1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 - Pearson's R (but not Spearman!) is off a little.
20 - T values for Spearman's R and Pearson's R are wrong.
21 - How to calculate significance of symmetric and directional measures?
22 - Asymmetric ASEs and T values for lambda are wrong.
23 - ASE of Goodman and Kruskal's tau is not calculated.
24 - ASE of symmetric somers' d is wrong.
25 - Approx. T of uncertainty coefficient is wrong.
32 #include <gsl/gsl_cdf.h>
36 #include <data/case.h>
37 #include <data/casegrouper.h>
38 #include <data/casereader.h>
39 #include <data/data-out.h>
40 #include <data/dictionary.h>
41 #include <data/format.h>
42 #include <data/procedure.h>
43 #include <data/value-labels.h>
44 #include <data/variable.h>
45 #include <language/command.h>
46 #include <language/dictionary/split-file.h>
47 #include <language/lexer/lexer.h>
48 #include <language/lexer/variable-parser.h>
49 #include <libpspp/array.h>
50 #include <libpspp/assertion.h>
51 #include <libpspp/compiler.h>
52 #include <libpspp/hash.h>
53 #include <libpspp/hmap.h>
54 #include <libpspp/hmapx.h>
55 #include <libpspp/message.h>
56 #include <libpspp/misc.h>
57 #include <libpspp/pool.h>
58 #include <libpspp/str.h>
59 #include <output/output.h>
60 #include <output/table.h>
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
76 missing=miss:!table/include/report;
77 +write[wr_]=none,cells,all;
78 +format=fmt:!labels/nolabels/novallabs,
81 tabl:!tables/notables,
84 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
86 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
92 /* Number of chi-square statistics. */
95 /* Number of symmetric statistics. */
98 /* Number of directional statistics. */
99 #define N_DIRECTIONAL 13
101 /* A single table entry for general mode. */
104 struct hmap_node node; /* Entry in hash table. */
105 double freq; /* Frequency count. */
106 union value values[1]; /* Values. */
110 table_entry_size (size_t n_values)
112 return (offsetof (struct table_entry, values)
113 + n_values * sizeof (union value));
116 /* Indexes into the 'vars' member of struct pivot_table and
117 struct crosstab member. */
120 ROW_VAR = 0, /* Row variable. */
121 COL_VAR = 1 /* Column variable. */
122 /* Higher indexes cause multiple tables to be output. */
125 /* A crosstabulation of 2 or more variables. */
128 struct fmt_spec weight_format; /* Format for weight variable. */
129 double missing; /* Weight of missing cases. */
131 /* Variables (2 or more). */
133 const struct variable **vars;
135 /* Constants (0 or more). */
137 const struct variable **const_vars;
138 union value *const_values;
142 struct table_entry **entries;
145 /* Column values, number of columns. */
149 /* Row values, number of rows. */
153 /* Number of statistically interesting columns/rows
154 (columns/rows with data in them). */
155 int ns_cols, ns_rows;
157 /* Matrix contents. */
158 double *mat; /* Matrix proper. */
159 double *row_tot; /* Row totals. */
160 double *col_tot; /* Column totals. */
161 double total; /* Grand total. */
164 /* A crosstabulation of exactly 2 variables, conditional on zero
165 or more other variables having given values. */
172 int n_vars; /* Number of variables (at least 2). */
173 const struct variable **vars;
174 union value *values; /* Values of variables beyond 2. */
177 struct table_entry **entries;
180 /* Column values, number of columns. */
184 /* Row values, number of rows. */
188 /* Number of statistically interesting columns/rows
189 (columns/rows with data in them). */
190 int ns_cols, ns_rows;
192 /* Matrix contents. */
193 double *mat; /* Matrix proper. */
194 double *row_tot; /* Row totals. */
195 double *col_tot; /* Column totals. */
196 double total; /* Grand total. */
199 /* Integer mode variable info. */
202 int min; /* Minimum value. */
203 int max; /* Maximum value + 1. */
204 int count; /* max - min. */
207 static inline struct var_range *
208 get_var_range (const struct variable *v)
210 return var_get_aux (v);
213 struct crosstabs_proc
215 enum { INTEGER, GENERAL } mode;
216 enum mv_class exclude;
219 struct fmt_spec weight_format;
221 /* Variables specifies on VARIABLES. */
222 const struct variable **variables;
226 struct pivot_table *pivots;
230 int n_cells; /* Number of cells requested. */
231 unsigned int cells; /* Bit k is 1 if cell k is requested. */
232 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
235 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
239 init_proc (struct crosstabs_proc *proc, struct dataset *ds)
241 const struct variable *wv = dict_get_weight (dataset_dict (ds));
242 proc->bad_warn = true;
243 proc->variables = NULL;
244 proc->n_variables = 0;
247 proc->weight_format = wv ? *var_get_print_format (wv) : F_8_0;
251 free_proc (struct crosstabs_proc *proc UNUSED)
256 static int internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
257 struct crosstabs_proc *);
258 static bool should_tabulate_case (const struct pivot_table *,
259 const struct ccase *, enum mv_class exclude);
260 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
262 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
264 static void postcalc (struct crosstabs_proc *);
265 static void submit (struct crosstabs_proc *, struct pivot_table *,
268 /* Parse and execute CROSSTABS, then clean up. */
270 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
272 struct crosstabs_proc proc;
275 init_proc (&proc, ds);
276 result = internal_cmd_crosstabs (lexer, ds, &proc);
282 /* Parses and executes the CROSSTABS procedure. */
284 internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
285 struct crosstabs_proc *proc)
287 struct casegrouper *grouper;
288 struct casereader *input, *group;
289 struct cmd_crosstabs cmd;
290 struct pivot_table *pt;
294 if (!parse_crosstabs (lexer, ds, &cmd, proc))
297 proc->mode = proc->n_variables ? INTEGER : GENERAL;
301 proc->cells = 1u << CRS_CL_COUNT;
302 else if (cmd.a_cells[CRS_CL_ALL])
303 proc->cells = UINT_MAX;
307 for (i = 0; i < CRS_CL_count; i++)
309 proc->cells |= 1u << i;
310 if (proc->cells == 0)
311 proc->cells = ((1u << CRS_CL_COUNT)
313 | (1u << CRS_CL_COLUMN)
314 | (1u << CRS_CL_TOTAL));
316 proc->cells &= ((1u << CRS_CL_count) - 1);
317 proc->cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
319 for (i = 0; i < CRS_CL_count; i++)
320 if (proc->cells & (1u << i))
321 proc->a_cells[proc->n_cells++] = i;
324 if (cmd.a_statistics[CRS_ST_ALL])
325 proc->statistics = UINT_MAX;
326 else if (cmd.sbc_statistics)
330 proc->statistics = 0;
331 for (i = 0; i < CRS_ST_count; i++)
332 if (cmd.a_statistics[i])
333 proc->statistics |= 1u << i;
334 if (proc->statistics == 0)
335 proc->statistics |= 1u << CRS_ST_CHISQ;
338 proc->statistics = 0;
341 proc->exclude = (cmd.miss == CRS_TABLE ? MV_ANY
342 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
344 if (proc->mode == GENERAL && proc->mode == MV_NEVER)
346 msg (SE, _("Missing mode REPORT not allowed in general mode. "
347 "Assuming MISSING=TABLE."));
352 proc->pivot = cmd.pivot == CRS_PIVOT;
354 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
356 grouper = casegrouper_create_splits (input, dataset_dict (ds));
357 while (casegrouper_get_next_group (grouper, &group))
361 /* Output SPLIT FILE variables. */
362 c = casereader_peek (group, 0);
365 output_split_file_values (ds, c);
370 for (; (c = casereader_read (group)) != NULL; case_unref (c))
371 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
