1818 if (sym_v[i] == SYSMIS)
1821 if (stats_categories[i] != last_cat)
1823 last_cat = stats_categories[i];
1824 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1827 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1828 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1829 if (sym_ase[i] != SYSMIS)
1830 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1831 if (sym_t[i] != SYSMIS)
1832 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1833 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1837 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1838 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1841 tab_offset (sym, 0, -1);
1844 static int calc_risk (struct pivot_table *,
1845 double[], double[], double[], union value *);
1847 /* Display risk estimate. */
1849 display_risk (struct pivot_table *pt, struct tab_table *risk)
1852 double risk_v[3], lower[3], upper[3];
1856 if (!calc_risk (pt, risk_v, upper, lower, c))
1859 tab_offset (risk, pt->n_vars - 2, -1);
1861 for (i = 0; i < 3; i++)
1863 const struct variable *cv = pt->vars[COL_VAR];
1864 const struct variable *rv = pt->vars[ROW_VAR];
1865 int cvw = var_get_width (cv);
1866 int rvw = var_get_width (rv);
1868 if (risk_v[i] == SYSMIS)
1874 if (var_is_numeric (cv))
1875 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1876 var_get_name (cv), c[0].f, c[1].f);
1878 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1880 cvw, value_str (&c[0], cvw),
1881 cvw, value_str (&c[1], cvw));
1885 if (var_is_numeric (rv))
1886 sprintf (buf, _("For cohort %s = %g"),
1887 var_get_name (rv), pt->rows[i - 1].f);
1889 sprintf (buf, _("For cohort %s = %.*s"),
1891 rvw, value_str (&pt->rows[i - 1], rvw));
1895 tab_text (risk, 0, 0, TAB_LEFT, buf);
1896 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1897 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1898 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1899 tab_next_row (risk);
1902 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1903 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1904 tab_next_row (risk);
1906 tab_offset (risk, 0, -1);
1909 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1910 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1911 double[N_DIRECTIONAL]);
1913 /* Display directional measures. */
1915 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1916 struct tab_table *direct)
1918 static const char *categories[] =
1920 N_("Nominal by Nominal"),
1921 N_("Ordinal by Ordinal"),
1922 N_("Nominal by Interval"),
1925 static const char *stats[] =
1928 N_("Goodman and Kruskal tau"),
1929 N_("Uncertainty Coefficient"),
1934 static const char *types[] =
1941 static const int stats_categories[N_DIRECTIONAL] =
1943 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1946 static const int stats_stats[N_DIRECTIONAL] =
1948 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1951 static const int stats_types[N_DIRECTIONAL] =
1953 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
1956 static const int *stats_lookup[] =
1963 static const char **stats_names[] =
1975 double direct_v[N_DIRECTIONAL];
1976 double direct_ase[N_DIRECTIONAL];
1977 double direct_t[N_DIRECTIONAL];
1981 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
1984 tab_offset (direct, pt->n_vars - 2, -1);
1986 for (i = 0; i < N_DIRECTIONAL; i++)
1988 if (direct_v[i] == SYSMIS)
1994 for (j = 0; j < 3; j++)
1995 if (last[j] != stats_lookup[j][i])
1998 tab_hline (direct, TAL_1, j, 6, 0);
2003 int k = last[j] = stats_lookup[j][i];
2008 string = var_get_name (pt->vars[0]);
2010 string = var_get_name (pt->vars[1]);
2012 tab_text_format (direct, j, 0, TAB_LEFT,
2013 gettext (stats_names[j][k]), string);
2018 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2019 if (direct_ase[i] != SYSMIS)
2020 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2021 if (direct_t[i] != SYSMIS)
2022 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2023 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2024 tab_next_row (direct);
2027 tab_offset (direct, 0, -1);
2030 /* Statistical calculations. */
2032 /* Returns the value of the gamma (factorial) function for an integer
2035 gamma_int (double pt)
2040 for (i = 2; i < pt; i++)
2045 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2047 static inline double
2048 Pr (int a, int b, int c, int d)
2050 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2051 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2052 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2053 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2054 / gamma_int (a + b + c + d + 1.));
2057 /* Swap the contents of A and B. */
2059 swap (int *a, int *b)
2066 /* Calculate significance for Fisher's exact test as specified in
2067 _SPSS Statistical Algorithms_, Appendix 5. */
2069 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2073 if (MIN (c, d) < MIN (a, b))
