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/casewriter.h"
40 #include "data/data-out.h"
41 #include "data/dictionary.h"
42 #include "data/format.h"
43 #include "data/procedure.h"
44 #include "data/subcase.h"
45 #include "data/value-labels.h"
46 #include "data/variable.h"
47 #include "language/command.h"
48 #include "language/dictionary/split-file.h"
49 #include "language/lexer/lexer.h"
50 #include "language/lexer/variable-parser.h"
51 #include "libpspp/array.h"
52 #include "libpspp/assertion.h"
53 #include "libpspp/compiler.h"
54 #include "libpspp/hash.h"
55 #include "libpspp/hmap.h"
56 #include "libpspp/hmapx.h"
57 #include "libpspp/message.h"
58 #include "libpspp/misc.h"
59 #include "libpspp/pool.h"
60 #include "libpspp/str.h"
61 #include "math/sort.h"
62 #include "output/tab.h"
64 #include "gl/minmax.h"
65 #include "gl/xalloc.h"
69 #define _(msgid) gettext (msgid)
70 #define N_(msgid) msgid
78 missing=miss:!table/include/report;
79 +write[wr_]=none,cells,all;
80 +format=fmt:!labels/nolabels/novallabs,
83 tabl:!tables/notables,
86 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
88 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
94 /* Number of chi-square statistics. */
97 /* Number of symmetric statistics. */
100 /* Number of directional statistics. */
101 #define N_DIRECTIONAL 13
103 /* A single table entry for general mode. */
106 double freq; /* Frequency count. */
107 union value values[1]; /* Values. */
111 table_entry_size (size_t n_values)
113 return (offsetof (struct table_entry, values)
114 + n_values * sizeof (union value));
117 /* Indexes into the 'vars' member of struct pivot_table and
118 struct crosstab member. */
121 ROW_VAR = 0, /* Row variable. */
122 COL_VAR = 1 /* Column variable. */
123 /* Higher indexes cause multiple tables to be output. */
126 /* A crosstabulation of 2 or more variables. */
129 struct fmt_spec weight_format; /* Format for weight variable. */
130 double missing; /* Weight of missing cases. */
132 /* Variables (2 or more). */
134 const struct variable **vars;
136 /* Constants (0 or more). */
138 const struct variable **const_vars;
139 union value *const_values;
142 struct subcase src_sc, dst_sc;
143 struct casewriter *sorter;
144 struct table_entry **entries;
147 /* Column values, number of columns. */
151 /* Row values, number of rows. */
155 /* Number of statistically interesting columns/rows
156 (columns/rows with data in them). */
157 int ns_cols, ns_rows;
159 /* Matrix contents. */
160 double *mat; /* Matrix proper. */
161 double *row_tot; /* Row totals. */
162 double *col_tot; /* Column totals. */
163 double total; /* Grand total. */
166 /* Integer mode variable info. */
169 int min; /* Minimum value. */
170 int max; /* Maximum value + 1. */
171 int count; /* max - min. */
174 static inline struct var_range *
175 get_var_range (const struct variable *v)
177 return var_get_aux (v);
180 struct crosstabs_proc
182 const struct dictionary *dict;
183 enum { INTEGER, GENERAL } mode;
184 enum mv_class exclude;
187 struct fmt_spec weight_format;
189 /* Variables specifies on VARIABLES. */
190 const struct variable **variables;
194 struct pivot_table *pivots;
198 int n_cells; /* Number of cells requested. */
199 unsigned int cells; /* Bit k is 1 if cell k is requested. */
200 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
203 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
206 static bool should_tabulate_case (const struct pivot_table *,
207 const struct ccase *, enum mv_class exclude,
209 static void postcalc (struct crosstabs_proc *);
210 static void submit (struct pivot_table *, struct tab_table *);
212 static struct ccase *
213 crs_combine_cases (struct ccase *a, struct ccase *b, void *aux UNUSED)
215 size_t weight_idx = caseproto_get_n_widths (case_get_proto (a)) - 1;
217 a = case_unshare (a);
218 case_data_rw_idx (a, weight_idx)->f += case_data_idx (b, weight_idx)->f;