373 double weight = dict_get_case_weight (dataset_dict (ds), c,
375 if (should_tabulate_case (pt, c, proc->exclude))
377 if (proc->mode == GENERAL)
378 tabulate_general_case (pt, c, weight);
380 tabulate_integer_case (pt, c, weight);
383 pt->missing += weight;
385 casereader_destroy (group);
390 ok = casegrouper_destroy (grouper);
391 ok = proc_commit (ds) && ok;
393 return ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
396 /* Parses the TABLES subcommand. */
398 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
399 struct cmd_crosstabs *cmd UNUSED, void *proc_)
401 struct crosstabs_proc *proc = proc_;
402 struct const_var_set *var_set;
404 const struct variable ***by = NULL;
406 size_t *by_nvar = NULL;
411 /* Ensure that this is a TABLES subcommand. */
412 if (!lex_match_id (lexer, "TABLES")
413 && (lex_token (lexer) != T_ID ||
414 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
415 && lex_token (lexer) != T_ALL)
417 lex_match (lexer, '=');
419 if (proc->variables != NULL)
420 var_set = const_var_set_create_from_array (proc->variables,
423 var_set = const_var_set_create_from_dict (dataset_dict (ds));
424 assert (var_set != NULL);
428 by = xnrealloc (by, n_by + 1, sizeof *by);
429 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
430 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
431 PV_NO_DUPLICATE | PV_NO_SCRATCH))
433 if (xalloc_oversized (nx, by_nvar[n_by]))
435 msg (SE, _("Too many cross-tabulation variables or dimensions."));
441 if (!lex_match (lexer, T_BY))
445 lex_error (lexer, _("expecting BY"));
453 by_iter = xcalloc (n_by, sizeof *by_iter);
454 proc->pivots = xnrealloc (proc->pivots,
455 proc->n_pivots + nx, sizeof *proc->pivots);
456 for (i = 0; i < nx; i++)
458 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
461 pt->weight_format = proc->weight_format;
464 pt->vars = xmalloc (n_by * sizeof *pt->vars);
466 pt->const_vars = NULL;
467 pt->const_values = NULL;
468 hmap_init (&pt->data);
472 for (j = 0; j < n_by; j++)
473 pt->vars[j] = by[j][by_iter[j]];
475 for (j = n_by - 1; j >= 0; j--)
477 if (++by_iter[j] < by_nvar[j])
486 /* All return paths lead here. */
487 for (i = 0; i < n_by; i++)
492 const_var_set_destroy (var_set);
497 /* Parses the VARIABLES subcommand. */
499 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
500 struct cmd_crosstabs *cmd UNUSED, void *proc_)
502 struct crosstabs_proc *proc = proc_;
505 msg (SE, _("VARIABLES must be specified before TABLES."));
509 lex_match (lexer, '=');
513 size_t orig_nv = proc->n_variables;
518 if (!parse_variables_const (lexer, dataset_dict (ds),
519 &proc->variables, &proc->n_variables,
520 (PV_APPEND | PV_NUMERIC
521 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
524 if (lex_token (lexer) != '(')
526 lex_error (lexer, "expecting `('");
531 if (!lex_force_int (lexer))
533 min = lex_integer (lexer);
536 lex_match (lexer, ',');
538 if (!lex_force_int (lexer))
540 max = lex_integer (lexer);
543 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
549 if (lex_token (lexer) != ')')
551 lex_error (lexer, "expecting `)'");
556 for (i = orig_nv; i < proc->n_variables; i++)
558 struct var_range *vr = xmalloc (sizeof *vr);
561 vr->count = max - min + 1;
562 var_attach_aux (proc->variables[i], vr, var_dtor_free);
565 if (lex_token (lexer) == '/')
572 free (proc->variables);
573 proc->variables = NULL;
574 proc->n_variables = 0;
578 /* Data file processing. */
581 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
582 enum mv_class exclude)
585 for (j = 0; j < pt->n_vars; j++)
587 const struct variable *var = pt->vars[j];
588 struct var_range *range = get_var_range (var);
590 if (var_is_value_missing (var, case_data (c, var), exclude))
595 double num = case_num (c, var);
596 if (num < range->min || num > range->max)
604 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
607 struct table_entry *te;
612 for (j = 0; j < pt->n_vars; j++)
614 /* Throw away fractional parts of values. */
615 hash = hash_int (case_num (c, pt->vars[j]), hash);
618 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
620 for (j = 0; j < pt->n_vars; j++)
621 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
624 /* Found an existing entry. */
631 /* No existing entry. Create a new one. */
632 te = xmalloc (table_entry_size (pt->n_vars));
634 for (j = 0; j < pt->n_vars; j++)
635 te->values[j].f = (int) case_num (c, pt->vars[j]);
636 hmap_insert (&pt->data, &te->node, hash);
640 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
643 struct table_entry *te;
648 for (j = 0; j < pt->n_vars; j++)
650 const struct variable *var = pt->vars[j];
651 hash = value_hash (case_data (c, var), var_get_width (var), hash);
654 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
656 for (j = 0; j < pt->n_vars; j++)
658 const struct variable *var = pt->vars[j];
659 if (!value_equal (case_data (c, var), &te->values[j],
660 var_get_width (var)))
664 /* Found an existing entry. */
671 /* No existing entry. Create a new one. */
672 te = xmalloc (table_entry_size (pt->n_vars));
674 for (j = 0; j < pt->n_vars; j++)
676 const struct variable *var = pt->vars[j];
677 int width = var_get_width (var);
678 value_init (&te->values[j], width);
679 value_copy (&te->values[j], case_data (c, var), width);
681 hmap_insert (&pt->data, &te->node, hash);
684 /* Post-data reading calculations. */
686 static int compare_table_entry_vars_3way (const struct table_entry *a,
687 const struct table_entry *b,
688 const struct pivot_table *pt,
690 static int compare_table_entry_3way (const void *ap_, const void *bp_,
692 static void enum_var_values (const struct pivot_table *, int var_idx,
693 union value **valuesp, int *n_values);
694 static void output_pivot_table (struct crosstabs_proc *,
695 struct pivot_table *);
696 static void make_pivot_table_subset (struct pivot_table *pt,
697 size_t row0, size_t row1,
698 struct pivot_table *subset);
699 static void make_summary_table (struct crosstabs_proc *);
700 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
703 postcalc (struct crosstabs_proc *proc)
705 struct pivot_table *pt;
707 /* Convert hash tables into sorted arrays of entries. */
708 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
710 struct table_entry *e;
713 pt->n_entries = hmap_count (&pt->data);
714 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
716 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
717 pt->entries[i++] = e;
718 hmap_destroy (&pt->data);
720 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
721 compare_table_entry_3way, pt);
724 make_summary_table (proc);
726 /* Output each pivot table. */
727 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
729 if (proc->pivot || pt->n_vars == 2)
730 output_pivot_table (proc, pt);
733 size_t row0 = 0, row1 = 0;
734 while (find_crosstab (pt, &row0, &row1))
736 struct pivot_table subset;
737 make_pivot_table_subset (pt, row0, row1, &subset);
738 output_pivot_table (proc, &subset);
743 /* XXX clear output and prepare for next split file. */
747 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
748 struct pivot_table *subset)
753 assert (pt->n_consts == 0);
754 subset->missing = pt->missing;
756 subset->vars = pt->vars;
757 subset->n_consts = pt->n_vars - 2;
758 subset->const_vars = pt->vars + 2;
759 subset->const_values = &pt->entries[row0]->values[2];
761 subset->entries = &pt->entries[row0];
762 subset->n_entries = row1 - row0;
766 compare_table_entry_var_3way (const struct table_entry *a,
767 const struct table_entry *b,