2074 swap (&a, &c), swap (&b, &d);
2075 if (MIN (b, d) < MIN (a, c))
2076 swap (&a, &b), swap (&c, &d);
2080 swap (&a, &b), swap (&c, &d);
2082 swap (&a, &c), swap (&b, &d);
2086 for (pt = 0; pt <= a; pt++)
2087 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2089 *fisher2 = *fisher1;
2090 for (pt = 1; pt <= b; pt++)
2091 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2094 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2095 columns with values COLS and N_ROWS rows with values ROWS. Values
2096 in the matrix sum to pt->total. */
2098 calc_chisq (struct pivot_table *pt,
2099 double chisq[N_CHISQ], int df[N_CHISQ],
2100 double *fisher1, double *fisher2)
2104 chisq[0] = chisq[1] = 0.;
2105 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2106 *fisher1 = *fisher2 = SYSMIS;
2108 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2110 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2112 chisq[0] = chisq[1] = SYSMIS;
2116 for (r = 0; r < pt->n_rows; r++)
2117 for (c = 0; c < pt->n_cols; c++)
2119 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2120 const double freq = pt->mat[pt->n_cols * r + c];
2121 const double residual = freq - expected;
2123 chisq[0] += residual * residual / expected;
2125 chisq[1] += freq * log (expected / freq);
2136 /* Calculate Yates and Fisher exact test. */
2137 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2139 double f11, f12, f21, f22;
2145 for (i = j = 0; i < pt->n_cols; i++)
2146 if (pt->col_tot[i] != 0.)
2155 f11 = pt->mat[nz_cols[0]];
2156 f12 = pt->mat[nz_cols[1]];
2157 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2158 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2163 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2166 chisq[3] = (pt->total * pow2 (pt_)
2167 / (f11 + f12) / (f21 + f22)
2168 / (f11 + f21) / (f12 + f22));
2176 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2177 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2180 /* Calculate Mantel-Haenszel. */
2181 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2183 double r, ase_0, ase_1;
2184 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2186 chisq[4] = (pt->total - 1.) * r * r;
2191 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2192 ASE_1, and ase_0 into ASE_0. The row and column values must be
2193 passed in PT and Y. */
2195 calc_r (struct pivot_table *pt,
2196 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2198 double SX, SY, S, T;
2200 double sum_XYf, sum_X2Y2f;
2201 double sum_Xr, sum_X2r;
2202 double sum_Yc, sum_Y2c;
2205 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2206 for (j = 0; j < pt->n_cols; j++)
2208 double fij = pt->mat[j + i * pt->n_cols];
2209 double product = PT[i] * Y[j];
2210 double temp = fij * product;
2212 sum_X2Y2f += temp * product;
2215 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2217 sum_Xr += PT[i] * pt->row_tot[i];
2218 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2220 Xbar = sum_Xr / pt->total;
2222 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2224 sum_Yc += Y[i] * pt->col_tot[i];
2225 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2227 Ybar = sum_Yc / pt->total;
2229 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2230 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2231 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2234 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2239 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2240 for (j = 0; j < pt->n_cols; j++)
2242 double Xresid, Yresid;
2245 Xresid = PT[i] - Xbar;
2246 Yresid = Y[j] - Ybar;
2247 temp = (T * Xresid * Yresid
2249 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2250 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2255 *ase_1 = sqrt (s) / (T * T);
2259 /* Calculate symmetric statistics and their asymptotic standard
2260 errors. Returns 0 if none could be calculated. */
2262 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2263 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2264 double t[N_SYMMETRIC],
2265 double somers_d_v[3], double somers_d_ase[3],
2266 double somers_d_t[3])
2270 q = MIN (pt->ns_rows, pt->ns_cols);
2274 for (i = 0; i < N_SYMMETRIC; i++)
2275 v[i] = ase[i] = t[i] = SYSMIS;
2277 /* Phi, Cramer's V, contingency coefficient. */
2278 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2280 double Xp = 0.; /* Pearson chi-square. */
2283 for (r = 0; r < pt->n_rows; r++)
2284 for (c = 0; c < pt->n_cols; c++)
2286 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2287 const double freq = pt->mat[pt->n_cols * r + c];
2288 const double residual = freq - expected;
2290 Xp += residual * residual / expected;
2293 if (proc->statistics & (1u << CRS_ST_PHI))
2295 v[0] = sqrt (Xp / pt->total);
2296 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2298 if (proc->statistics & (1u << CRS_ST_CC))
2299 v[2] = sqrt (Xp / (Xp + pt->total));