224 /* Parses and executes the CROSSTABS procedure. */
226 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
228 const struct variable *wv = dict_get_weight (dataset_dict (ds));
229 const struct dictionary *dict = dataset_dict (ds);
230 size_t n_splits = dict_get_split_cnt (dict);
231 struct crosstabs_proc proc;
232 struct casereader *input;
233 struct cmd_crosstabs cmd;
234 struct pivot_table *pt;
240 proc.dict = dataset_dict (ds);
241 proc.bad_warn = true;
242 proc.variables = NULL;
243 proc.n_variables = 0;
246 proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
248 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
250 result = CMD_FAILURE;
254 proc.mode = proc.n_variables ? INTEGER : GENERAL;
258 proc.cells = 1u << CRS_CL_COUNT;
259 else if (cmd.a_cells[CRS_CL_ALL])
260 proc.cells = UINT_MAX;
264 for (i = 0; i < CRS_CL_count; i++)
266 proc.cells |= 1u << i;
268 proc.cells = ((1u << CRS_CL_COUNT)
270 | (1u << CRS_CL_COLUMN)
271 | (1u << CRS_CL_TOTAL));
273 proc.cells &= ((1u << CRS_CL_count) - 1);
274 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
276 for (i = 0; i < CRS_CL_count; i++)
277 if (proc.cells & (1u << i))
278 proc.a_cells[proc.n_cells++] = i;
281 if (cmd.a_statistics[CRS_ST_ALL])
282 proc.statistics = UINT_MAX;
283 else if (cmd.sbc_statistics)
288 for (i = 0; i < CRS_ST_count; i++)
289 if (cmd.a_statistics[i])
290 proc.statistics |= 1u << i;
291 if (proc.statistics == 0)
292 proc.statistics |= 1u << CRS_ST_CHISQ;
298 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
299 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
301 if (proc.mode == GENERAL && proc.mode == MV_NEVER)
303 msg (SE, _("Missing mode REPORT not allowed in general mode. "
304 "Assuming MISSING=TABLE."));
309 proc.pivot = cmd.pivot == CRS_PIVOT;
311 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
313 struct caseproto *proto;
316 subcase_init_empty (&pt->src_sc);
317 subcase_add_vars_always (&pt->src_sc, dict_get_split_vars (dict),
318 n_splits, SC_ASCEND);
319 subcase_add_vars_always (&pt->src_sc, pt->vars, pt->n_vars, SC_ASCEND);
321 subcase_clone (&pt->dst_sc, &pt->src_sc);
322 subcase_project (&pt->dst_sc, 0);
324 subcase_init_empty (&sort);
325 for (i = 0; i < n_splits; i++)
326 subcase_add_always (&sort, i, subcase_get_width (&pt->src_sc, i),
328 for (i = 0; i < pt->n_vars; i++)
330 size_t var_idx = n_splits + (i == pt->n_vars - 2 ? ROW_VAR
331 : i == pt->n_vars - 1 ? COL_VAR
333 subcase_add_always (&sort, var_idx,
334 subcase_get_width (&pt->src_sc, var_idx),
338 proto = caseproto_ref (subcase_get_proto (&pt->dst_sc));
339 proto = caseproto_add_width (proto, 0);
340 pt->sorter = sort_distinct_create_writer (&sort, proto,
341 crs_combine_cases, NULL, NULL);
342 caseproto_unref (proto);
345 input = casereader_create_filter_weight (proc_open (ds), dict, NULL, NULL);
346 for (; (c = casereader_read (input)) != NULL; case_unref (c))
348 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
350 const struct caseproto *proto = casewriter_get_proto (pt->sorter);
351 struct ccase *pt_case;
353 pt_case = case_create (proto);
355 subcase_copy (&pt->src_sc, c, &pt->dst_sc, pt_case);
356 if (should_tabulate_case (pt, pt_case, proc.exclude, n_splits)
357 && proc.mode == INTEGER)
359 for (i = 0; i < pt->n_vars; i++)
361 double *d = &case_data_rw_idx (pt_case, i + n_splits)->f;
366 case_data_rw_idx (pt_case, caseproto_get_n_widths (proto) - 1)->f
367 = dict_get_case_weight (dict, c, &proc.bad_warn);
369 casewriter_write (pt->sorter, pt_case);
372 ok = casereader_destroy (input);
373 ok = proc_commit (ds) && ok;
375 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
377 const struct caseproto *proto;
378 struct casegrouper *grouper;
379 struct casereader *data;
380 struct subcase group_sc;
381 struct casereader *group;
383 subcase_init_vars (&group_sc, dict_get_split_vars (dict),