768 const struct pivot_table *pt,
771 return value_compare_3way (&a->values[idx], &b->values[idx],
772 var_get_width (pt->vars[idx]));
776 compare_table_entry_vars_3way (const struct table_entry *a,
777 const struct table_entry *b,
778 const struct pivot_table *pt,
783 for (i = idx1 - 1; i >= idx0; i--)
785 int cmp = compare_table_entry_var_3way (a, b, pt, i);
792 /* Compare the struct table_entry at *AP to the one at *BP and
793 return a strcmp()-type result. */
795 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
797 const struct table_entry *const *ap = ap_;
798 const struct table_entry *const *bp = bp_;
799 const struct table_entry *a = *ap;
800 const struct table_entry *b = *bp;
801 const struct pivot_table *pt = pt_;
804 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
808 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
812 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
816 find_first_difference (const struct pivot_table *pt, size_t row)
819 return pt->n_vars - 1;
822 const struct table_entry *a = pt->entries[row];
823 const struct table_entry *b = pt->entries[row - 1];
826 for (col = pt->n_vars - 1; col >= 0; col--)
827 if (compare_table_entry_var_3way (a, b, pt, col))
833 /* Output a table summarizing the cases processed. */
835 make_summary_table (struct crosstabs_proc *proc)
837 struct tab_table *summary;
838 struct pivot_table *pt;
842 summary = tab_create (7, 3 + proc->n_pivots, 1);
843 tab_title (summary, _("Summary."));
844 tab_headers (summary, 1, 0, 3, 0);
845 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
846 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
847 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
848 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
849 tab_hline (summary, TAL_1, 1, 6, 1);
850 tab_hline (summary, TAL_1, 1, 6, 2);
851 tab_vline (summary, TAL_1, 3, 1, 1);
852 tab_vline (summary, TAL_1, 5, 1, 1);
853 for (i = 0; i < 3; i++)
855 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
856 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
858 tab_offset (summary, 0, 3);
860 ds_init_empty (&name);
861 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
867 tab_hline (summary, TAL_1, 0, 6, 0);
870 for (i = 0; i < pt->n_vars; i++)
873 ds_put_cstr (&name, " * ");
874 ds_put_cstr (&name, var_to_string (pt->vars[i]));
876 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
879 for (i = 0; i < pt->n_entries; i++)
880 valid += pt->entries[i]->freq;
885 for (i = 0; i < 3; i++)
887 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
888 &proc->weight_format);
889 tab_text (summary, i * 2 + 2, 0, TAB_RIGHT | TAT_PRINTF, "%.1f%%",
893 tab_next_row (summary);
897 submit (proc, NULL, summary);
902 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
903 struct pivot_table *);
904 static struct tab_table *create_chisq_table (struct pivot_table *);
905 static struct tab_table *create_sym_table (struct pivot_table *);
906 static struct tab_table *create_risk_table (struct pivot_table *);
907 static struct tab_table *create_direct_table (struct pivot_table *);
908 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
909 struct tab_table *, int first_difference);
910 static void display_crosstabulation (struct crosstabs_proc *,
911 struct pivot_table *,
913 static void display_chisq (struct pivot_table *, struct tab_table *,
914 bool *showed_fisher);
915 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
917 static void display_risk (struct pivot_table *, struct tab_table *);
918 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
920 static void crosstabs_dim (struct tab_table *, struct outp_driver *,
922 static void table_value_missing (struct crosstabs_proc *proc,
923 struct tab_table *table, int c, int r,
924 unsigned char opt, const union value *v,
925 const struct variable *var);
926 static void delete_missing (struct pivot_table *);
927 static void build_matrix (struct pivot_table *);
929 /* Output pivot table beginning at PB and continuing until PE,
930 exclusive. For efficiency, *MATP is a pointer to a matrix that can
931 hold *MAXROWS entries. */
933 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
935 struct tab_table *table = NULL; /* Crosstabulation table. */
936 struct tab_table *chisq = NULL; /* Chi-square table. */
937 bool showed_fisher = false;
938 struct tab_table *sym = NULL; /* Symmetric measures table. */
939 struct tab_table *risk = NULL; /* Risk estimate table. */
940 struct tab_table *direct = NULL; /* Directional measures table. */
943 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
946 table = create_crosstab_table (proc, pt);
947 if (proc->statistics & (1u << CRS_ST_CHISQ))
948 chisq = create_chisq_table (pt);
949 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
950 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
951 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
952 | (1u << CRS_ST_KAPPA)))
953 sym = create_sym_table (pt);
954 if (proc->statistics & (1u << CRS_ST_RISK))
955 risk = create_risk_table (pt);
956 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
957 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
958 direct = create_direct_table (pt);
961 while (find_crosstab (pt, &row0, &row1))
963 struct pivot_table x;
964 int first_difference;
966 make_pivot_table_subset (pt, row0, row1, &x);
968 /* Find all the row variable values. */
969 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
971 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
974 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
975 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
976 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
978 /* Allocate table space for the matrix. */
980 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
981 tab_realloc (table, -1,
982 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
983 tab_nr (table) * pt->n_entries / x.n_entries));
987 /* Find the first variable that differs from the last subtable. */
988 first_difference = find_first_difference (pt, row0);
991 display_dimensions (proc, &x, table, first_difference);
992 display_crosstabulation (proc, &x, table);
995 if (proc->exclude == MV_NEVER)
1000 display_dimensions (proc, &x, chisq, first_difference);
1001 display_chisq (pt, chisq, &showed_fisher);
1005 display_dimensions (proc, &x, sym, first_difference);
1006 display_symmetric (proc, pt, sym);
1010 display_dimensions (proc, &x, risk, first_difference);
1011 display_risk (pt, risk);
1015 display_dimensions (proc, &x, direct, first_difference);
1016 display_directional (proc, pt, direct);
1019 /* XXX Free data in x. */
1023 submit (proc, NULL, table);
1028 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1029 submit (proc, pt, chisq);
1032 submit (proc, pt, sym);
1033 submit (proc, pt, risk);
1034 submit (proc, 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,
1149 tab_headers (table, pt->n_consts + 1, 0, 2, 0);
1151 /* First header line. */
1152 tab_joint_text (table, pt->n_consts + 1, 0,
1153 (pt->n_consts + 1) + (pt->n_cols - 1), 0,
1154 TAB_CENTER | TAT_TITLE, var_get_name (pt->vars[COL_VAR]));
1156 tab_hline (table, TAL_1, pt->n_consts + 1,
1157 pt->n_consts + 2 + pt->n_cols - 2, 1);
1159 /* Second header line. */
1160 for (i = 2; i < pt->n_consts + 2; i++)
1161 tab_joint_text (table, pt->n_consts + 2 - i - 1, 0,
1162 pt->n_consts + 2 - i - 1, 1,
1163 TAB_RIGHT | TAT_TITLE, var_to_string (pt->vars[i]));