2302 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2303 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2308 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2312 Dr = Dc = pow2 (pt->total);
2313 for (r = 0; r < pt->n_rows; r++)
2314 Dr -= pow2 (pt->row_tot[r]);
2315 for (c = 0; c < pt->n_cols; c++)
2316 Dc -= pow2 (pt->col_tot[c]);
2318 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2319 for (c = 0; c < pt->n_cols; c++)
2323 for (r = 0; r < pt->n_rows; r++)
2324 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2333 for (i = 0; i < pt->n_rows; i++)
2337 for (j = 1; j < pt->n_cols; j++)
2338 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2341 for (j = 1; j < pt->n_cols; j++)
2342 Dij += cum[j + (i - 1) * pt->n_cols];
2346 double fij = pt->mat[j + i * pt->n_cols];
2350 if (++j == pt->n_cols)
2352 assert (j < pt->n_cols);
2354 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2355 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2359 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2360 Dij -= cum[j + (i - 1) * pt->n_cols];
2366 if (proc->statistics & (1u << CRS_ST_BTAU))
2367 v[3] = (P - Q) / sqrt (Dr * Dc);
2368 if (proc->statistics & (1u << CRS_ST_CTAU))
2369 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2370 if (proc->statistics & (1u << CRS_ST_GAMMA))
2371 v[5] = (P - Q) / (P + Q);
2373 /* ASE for tau-b, tau-c, gamma. Calculations could be
2374 eliminated here, at expense of memory. */
2379 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2380 for (i = 0; i < pt->n_rows; i++)
2384 for (j = 1; j < pt->n_cols; j++)
2385 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2388 for (j = 1; j < pt->n_cols; j++)
2389 Dij += cum[j + (i - 1) * pt->n_cols];
2393 double fij = pt->mat[j + i * pt->n_cols];
2395 if (proc->statistics & (1u << CRS_ST_BTAU))
2397 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2398 + v[3] * (pt->row_tot[i] * Dc
2399 + pt->col_tot[j] * Dr));
2400 btau_cum += fij * temp * temp;
2404 const double temp = Cij - Dij;
2405 ctau_cum += fij * temp * temp;
2408 if (proc->statistics & (1u << CRS_ST_GAMMA))
2410 const double temp = Q * Cij - P * Dij;
2411 gamma_cum += fij * temp * temp;
2414 if (proc->statistics & (1u << CRS_ST_D))
2416 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2417 - (P - Q) * (pt->total - pt->row_tot[i]));
2418 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2419 - (Q - P) * (pt->total - pt->col_tot[j]));
2422 if (++j == pt->n_cols)
2424 assert (j < pt->n_cols);
2426 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2427 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2431 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2432 Dij -= cum[j + (i - 1) * pt->n_cols];
2438 btau_var = ((btau_cum
2439 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2441 if (proc->statistics & (1u << CRS_ST_BTAU))
2443 ase[3] = sqrt (btau_var);
2444 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2447 if (proc->statistics & (1u << CRS_ST_CTAU))
2449 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2450 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2451 t[4] = v[4] / ase[4];
2453 if (proc->statistics & (1u << CRS_ST_GAMMA))
2455 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2456 t[5] = v[5] / (2. / (P + Q)
2457 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2459 if (proc->statistics & (1u << CRS_ST_D))
2461 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2462 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2463 somers_d_t[0] = (somers_d_v[0]
2465 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2466 somers_d_v[1] = (P - Q) / Dc;
2467 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2468 somers_d_t[1] = (somers_d_v[1]
2470 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2471 somers_d_v[2] = (P - Q) / Dr;
2472 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2473 somers_d_t[2] = (somers_d_v[2]
2475 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2481 /* Spearman correlation, Pearson's r. */
2482 if (proc->statistics & (1u << CRS_ST_CORR))
2484 double *R = xmalloc (sizeof *R * pt->n_rows);
2485 double *C = xmalloc (sizeof *C * pt->n_cols);
2488 double y, t, c = 0., s = 0.;
2493 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2494 y = pt->row_tot[i] - c;
2498 if (++i == pt->n_rows)
2500 assert (i < pt->n_rows);
2505 double y, t, c = 0., s = 0.;
2510 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2511 y = pt->col_tot[j] - c;
2515 if (++j == pt->n_cols)
2517 assert (j < pt->n_cols);
2521 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2527 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2531 /* Cohen's kappa. */
2532 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2534 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2537 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2538 i < pt->ns_rows; i++, j++)
2542 while (pt->col_tot[j] == 0.)