384 dict_get_split_cnt (dict));
385 subcase_project (&group_sc, 0);
387 data = casewriter_make_reader (pt->sorter);
388 proto = casereader_get_proto (data);
389 grouper = casegrouper_create_subcase (data, &group_sc);
390 subcase_destroy (&group_sc);
392 for (; casegrouper_get_next_group (grouper, &group);
393 casereader_destroy (group))
395 casenumber n_entries;
398 c = casereader_peek (group, 0);
401 /* XXX output_split_file_values (ds, c); */
405 n_entries = casereader_count_cases (group);
406 if (n_entries > 1000000)
408 msg (SW, _("Omitting analysis of crosstabulation that has %lu "
410 (unsigned long int) n_entries);
414 pt->entries = xmalloc (n_entries * sizeof *pt->entries);
417 for (; (c = casereader_read (group)) != NULL; case_unref (c))
418 if (should_tabulate_case (pt, c, proc.exclude, n_splits))
420 struct table_entry *e;
422 e = xmalloc (table_entry_size (pt->n_vars));
423 for (i = 0; i < pt->n_vars; i++)
424 value_clone (&e->values[i], case_data_idx (c, i + n_splits),
425 caseproto_get_width (proto, i + n_splits));
426 e->freq = case_num_idx (c, pt->n_vars + n_splits);
428 pt->entries[pt->n_entries++] = e;
431 pt->missing += case_num_idx (c, pt->n_vars + n_splits);
435 ok = casegrouper_destroy (grouper) && ok;
438 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
441 free (proc.variables);
442 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
445 free (pt->const_vars);
446 /* We must not call value_destroy on const_values because
447 it is a wild pointer; it never pointed to anything owned
450 The rest of the data was allocated and destroyed at a
451 lower level already. */
458 /* Parses the TABLES subcommand. */
460 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
461 struct cmd_crosstabs *cmd UNUSED, void *proc_)
463 struct crosstabs_proc *proc = proc_;
464 struct const_var_set *var_set;
466 const struct variable ***by = NULL;
468 size_t *by_nvar = NULL;
473 /* Ensure that this is a TABLES subcommand. */
474 if (!lex_match_id (lexer, "TABLES")
475 && (lex_token (lexer) != T_ID ||
476 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
477 && lex_token (lexer) != T_ALL)
479 lex_match (lexer, '=');
481 if (proc->variables != NULL)
482 var_set = const_var_set_create_from_array (proc->variables,
485 var_set = const_var_set_create_from_dict (dataset_dict (ds));
486 assert (var_set != NULL);
490 by = xnrealloc (by, n_by + 1, sizeof *by);
491 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
492 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
493 PV_NO_DUPLICATE | PV_NO_SCRATCH))
495 if (xalloc_oversized (nx, by_nvar[n_by]))
497 msg (SE, _("Too many cross-tabulation variables or dimensions."));
503 if (!lex_match (lexer, T_BY))
507 lex_error (lexer, _("expecting BY"));
515 by_iter = xcalloc (n_by, sizeof *by_iter);
516 proc->pivots = xnrealloc (proc->pivots,
517 proc->n_pivots + nx, sizeof *proc->pivots);
518 for (i = 0; i < nx; i++)
520 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
523 pt->weight_format = proc->weight_format;
526 pt->vars = xmalloc (n_by * sizeof *pt->vars);
528 pt->const_vars = NULL;
529 pt->const_values = NULL;
531 for (j = 0; j < n_by; j++)
532 pt->vars[j] = by[j][by_iter[j]];
534 for (j = n_by - 1; j >= 0; j--)
536 if (++by_iter[j] < by_nvar[j])
545 /* All return paths lead here. */
546 for (i = 0; i < n_by; i++)
551 const_var_set_destroy (var_set);
556 /* Parses the VARIABLES subcommand. */
558 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
559 struct cmd_crosstabs *cmd UNUSED, void *proc_)
561 struct crosstabs_proc *proc = proc_;
564 msg (SE, _("VARIABLES must be specified before TABLES."));
568 lex_match (lexer, '=');
572 size_t orig_nv = proc->n_variables;
577 if (!parse_variables_const (lexer, dataset_dict (ds),
578 &proc->variables, &proc->n_variables,
579 (PV_APPEND | PV_NUMERIC
580 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