1164 tab_text (table, pt->n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1165 var_get_name (pt->vars[ROW_VAR]));
1166 for (i = 0; i < pt->n_cols; i++)
1167 table_value_missing (proc, table, pt->n_consts + 2 + i - 1, 1, TAB_RIGHT,
1168 &pt->cols[i], pt->vars[COL_VAR]);
1169 tab_text (table, pt->n_consts + 2 + pt->n_cols - 1, 1, TAB_CENTER, _("Total"));
1171 tab_hline (table, TAL_1, 0, pt->n_consts + 2 + pt->n_cols - 1, 2);
1172 tab_vline (table, TAL_1, pt->n_consts + 2 + pt->n_cols - 1, 0, 1);
1175 ds_init_empty (&title);
1176 for (i = 0; i < pt->n_consts + 2; i++)
1179 ds_put_cstr (&title, " * ");
1180 ds_put_cstr (&title, var_get_name (pt->vars[i]));
1182 for (i = 0; i < pt->n_consts; i++)
1184 const struct variable *var = pt->const_vars[i];
1185 ds_put_format (&title, ", %s=", var_get_name (var));
1186 data_out (&pt->const_values[i], var_get_print_format (var),
1187 ds_put_uninit (&title, var_get_width (var)));
1188 /* XXX remove any leading space in what was just inserted. */
1191 ds_put_cstr (&title, " [");
1193 for (t = names; t < &names[n_names]; t++)
1194 if (proc->cells & (1u << t->value))
1197 ds_put_cstr (&title, ", ");
1198 ds_put_cstr (&title, gettext (t->name));
1200 ds_put_cstr (&title, "].");
1202 tab_title (table, "%s", ds_cstr (&title));
1203 ds_destroy (&title);
1205 tab_offset (table, 0, 2);
1209 static struct tab_table *
1210 create_chisq_table (struct pivot_table *pt)
1212 struct tab_table *chisq;
1214 chisq = tab_create (6 + (pt->n_vars - 2),
1215 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10,
1217 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1219 tab_title (chisq, _("Chi-square tests."));
1221 tab_offset (chisq, pt->n_vars - 2, 0);
1222 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1223 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1224 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1225 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1226 _("Asymp. Sig. (2-sided)"));
1227 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1228 _("Exact. Sig. (2-sided)"));
1229 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1230 _("Exact. Sig. (1-sided)"));
1232 tab_offset (chisq, 0, 1);
1237 /* Symmetric measures. */
1238 static struct tab_table *
1239 create_sym_table (struct pivot_table *pt)
1241 struct tab_table *sym;
1243 sym = tab_create (6 + (pt->n_vars - 2),
1244 pt->n_entries / pt->n_cols * 7 + 10, 1);
1245 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1246 tab_title (sym, _("Symmetric measures."));
1248 tab_offset (sym, pt->n_vars - 2, 0);
1249 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1250 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1251 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1252 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1253 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1254 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1255 tab_offset (sym, 0, 1);
1260 /* Risk estimate. */
1261 static struct tab_table *
1262 create_risk_table (struct pivot_table *pt)
1264 struct tab_table *risk;
1266 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10,
1268 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1269 tab_title (risk, _("Risk estimate."));
1271 tab_offset (risk, pt->n_vars - 2, 0);
1272 tab_joint_text (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE | TAT_PRINTF,
1273 _("95%% Confidence Interval"));
1274 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1275 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1276 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1277 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1278 tab_hline (risk, TAL_1, 2, 3, 1);
1279 tab_vline (risk, TAL_1, 2, 0, 1);
1280 tab_offset (risk, 0, 2);
1285 /* Directional measures. */
1286 static struct tab_table *
1287 create_direct_table (struct pivot_table *pt)
1289 struct tab_table *direct;
1291 direct = tab_create (7 + (pt->n_vars - 2),
1292 pt->n_entries / pt->n_cols * 7 + 10, 1);
1293 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1294 tab_title (direct, _("Directional measures."));
1296 tab_offset (direct, pt->n_vars - 2, 0);
1297 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1298 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1299 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1300 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1301 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1302 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1303 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1304 tab_offset (direct, 0, 1);
1310 /* Delete missing rows and columns for statistical analysis when
1313 delete_missing (struct pivot_table *pt)
1317 for (r = 0; r < pt->n_rows; r++)
1318 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1320 for (c = 0; c < pt->n_cols; c++)
1321 pt->mat[c + r * pt->n_cols] = 0.;
1326 for (c = 0; c < pt->n_cols; c++)
1327 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1329 for (r = 0; r < pt->n_rows; r++)
1330 pt->mat[c + r * pt->n_cols] = 0.;
1335 /* Prepare table T for submission, and submit it. */
1337 submit (struct crosstabs_proc *proc, struct pivot_table *pt,
1338 struct tab_table *t)
1345 tab_resize (t, -1, 0);
1346 if (tab_nr (t) == tab_t (t))
1351 tab_offset (t, 0, 0);
1353 for (i = 2; i < pt->n_vars; i++)
1354 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1355 var_to_string (pt->vars[i]));
1356 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1357 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1359 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1361 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1362 tab_dim (t, crosstabs_dim, proc);
1366 /* Sets the widths of all the columns and heights of all the rows in
1367 table T for driver D. */
1369 crosstabs_dim (struct tab_table *t, struct outp_driver *d, void *proc_)
1371 struct crosstabs_proc *proc = proc_;
1374 /* Width of a numerical column. */
1375 int c = outp_string_width (d, "0.000000", OUTP_PROPORTIONAL);
1376 if (proc->exclude == MV_NEVER)
1377 c += outp_string_width (d, "M", OUTP_PROPORTIONAL);
1379 /* Set width for header columns. */
1385 w = d->width - c * (t->nc - t->l);
1386 for (i = 0; i <= t->nc; i++)
1390 if (w < d->prop_em_width * 8)
1391 w = d->prop_em_width * 8;
1393 if (w > d->prop_em_width * 15)
1394 w = d->prop_em_width * 15;
1396 for (i = 0; i < t->l; i++)
1400 for (i = t->l; i < t->nc; i++)
1403 for (i = 0; i < t->nr; i++)
1404 t->h[i] = tab_natural_height (t, d, i);
1408 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1410 size_t row0 = *row1p;
1413 if (row0 >= pt->n_entries)
1416 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1418 struct table_entry *a = pt->entries[row0];
1419 struct table_entry *b = pt->entries[row1];
1420 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1428 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1429 result. WIDTH_ points to an int which is either 0 for a
1430 numeric value or a string width for a string value. */
1432 compare_value_3way (const void *a_, const void *b_, const void *width_)
1434 const union value *a = a_;
1435 const union value *b = b_;
1436 const int *width = width_;
1438 return value_compare_3way (a, b, *width);
1441 /* Given an array of ENTRY_CNT table_entry structures starting at
1442 ENTRIES, creates a sorted list of the values that the variable
1443 with index VAR_IDX takes on. The values are returned as a
1444 malloc()'d array stored in *VALUES, with the number of values
1445 stored in *VALUE_CNT.