2545 prod = pt->row_tot[i] * pt->col_tot[j];
2546 sum = pt->row_tot[i] + pt->col_tot[j];
2548 sum_fii += pt->mat[j + i * pt->n_cols];
2550 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2551 sum_riciri_ci += prod * sum;
2553 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2554 for (j = 0; j < pt->ns_cols; j++)
2556 double sum = pt->row_tot[i] + pt->col_tot[j];
2557 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2560 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2562 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2563 + sum_rici * sum_rici
2564 - pt->total * sum_riciri_ci)
2565 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2567 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2568 / pow2 (pow2 (pt->total) - sum_rici))
2569 + ((2. * (pt->total - sum_fii)
2570 * (2. * sum_fii * sum_rici
2571 - pt->total * sum_fiiri_ci))
2572 / cube (pow2 (pt->total) - sum_rici))
2573 + (pow2 (pt->total - sum_fii)
2574 * (pt->total * sum_fijri_ci2 - 4.
2575 * sum_rici * sum_rici)
2576 / pow4 (pow2 (pt->total) - sum_rici))));
2578 t[8] = v[8] / ase[8];
2585 /* Calculate risk estimate. */
2587 calc_risk (struct pivot_table *pt,
2588 double *value, double *upper, double *lower, union value *c)
2590 double f11, f12, f21, f22;
2596 for (i = 0; i < 3; i++)
2597 value[i] = upper[i] = lower[i] = SYSMIS;
2600 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2607 for (i = j = 0; i < pt->n_cols; i++)
2608 if (pt->col_tot[i] != 0.)
2617 f11 = pt->mat[nz_cols[0]];
2618 f12 = pt->mat[nz_cols[1]];
2619 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2620 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2622 c[0] = pt->cols[nz_cols[0]];
2623 c[1] = pt->cols[nz_cols[1]];
2626 value[0] = (f11 * f22) / (f12 * f21);
2627 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2628 lower[0] = value[0] * exp (-1.960 * v);
2629 upper[0] = value[0] * exp (1.960 * v);
2631 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2632 v = sqrt ((f12 / (f11 * (f11 + f12)))
2633 + (f22 / (f21 * (f21 + f22))));
2634 lower[1] = value[1] * exp (-1.960 * v);
2635 upper[1] = value[1] * exp (1.960 * v);
2637 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2638 v = sqrt ((f11 / (f12 * (f11 + f12)))
2639 + (f21 / (f22 * (f21 + f22))));
2640 lower[2] = value[2] * exp (-1.960 * v);
2641 upper[2] = value[2] * exp (1.960 * v);
2646 /* Calculate directional measures. */
2648 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2649 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2650 double t[N_DIRECTIONAL])
2655 for (i = 0; i < N_DIRECTIONAL; i++)
2656 v[i] = ase[i] = t[i] = SYSMIS;
2660 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2662 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2663 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2664 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2665 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2666 double sum_fim, sum_fmj;
2668 int rm_index, cm_index;
2671 /* Find maximum for each row and their sum. */
2672 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2674 double max = pt->mat[i * pt->n_cols];
2677 for (j = 1; j < pt->n_cols; j++)
2678 if (pt->mat[j + i * pt->n_cols] > max)
2680 max = pt->mat[j + i * pt->n_cols];
2684 sum_fim += fim[i] = max;
2685 fim_index[i] = index;
2688 /* Find maximum for each column. */
2689 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2691 double max = pt->mat[j];
2694 for (i = 1; i < pt->n_rows; i++)
2695 if (pt->mat[j + i * pt->n_cols] > max)
2697 max = pt->mat[j + i * pt->n_cols];
2701 sum_fmj += fmj[j] = max;
2702 fmj_index[j] = index;
2705 /* Find maximum row total. */
2706 rm = pt->row_tot[0];
2708 for (i = 1; i < pt->n_rows; i++)
2709 if (pt->row_tot[i] > rm)
2711 rm = pt->row_tot[i];
2715 /* Find maximum column total. */
2716 cm = pt->col_tot[0];
2718 for (j = 1; j < pt->n_cols; j++)
2719 if (pt->col_tot[j] > cm)
2721 cm = pt->col_tot[j];
2725 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2726 v[1] = (sum_fmj - rm) / (pt->total - rm);
2727 v[2] = (sum_fim - cm) / (pt->total - cm);
2729 /* ASE1 for Y given PT. */
2733 for (accum = 0., i = 0; i < pt->n_rows; i++)
2734 for (j = 0; j < pt->n_cols; j++)
2736 const int deltaj = j == cm_index;
2737 accum += (pt->mat[j + i * pt->n_cols]
2738 * pow2 ((j == fim_index[i])
2743 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2746 /* ASE0 for Y given PT. */
2750 for (accum = 0., i = 0; i < pt->n_rows; i++)
2751 if (cm_index != fim_index[i])
2752 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2753 + pt->mat[i * pt->n_cols + cm_index]);
2754 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2757 /* ASE1 for PT given Y. */
2761 for (accum = 0., i = 0; i < pt->n_rows; i++)
2762 for (j = 0; j < pt->n_cols; j++)
2764 const int deltaj = i == rm_index;
2765 accum += (pt->mat[j + i * pt->n_cols]