583 if (lex_token (lexer) != '(')
585 lex_error (lexer, "expecting `('");
590 if (!lex_force_int (lexer))
592 min = lex_integer (lexer);
595 lex_match (lexer, ',');
597 if (!lex_force_int (lexer))
599 max = lex_integer (lexer);
602 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
608 if (lex_token (lexer) != ')')
610 lex_error (lexer, "expecting `)'");
615 for (i = orig_nv; i < proc->n_variables; i++)
617 struct var_range *vr = xmalloc (sizeof *vr);
620 vr->count = max - min + 1;
621 var_attach_aux (proc->variables[i], vr, var_dtor_free);
624 if (lex_token (lexer) == '/')
631 free (proc->variables);
632 proc->variables = NULL;
633 proc->n_variables = 0;
637 /* Data file processing. */
640 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
641 enum mv_class exclude, size_t n_splits)
644 for (j = 0; j < pt->n_vars; j++)
646 const struct variable *var = pt->vars[j];
647 struct var_range *range = get_var_range (var);
648 const union value *value = case_data_idx (c, j + n_splits);
650 if (var_is_value_missing (var, value, exclude))
655 double num = value->f;
656 if (num < range->min || num > range->max)
663 /* Post-data reading calculations. */
665 static int compare_table_entry_vars_3way (const struct table_entry *a,
666 const struct table_entry *b,
667 const struct pivot_table *pt,
669 static void enum_var_values (const struct pivot_table *, int var_idx,
670 union value **valuesp, int *n_values);
671 static void output_pivot_table (struct crosstabs_proc *,
672 struct pivot_table *);
673 static void make_pivot_table_subset (struct pivot_table *pt,
674 size_t row0, size_t row1,
675 struct pivot_table *subset);
676 static void make_summary_table (struct crosstabs_proc *);
677 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
680 postcalc (struct crosstabs_proc *proc)
682 struct pivot_table *pt;
684 make_summary_table (proc);
686 /* Output each pivot table. */
687 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
689 if (proc->pivot || pt->n_vars == 2)
690 output_pivot_table (proc, pt);
693 size_t row0 = 0, row1 = 0;
694 while (find_crosstab (pt, &row0, &row1))
696 struct pivot_table subset;
697 make_pivot_table_subset (pt, row0, row1, &subset);
698 output_pivot_table (proc, &subset);
703 /* Free output and prepare for next split file. */
704 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
708 /* Free only the members that were allocated in this
709 function. The other pointer members are either both
710 allocated and destroyed at a lower level (in
711 output_pivot_table), or both allocated and destroyed at
712 a higher level (in crs_custom_tables and free_proc,
714 for (i = 0; i < pt->n_entries; i++)
715 free (pt->entries[i]);
721 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
722 struct pivot_table *subset)
727 assert (pt->n_consts == 0);
728 subset->missing = pt->missing;
730 subset->vars = pt->vars;
731 subset->n_consts = pt->n_vars - 2;
732 subset->const_vars = pt->vars + 2;
733 subset->const_values = &pt->entries[row0]->values[2];
735 subset->entries = &pt->entries[row0];
736 subset->n_entries = row1 - row0;
740 compare_table_entry_var_3way (const struct table_entry *a,
741 const struct table_entry *b,
742 const struct pivot_table *pt,
745 return value_compare_3way (&a->values[idx], &b->values[idx],
746 var_get_width (pt->vars[idx]));
750 compare_table_entry_vars_3way (const struct table_entry *a,
751 const struct table_entry *b,
752 const struct pivot_table *pt,
757 for (i = idx1 - 1; i >= idx0; i--)
759 int cmp = compare_table_entry_var_3way (a, b, pt, i);
767 find_first_difference (const struct pivot_table *pt, size_t row)
770 return pt->n_vars - 1;
773 const struct table_entry *a = pt->entries[row];
774 const struct table_entry *b = pt->entries[row - 1];
777 for (col = pt->n_vars - 1; col >= 0; col--)
778 if (compare_table_entry_var_3way (a, b, pt, col))