1448 enum_var_values (const struct pivot_table *pt, int var_idx,
1449 union value **valuesp, int *n_values)
1451 const struct variable *var = pt->vars[var_idx];
1452 struct var_range *range = get_var_range (var);
1453 union value *values;
1458 values = *valuesp = xnmalloc (range->count, sizeof *values);
1459 *n_values = range->count;
1460 for (i = 0; i < range->count; i++)
1461 values[i].f = range->min + i;
1465 int width = var_get_width (var);
1466 struct hmapx_node *node;
1467 const union value *iter;
1471 for (i = 0; i < pt->n_entries; i++)
1473 const struct table_entry *te = pt->entries[i];
1474 const union value *value = &te->values[var_idx];
1475 size_t hash = value_hash (value, width, 0);
1477 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1478 if (value_equal (iter, value, width))
1481 hmapx_insert (&set, (union value *) value, hash);
1486 *n_values = hmapx_count (&set);
1487 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1489 HMAPX_FOR_EACH (iter, node, &set)
1490 values[i++] = *iter;
1491 hmapx_destroy (&set);
1493 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1497 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1498 from V, displayed with print format spec from variable VAR. When
1499 in REPORT missing-value mode, missing values have an M appended. */
1501 table_value_missing (struct crosstabs_proc *proc,
1502 struct tab_table *table, int c, int r, unsigned char opt,
1503 const union value *v, const struct variable *var)
1506 const struct fmt_spec *print = var_get_print_format (var);
1508 const char *label = var_lookup_value_label (var, v);
1511 tab_text (table, c, r, TAB_LEFT, label);
1515 s.string = tab_alloc (table, print->w);
1516 data_out (v, print, s.string);
1517 s.length = print->w;
1518 if (proc->exclude == MV_NEVER && var_is_num_missing (var, v->f, MV_USER))
1519 s.string[s.length++] = 'M';
1520 while (s.length && *s.string == ' ')
1525 tab_raw (table, c, r, opt, &s);
1528 /* Draws a line across TABLE at the current row to indicate the most
1529 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1530 that changed, and puts the values that changed into the table. TB
1531 and PT must be the corresponding table_entry and crosstab,
1534 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1535 struct tab_table *table, int first_difference)
1537 tab_hline (table, TAL_1, pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1539 for (; first_difference >= 2; first_difference--)
1540 table_value_missing (proc, table, pt->n_vars - first_difference - 1, 0,
1541 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1542 pt->vars[first_difference]);
1545 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1546 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1547 additionally suffixed with a letter `M'. */
1549 format_cell_entry (struct tab_table *table, int c, int r, double value,
1550 char suffix, bool mark_missing)
1552 const struct fmt_spec f = {FMT_F, 10, 1};
1557 s.string = tab_alloc (table, 16);
1559 data_out (&v, &f, s.string);
1560 while (*s.string == ' ')
1566 s.string[s.length++] = suffix;
1568 s.string[s.length++] = 'M';
1570 tab_raw (table, c, r, TAB_RIGHT, &s);
1573 /* Displays the crosstabulation table. */
1575 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1576 struct tab_table *table)
1582 for (r = 0; r < pt->n_rows; r++)
1583 table_value_missing (proc, table, pt->n_vars - 2, r * proc->n_cells,
1584 TAB_RIGHT, &pt->rows[r], pt->vars[ROW_VAR]);
1586 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1587 TAB_LEFT, _("Total"));
1589 /* Put in the actual cells. */
1591 tab_offset (table, pt->n_vars - 1, -1);
1592 for (r = 0; r < pt->n_rows; r++)
1594 if (proc->n_cells > 1)
1595 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1596 for (c = 0; c < pt->n_cols; c++)
1598 bool mark_missing = false;
1599 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1600 if (proc->exclude == MV_NEVER
1601 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1602 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1604 mark_missing = true;
1605 for (i = 0; i < proc->n_cells; i++)
1610 switch (proc->a_cells[i])
1616 v = *mp / pt->row_tot[r] * 100.;
1620 v = *mp / pt->col_tot[c] * 100.;
1624 v = *mp / pt->total * 100.;
1627 case CRS_CL_EXPECTED:
1630 case CRS_CL_RESIDUAL:
1631 v = *mp - expected_value;
1633 case CRS_CL_SRESIDUAL:
1634 v = (*mp - expected_value) / sqrt (expected_value);
1636 case CRS_CL_ASRESIDUAL:
1637 v = ((*mp - expected_value)
1638 / sqrt (expected_value
1639 * (1. - pt->row_tot[r] / pt->total)
1640 * (1. - pt->col_tot[c] / pt->total)));
1645 format_cell_entry (table, c, i, v, suffix, mark_missing);
1651 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1655 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1656 for (r = 0; r < pt->n_rows; r++)
1658 bool mark_missing = false;
1660 if (proc->exclude == MV_NEVER
1661 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1662 mark_missing = true;
1664 for (i = 0; i < proc->n_cells; i++)
1669 switch (proc->a_cells[i])
1679 v = pt->row_tot[r] / pt->total * 100.;
1683 v = pt->row_tot[r] / pt->total * 100.;
1686 case CRS_CL_EXPECTED:
1687 case CRS_CL_RESIDUAL:
1688 case CRS_CL_SRESIDUAL:
1689 case CRS_CL_ASRESIDUAL:
1696 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing);
1697 tab_next_row (table);
1701 /* Column totals, grand total. */
1703 if (proc->n_cells > 1)
1704 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1705 for (c = 0; c <= pt->n_cols; c++)
1707 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1708 bool mark_missing = false;
1711 if (proc->exclude == MV_NEVER && c < pt->n_cols
1712 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1713 mark_missing = true;
1715 for (i = 0; i < proc->n_cells; i++)
1720 switch (proc->a_cells[i])
1726 v = ct / pt->total * 100.;
1734 v = ct / pt->total * 100.;
1737 case CRS_CL_EXPECTED:
1738 case CRS_CL_RESIDUAL:
1739 case CRS_CL_SRESIDUAL:
1740 case CRS_CL_ASRESIDUAL:
1746 format_cell_entry (table, c, i, v, suffix, mark_missing);
1751 tab_offset (table, -1, tab_row (table) + last_row);
1752 tab_offset (table, 0, -1);
1755 static void calc_r (struct pivot_table *,
1756 double *PT, double *Y, double *, double *, double *);
1757 static void calc_chisq (struct pivot_table *,
1758 double[N_CHISQ], int[N_CHISQ], double *, double *);
1760 /* Display chi-square statistics. */
1762 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1763 bool *showed_fisher)
1765 static const char *chisq_stats[N_CHISQ] =
1767 N_("Pearson Chi-Square"),
1768 N_("Likelihood Ratio"),
1769 N_("Fisher's Exact Test"),
1770 N_("Continuity Correction"),
1771 N_("Linear-by-Linear Association"),
1773 double chisq_v[N_CHISQ];
1774 double fisher1, fisher2;
1780 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1782 tab_offset (chisq, pt->n_vars - 2, -1);
1784 for (i = 0; i < N_CHISQ; i++)
1786 if ((i != 2 && chisq_v[i] == SYSMIS)
1787 || (i == 2 && fisher1 == SYSMIS))
1791 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1794 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1795 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1796 tab_double (chisq, 3, 0, TAB_RIGHT,
1797 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1801 *showed_fisher = true;
1802 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1803 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1805 tab_next_row (chisq);
1808 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1809 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1810 tab_next_row (chisq);