2766 * pow2 ((i == fmj_index[j])
2771 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2774 /* ASE0 for PT given Y. */
2778 for (accum = 0., j = 0; j < pt->n_cols; j++)
2779 if (rm_index != fmj_index[j])
2780 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2781 + pt->mat[j + pt->n_cols * rm_index]);
2782 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2785 /* Symmetric ASE0 and ASE1. */
2790 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2791 for (j = 0; j < pt->n_cols; j++)
2793 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2794 int temp1 = (i == rm_index) + (j == cm_index);
2795 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2796 accum1 += (pt->mat[j + i * pt->n_cols]
2797 * pow2 (temp0 + (v[0] - 1.) * temp1));
2799 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2800 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2801 / (2. * pt->total - rm - cm));
2810 double sum_fij2_ri, sum_fij2_ci;
2811 double sum_ri2, sum_cj2;
2813 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2814 for (j = 0; j < pt->n_cols; j++)
2816 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2817 sum_fij2_ri += temp / pt->row_tot[i];
2818 sum_fij2_ci += temp / pt->col_tot[j];
2821 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2822 sum_ri2 += pow2 (pt->row_tot[i]);
2824 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2825 sum_cj2 += pow2 (pt->col_tot[j]);
2827 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2828 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2832 if (proc->statistics & (1u << CRS_ST_UC))
2834 double UX, UY, UXY, P;
2835 double ase1_yx, ase1_xy, ase1_sym;
2838 for (UX = 0., i = 0; i < pt->n_rows; i++)
2839 if (pt->row_tot[i] > 0.)
2840 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2842 for (UY = 0., j = 0; j < pt->n_cols; j++)
2843 if (pt->col_tot[j] > 0.)
2844 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2846 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2847 for (j = 0; j < pt->n_cols; j++)
2849 double entry = pt->mat[j + i * pt->n_cols];
2854 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2855 UXY -= entry / pt->total * log (entry / pt->total);
2858 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2859 for (j = 0; j < pt->n_cols; j++)
2861 double entry = pt->mat[j + i * pt->n_cols];
2866 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2867 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2868 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2869 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2870 ase1_sym += entry * pow2 ((UXY
2871 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2872 - (UX + UY) * log (entry / pt->total));
2875 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2876 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2877 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2878 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2880 v[6] = (UX + UY - UXY) / UX;
2881 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2882 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2884 v[7] = (UX + UY - UXY) / UY;
2885 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2886 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2890 if (proc->statistics & (1u << CRS_ST_D))
2892 double v_dummy[N_SYMMETRIC];
2893 double ase_dummy[N_SYMMETRIC];
2894 double t_dummy[N_SYMMETRIC];
2895 double somers_d_v[3];
2896 double somers_d_ase[3];
2897 double somers_d_t[3];
2899 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2900 somers_d_v, somers_d_ase, somers_d_t))
2903 for (i = 0; i < 3; i++)
2905 v[8 + i] = somers_d_v[i];
2906 ase[8 + i] = somers_d_ase[i];
2907 t[8 + i] = somers_d_t[i];
2913 if (proc->statistics & (1u << CRS_ST_ETA))
2916 double sum_Xr, sum_X2r;
2920 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2922 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2923 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2925 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2927 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2931 for (cum = 0., i = 0; i < pt->n_rows; i++)
2933 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2934 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2937 SXW -= cum * cum / pt->col_tot[j];
2939 v[11] = sqrt (1. - SXW / SX);
2943 double sum_Yc, sum_Y2c;
2947 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2949 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2950 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2952 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
2954 for (SYW = 0., i = 0; i < pt->n_rows; i++)
2958 for (cum = 0., j = 0; j < pt->n_cols; j++)
2960 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
2961 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
2964 SYW -= cum * cum / pt->row_tot[i];
2966 v[12] = sqrt (1. - SYW / SY);