1812 tab_offset (chisq, 0, -1);
1815 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1816 double[N_SYMMETRIC], double[N_SYMMETRIC],
1817 double[N_SYMMETRIC],
1818 double[3], double[3], double[3]);
1820 /* Display symmetric measures. */
1822 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1823 struct tab_table *sym)
1825 static const char *categories[] =
1827 N_("Nominal by Nominal"),
1828 N_("Ordinal by Ordinal"),
1829 N_("Interval by Interval"),
1830 N_("Measure of Agreement"),
1833 static const char *stats[N_SYMMETRIC] =
1837 N_("Contingency Coefficient"),
1838 N_("Kendall's tau-b"),
1839 N_("Kendall's tau-c"),
1841 N_("Spearman Correlation"),
1846 static const int stats_categories[N_SYMMETRIC] =
1848 0, 0, 0, 1, 1, 1, 1, 2, 3,
1852 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1853 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1856 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1857 somers_d_v, somers_d_ase, somers_d_t))
1860 tab_offset (sym, pt->n_vars - 2, -1);
1862 for (i = 0; i < N_SYMMETRIC; i++)
1864 if (sym_v[i] == SYSMIS)
1867 if (stats_categories[i] != last_cat)
1869 last_cat = stats_categories[i];
1870 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1873 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1874 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1875 if (sym_ase[i] != SYSMIS)
1876 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1877 if (sym_t[i] != SYSMIS)
1878 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1879 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1883 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1884 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1887 tab_offset (sym, 0, -1);
1890 static int calc_risk (struct pivot_table *,
1891 double[], double[], double[], union value *);
1893 /* Display risk estimate. */
1895 display_risk (struct pivot_table *pt, struct tab_table *risk)
1898 double risk_v[3], lower[3], upper[3];
1902 if (!calc_risk (pt, risk_v, upper, lower, c))
1905 tab_offset (risk, pt->n_vars - 2, -1);
1907 for (i = 0; i < 3; i++)
1909 const struct variable *cv = pt->vars[COL_VAR];
1910 const struct variable *rv = pt->vars[ROW_VAR];
1911 int cvw = var_get_width (cv);
1912 int rvw = var_get_width (rv);
1914 if (risk_v[i] == SYSMIS)
1920 if (var_is_numeric (cv))
1921 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1922 var_get_name (cv), c[0].f, c[1].f);
1924 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1926 cvw, value_str (&c[0], cvw),
1927 cvw, value_str (&c[1], cvw));
1931 if (var_is_numeric (rv))
1932 sprintf (buf, _("For cohort %s = %g"),
1933 var_get_name (rv), pt->rows[i - 1].f);
1935 sprintf (buf, _("For cohort %s = %.*s"),
1937 rvw, value_str (&pt->rows[i - 1], rvw));
1941 tab_text (risk, 0, 0, TAB_LEFT, buf);
1942 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1943 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1944 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1945 tab_next_row (risk);
1948 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1949 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1950 tab_next_row (risk);
1952 tab_offset (risk, 0, -1);
1955 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1956 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1957 double[N_DIRECTIONAL]);
1959 /* Display directional measures. */
1961 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1962 struct tab_table *direct)
1964 static const char *categories[] =
1966 N_("Nominal by Nominal"),
1967 N_("Ordinal by Ordinal"),
1968 N_("Nominal by Interval"),
1971 static const char *stats[] =
1974 N_("Goodman and Kruskal tau"),
1975 N_("Uncertainty Coefficient"),
1980 static const char *types[] =
1987 static const int stats_categories[N_DIRECTIONAL] =
1989 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1992 static const int stats_stats[N_DIRECTIONAL] =
1994 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1997 static const int stats_types[N_DIRECTIONAL] =
1999 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2002 static const int *stats_lookup[] =
2009 static const char **stats_names[] =
2021 double direct_v[N_DIRECTIONAL];
2022 double direct_ase[N_DIRECTIONAL];
2023 double direct_t[N_DIRECTIONAL];
2027 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2030 tab_offset (direct, pt->n_vars - 2, -1);
2032 for (i = 0; i < N_DIRECTIONAL; i++)
2034 if (direct_v[i] == SYSMIS)
2040 for (j = 0; j < 3; j++)
2041 if (last[j] != stats_lookup[j][i])
2044 tab_hline (direct, TAL_1, j, 6, 0);
2049 int k = last[j] = stats_lookup[j][i];
2054 string = var_get_name (pt->vars[0]);
2056 string = var_get_name (pt->vars[1]);
2058 tab_text (direct, j, 0, TAB_LEFT | TAT_PRINTF,
2059 gettext (stats_names[j][k]), string);
2064 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2065 if (direct_ase[i] != SYSMIS)
2066 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2067 if (direct_t[i] != SYSMIS)
2068 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2069 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2070 tab_next_row (direct);
2073 tab_offset (direct, 0, -1);
2076 /* Statistical calculations. */
2078 /* Returns the value of the gamma (factorial) function for an integer
2081 gamma_int (double pt)
2086 for (i = 2; i < pt; i++)
2091 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2093 static inline double
2094 Pr (int a, int b, int c, int d)
2096 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2097 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2098 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2099 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2100 / gamma_int (a + b + c + d + 1.));
2103 /* Swap the contents of A and B. */
2105 swap (int *a, int *b)
2112 /* Calculate significance for Fisher's exact test as specified in
2113 _SPSS Statistical Algorithms_, Appendix 5. */
2115 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2119 if (MIN (c, d) < MIN (a, b))
2120 swap (&a, &c), swap (&b, &d);
2121 if (MIN (b, d) < MIN (a, c))
2122 swap (&a, &b), swap (&c, &d);
2126 swap (&a, &b), swap (&c, &d);
2128 swap (&a, &c), swap (&b, &d);
2132 for (pt = 0; pt <= a; pt++)
2133 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2135 *fisher2 = *fisher1;
2136 for (pt = 1; pt <= b; pt++)
2137 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2140 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2141 columns with values COLS and N_ROWS rows with values ROWS. Values
2142 in the matrix sum to pt->total. */
2144 calc_chisq (struct pivot_table *pt,
2145 double chisq[N_CHISQ], int df[N_CHISQ],
2146 double *fisher1, double *fisher2)
2150 chisq[0] = chisq[1] = 0.;
2151 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2152 *fisher1 = *fisher2 = SYSMIS;
2154 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2156 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2158 chisq[0] = chisq[1] = SYSMIS;
2162 for (r = 0; r < pt->n_rows; r++)
2163 for (c = 0; c < pt->n_cols; c++)
2165 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2166 const double freq = pt->mat[pt->n_cols * r + c];
2167 const double residual = freq - expected;
2169 chisq[0] += residual * residual / expected;
2171 chisq[1] += freq * log (expected / freq);
2182 /* Calculate Yates and Fisher exact test. */
2183 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2185 double f11, f12, f21, f22;
2191 for (i = j = 0; i < pt->n_cols; i++)
2192 if (pt->col_tot[i] != 0.)
2201 f11 = pt->mat[nz_cols[0]];
2202 f12 = pt->mat[nz_cols[1]];
2203 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2204 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2209 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2212 chisq[3] = (pt->total * pow2 (pt_)
2213 / (f11 + f12) / (f21 + f22)
2214 / (f11 + f21) / (f12 + f22));
2222 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2223 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2226 /* Calculate Mantel-Haenszel. */
2227 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2229 double r, ase_0, ase_1;
2230 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2232 chisq[4] = (pt->total - 1.) * r * r;
2237 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2238 ASE_1, and ase_0 into ASE_0. The row and column values must be
2239 passed in PT and Y. */
2241 calc_r (struct pivot_table *pt,
2242 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2244 double SX, SY, S, T;
2246 double sum_XYf, sum_X2Y2f;
2247 double sum_Xr, sum_X2r;
2248 double sum_Yc, sum_Y2c;
2251 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2252 for (j = 0; j < pt->n_cols; j++)
2254 double fij = pt->mat[j + i * pt->n_cols];
2255 double product = PT[i] * Y[j];
2256 double temp = fij * product;
2258 sum_X2Y2f += temp * product;
2261 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2263 sum_Xr += PT[i] * pt->row_tot[i];
2264 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2266 Xbar = sum_Xr / pt->total;
2268 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2270 sum_Yc += Y[i] * pt->col_tot[i];
2271 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2273 Ybar = sum_Yc / pt->total;
2275 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2276 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2277 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2280 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2285 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2286 for (j = 0; j < pt->n_cols; j++)
2288 double Xresid, Yresid;
2291 Xresid = PT[i] - Xbar;
2292 Yresid = Y[j] - Ybar;
2293 temp = (T * Xresid * Yresid
2295 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2296 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2301 *ase_1 = sqrt (s) / (T * T);
2305 /* Calculate symmetric statistics and their asymptotic standard
2306 errors. Returns 0 if none could be calculated. */
2308 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2309 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2310 double t[N_SYMMETRIC],
2311 double somers_d_v[3], double somers_d_ase[3],
2312 double somers_d_t[3])
2316 q = MIN (pt->ns_rows, pt->ns_cols);
2320 for (i = 0; i < N_SYMMETRIC; i++)
2321 v[i] = ase[i] = t[i] = SYSMIS;
2323 /* Phi, Cramer's V, contingency coefficient. */
2324 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2326 double Xp = 0.; /* Pearson chi-square. */
2329 for (r = 0; r < pt->n_rows; r++)
2330 for (c = 0; c < pt->n_cols; c++)
2332 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2333 const double freq = pt->mat[pt->n_cols * r + c];
2334 const double residual = freq - expected;
2336 Xp += residual * residual / expected;
2339 if (proc->statistics & (1u << CRS_ST_PHI))
2341 v[0] = sqrt (Xp / pt->total);
2342 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2344 if (proc->statistics & (1u << CRS_ST_CC))
2345 v[2] = sqrt (Xp / (Xp + pt->total));
2348 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2349 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2354 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2358 Dr = Dc = pow2 (pt->total);
2359 for (r = 0; r < pt->n_rows; r++)
2360 Dr -= pow2 (pt->row_tot[r]);
2361 for (c = 0; c < pt->n_cols; c++)
2362 Dc -= pow2 (pt->col_tot[c]);
2364 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2365 for (c = 0; c < pt->n_cols; c++)
2369 for (r = 0; r < pt->n_rows; r++)
2370 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2379 for (i = 0; i < pt->n_rows; i++)
2383 for (j = 1; j < pt->n_cols; j++)
2384 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2387 for (j = 1; j < pt->n_cols; j++)
2388 Dij += cum[j + (i - 1) * pt->n_cols];
2392 double fij = pt->mat[j + i * pt->n_cols];
2396 if (++j == pt->n_cols)
2398 assert (j < pt->n_cols);
2400 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2401 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2405 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2406 Dij -= cum[j + (i - 1) * pt->n_cols];
2412 if (proc->statistics & (1u << CRS_ST_BTAU))
2413 v[3] = (P - Q) / sqrt (Dr * Dc);
2414 if (proc->statistics & (1u << CRS_ST_CTAU))
2415 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2416 if (proc->statistics & (1u << CRS_ST_GAMMA))
2417 v[5] = (P - Q) / (P + Q);
2419 /* ASE for tau-b, tau-c, gamma. Calculations could be
2420 eliminated here, at expense of memory. */
2425 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2426 for (i = 0; i < pt->n_rows; i++)
2430 for (j = 1; j < pt->n_cols; j++)
2431 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2434 for (j = 1; j < pt->n_cols; j++)
2435 Dij += cum[j + (i - 1) * pt->n_cols];
2439 double fij = pt->mat[j + i * pt->n_cols];
2441 if (proc->statistics & (1u << CRS_ST_BTAU))
2443 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2444 + v[3] * (pt->row_tot[i] * Dc
2445 + pt->col_tot[j] * Dr));
2446 btau_cum += fij * temp * temp;
2450 const double temp = Cij - Dij;
2451 ctau_cum += fij * temp * temp;
2454 if (proc->statistics & (1u << CRS_ST_GAMMA))
2456 const double temp = Q * Cij - P * Dij;
2457 gamma_cum += fij * temp * temp;
2460 if (proc->statistics & (1u << CRS_ST_D))
2462 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2463 - (P - Q) * (pt->total - pt->row_tot[i]));
2464 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2465 - (Q - P) * (pt->total - pt->col_tot[j]));
2468 if (++j == pt->n_cols)
2470 assert (j < pt->n_cols);
2472 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2473 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2477 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2478 Dij -= cum[j + (i - 1) * pt->n_cols];
2484 btau_var = ((btau_cum
2485 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2487 if (proc->statistics & (1u << CRS_ST_BTAU))
2489 ase[3] = sqrt (btau_var);
2490 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2493 if (proc->statistics & (1u << CRS_ST_CTAU))
2495 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2496 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2497 t[4] = v[4] / ase[4];
2499 if (proc->statistics & (1u << CRS_ST_GAMMA))
2501 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2502 t[5] = v[5] / (2. / (P + Q)
2503 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2505 if (proc->statistics & (1u << CRS_ST_D))
2507 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2508 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2509 somers_d_t[0] = (somers_d_v[0]
2511 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2512 somers_d_v[1] = (P - Q) / Dc;
2513 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2514 somers_d_t[1] = (somers_d_v[1]
2516 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2517 somers_d_v[2] = (P - Q) / Dr;
2518 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2519 somers_d_t[2] = (somers_d_v[2]
2521 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2527 /* Spearman correlation, Pearson's r. */
2528 if (proc->statistics & (1u << CRS_ST_CORR))
2530 double *R = xmalloc (sizeof *R * pt->n_rows);
2531 double *C = xmalloc (sizeof *C * pt->n_cols);
2534 double y, t, c = 0., s = 0.;
2539 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2540 y = pt->row_tot[i] - c;
2544 if (++i == pt->n_rows)
2546 assert (i < pt->n_rows);
2551 double y, t, c = 0., s = 0.;
2556 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2557 y = pt->col_tot[j] - c;
2561 if (++j == pt->n_cols)
2563 assert (j < pt->n_cols);
2567 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2573 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2577 /* Cohen's kappa. */
2578 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2580 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2583 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2584 i < pt->ns_rows; i++, j++)
2588 while (pt->col_tot[j] == 0.)
2591 prod = pt->row_tot[i] * pt->col_tot[j];
2592 sum = pt->row_tot[i] + pt->col_tot[j];
2594 sum_fii += pt->mat[j + i * pt->n_cols];
2596 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2597 sum_riciri_ci += prod * sum;
2599 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2600 for (j = 0; j < pt->ns_cols; j++)
2602 double sum = pt->row_tot[i] + pt->col_tot[j];
2603 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2606 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2608 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2609 + sum_rici * sum_rici
2610 - pt->total * sum_riciri_ci)
2611 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2613 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2614 / pow2 (pow2 (pt->total) - sum_rici))
2615 + ((2. * (pt->total - sum_fii)
2616 * (2. * sum_fii * sum_rici
2617 - pt->total * sum_fiiri_ci))
2618 / cube (pow2 (pt->total) - sum_rici))
2619 + (pow2 (pt->total - sum_fii)
2620 * (pt->total * sum_fijri_ci2 - 4.
2621 * sum_rici * sum_rici)
2622 / pow4 (pow2 (pt->total) - sum_rici))));
2624 t[8] = v[8] / ase[8];
2631 /* Calculate risk estimate. */
2633 calc_risk (struct pivot_table *pt,
2634 double *value, double *upper, double *lower, union value *c)
2636 double f11, f12, f21, f22;
2642 for (i = 0; i < 3; i++)
2643 value[i] = upper[i] = lower[i] = SYSMIS;
2646 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2653 for (i = j = 0; i < pt->n_cols; i++)
2654 if (pt->col_tot[i] != 0.)
2663 f11 = pt->mat[nz_cols[0]];
2664 f12 = pt->mat[nz_cols[1]];
2665 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2666 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2668 c[0] = pt->cols[nz_cols[0]];
2669 c[1] = pt->cols[nz_cols[1]];
2672 value[0] = (f11 * f22) / (f12 * f21);
2673 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2674 lower[0] = value[0] * exp (-1.960 * v);
2675 upper[0] = value[0] * exp (1.960 * v);
2677 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2678 v = sqrt ((f12 / (f11 * (f11 + f12)))
2679 + (f22 / (f21 * (f21 + f22))));
2680 lower[1] = value[1] * exp (-1.960 * v);
2681 upper[1] = value[1] * exp (1.960 * v);
2683 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2684 v = sqrt ((f11 / (f12 * (f11 + f12)))
2685 + (f21 / (f22 * (f21 + f22))));
2686 lower[2] = value[2] * exp (-1.960 * v);
2687 upper[2] = value[2] * exp (1.960 * v);
2692 /* Calculate directional measures. */
2694 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2695 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2696 double t[N_DIRECTIONAL])
2701 for (i = 0; i < N_DIRECTIONAL; i++)
2702 v[i] = ase[i] = t[i] = SYSMIS;
2706 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2708 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2709 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2710 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2711 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2712 double sum_fim, sum_fmj;
2714 int rm_index, cm_index;
2717 /* Find maximum for each row and their sum. */
2718 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2720 double max = pt->mat[i * pt->n_cols];
2723 for (j = 1; j < pt->n_cols; j++)
2724 if (pt->mat[j + i * pt->n_cols] > max)
2726 max = pt->mat[j + i * pt->n_cols];
2730 sum_fim += fim[i] = max;
2731 fim_index[i] = index;
2734 /* Find maximum for each column. */
2735 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2737 double max = pt->mat[j];
2740 for (i = 1; i < pt->n_rows; i++)
2741 if (pt->mat[j + i * pt->n_cols] > max)
2743 max = pt->mat[j + i * pt->n_cols];
2747 sum_fmj += fmj[j] = max;
2748 fmj_index[j] = index;
2751 /* Find maximum row total. */
2752 rm = pt->row_tot[0];
2754 for (i = 1; i < pt->n_rows; i++)
2755 if (pt->row_tot[i] > rm)
2757 rm = pt->row_tot[i];
2761 /* Find maximum column total. */
2762 cm = pt->col_tot[0];
2764 for (j = 1; j < pt->n_cols; j++)
2765 if (pt->col_tot[j] > cm)
2767 cm = pt->col_tot[j];
2771 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2772 v[1] = (sum_fmj - rm) / (pt->total - rm);
2773 v[2] = (sum_fim - cm) / (pt->total - cm);
2775 /* ASE1 for Y given PT. */
2779 for (accum = 0., i = 0; i < pt->n_rows; i++)
2780 for (j = 0; j < pt->n_cols; j++)
2782 const int deltaj = j == cm_index;
2783 accum += (pt->mat[j + i * pt->n_cols]
2784 * pow2 ((j == fim_index[i])
2789 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2792 /* ASE0 for Y given PT. */
2796 for (accum = 0., i = 0; i < pt->n_rows; i++)
2797 if (cm_index != fim_index[i])
2798 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2799 + pt->mat[i * pt->n_cols + cm_index]);
2800 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2803 /* ASE1 for PT given Y. */
2807 for (accum = 0., i = 0; i < pt->n_rows; i++)
2808 for (j = 0; j < pt->n_cols; j++)
2810 const int deltaj = i == rm_index;
2811 accum += (pt->mat[j + i * pt->n_cols]
2812 * pow2 ((i == fmj_index[j])
2817 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2820 /* ASE0 for PT given Y. */
2824 for (accum = 0., j = 0; j < pt->n_cols; j++)
2825 if (rm_index != fmj_index[j])
2826 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2827 + pt->mat[j + pt->n_cols * rm_index]);
2828 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2831 /* Symmetric ASE0 and ASE1. */
2836 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2837 for (j = 0; j < pt->n_cols; j++)
2839 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2840 int temp1 = (i == rm_index) + (j == cm_index);
2841 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2842 accum1 += (pt->mat[j + i * pt->n_cols]
2843 * pow2 (temp0 + (v[0] - 1.) * temp1));
2845 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2846 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2847 / (2. * pt->total - rm - cm));
2856 double sum_fij2_ri, sum_fij2_ci;
2857 double sum_ri2, sum_cj2;
2859 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2860 for (j = 0; j < pt->n_cols; j++)
2862 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2863 sum_fij2_ri += temp / pt->row_tot[i];
2864 sum_fij2_ci += temp / pt->col_tot[j];
2867 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2868 sum_ri2 += pow2 (pt->row_tot[i]);
2870 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2871 sum_cj2 += pow2 (pt->col_tot[j]);
2873 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2874 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2878 if (proc->statistics & (1u << CRS_ST_UC))
2880 double UX, UY, UXY, P;
2881 double ase1_yx, ase1_xy, ase1_sym;
2884 for (UX = 0., i = 0; i < pt->n_rows; i++)
2885 if (pt->row_tot[i] > 0.)
2886 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2888 for (UY = 0., j = 0; j < pt->n_cols; j++)
2889 if (pt->col_tot[j] > 0.)
2890 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2892 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2893 for (j = 0; j < pt->n_cols; j++)
2895 double entry = pt->mat[j + i * pt->n_cols];
2900 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2901 UXY -= entry / pt->total * log (entry / pt->total);
2904 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2905 for (j = 0; j < pt->n_cols; j++)
2907 double entry = pt->mat[j + i * pt->n_cols];
2912 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2913 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2914 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2915 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2916 ase1_sym += entry * pow2 ((UXY
2917 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2918 - (UX + UY) * log (entry / pt->total));
2921 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2922 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2923 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2924 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2926 v[6] = (UX + UY - UXY) / UX;
2927 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2928 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2930 v[7] = (UX + UY - UXY) / UY;
2931 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2932 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2936 if (proc->statistics & (1u << CRS_ST_D))
2938 double v_dummy[N_SYMMETRIC];
2939 double ase_dummy[N_SYMMETRIC];
2940 double t_dummy[N_SYMMETRIC];
2941 double somers_d_v[3];
2942 double somers_d_ase[3];
2943 double somers_d_t[3];
2945 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2946 somers_d_v, somers_d_ase, somers_d_t))
2949 for (i = 0; i < 3; i++)
2951 v[8 + i] = somers_d_v[i];
2952 ase[8 + i] = somers_d_ase[i];
2953 t[8 + i] = somers_d_t[i];
2959 if (proc->statistics & (1u << CRS_ST_ETA))
2962 double sum_Xr, sum_X2r;
2966 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2968 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2969 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2971 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2973 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2977 for (cum = 0., i = 0; i < pt->n_rows; i++)
2979 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2980 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2983 SXW -= cum * cum / pt->col_tot[j];
2985 v[11] = sqrt (1. - SXW / SX);
2989 double sum_Yc, sum_Y2c;
2993 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2995 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2996 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2998 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3000 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3004 for (cum = 0., j = 0; j < pt->n_cols; j++)
3006 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3007 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3010 SYW -= cum * cum / pt->row_tot[i];
3012 v[12] = sqrt (1. - SYW / SY);