784 /* Output a table summarizing the cases processed. */
786 make_summary_table (struct crosstabs_proc *proc)
788 struct tab_table *summary;
789 struct pivot_table *pt;
793 summary = tab_create (7, 3 + proc->n_pivots);
794 tab_title (summary, _("Summary."));
795 tab_headers (summary, 1, 0, 3, 0);
796 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
797 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
798 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
799 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
800 tab_hline (summary, TAL_1, 1, 6, 1);
801 tab_hline (summary, TAL_1, 1, 6, 2);
802 tab_vline (summary, TAL_1, 3, 1, 1);
803 tab_vline (summary, TAL_1, 5, 1, 1);
804 for (i = 0; i < 3; i++)
806 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
807 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
809 tab_offset (summary, 0, 3);
811 ds_init_empty (&name);
812 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
818 tab_hline (summary, TAL_1, 0, 6, 0);
821 for (i = 0; i < pt->n_vars; i++)
824 ds_put_cstr (&name, " * ");
825 ds_put_cstr (&name, var_to_string (pt->vars[i]));
827 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
830 for (i = 0; i < pt->n_entries; i++)
831 valid += pt->entries[i]->freq;
836 for (i = 0; i < 3; i++)
838 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
839 &proc->weight_format);
840 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
844 tab_next_row (summary);
848 submit (NULL, summary);
853 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
854 struct pivot_table *);
855 static struct tab_table *create_chisq_table (struct pivot_table *);
856 static struct tab_table *create_sym_table (struct pivot_table *);
857 static struct tab_table *create_risk_table (struct pivot_table *);
858 static struct tab_table *create_direct_table (struct pivot_table *);
859 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
860 struct tab_table *, int first_difference);
861 static void display_crosstabulation (struct crosstabs_proc *,
862 struct pivot_table *,
864 static void display_chisq (struct pivot_table *, struct tab_table *,
865 bool *showed_fisher);
866 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
868 static void display_risk (struct pivot_table *, struct tab_table *);
869 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
871 static void table_value_missing (struct crosstabs_proc *proc,
872 struct tab_table *table, int c, int r,
873 unsigned char opt, const union value *v,
874 const struct variable *var);
875 static void delete_missing (struct pivot_table *);
876 static void build_matrix (struct pivot_table *);
878 /* Output pivot table beginning at PB and continuing until PE,
879 exclusive. For efficiency, *MATP is a pointer to a matrix that can
880 hold *MAXROWS entries. */
882 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
884 struct tab_table *table = NULL; /* Crosstabulation table. */
885 struct tab_table *chisq = NULL; /* Chi-square table. */
886 bool showed_fisher = false;
887 struct tab_table *sym = NULL; /* Symmetric measures table. */
888 struct tab_table *risk = NULL; /* Risk estimate table. */
889 struct tab_table *direct = NULL; /* Directional measures table. */
892 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
895 table = create_crosstab_table (proc, pt);
896 if (proc->statistics & (1u << CRS_ST_CHISQ))
897 chisq = create_chisq_table (pt);
898 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
899 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
900 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
901 | (1u << CRS_ST_KAPPA)))
902 sym = create_sym_table (pt);
903 if (proc->statistics & (1u << CRS_ST_RISK))
904 risk = create_risk_table (pt);
905 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
906 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
907 direct = create_direct_table (pt);
910 while (find_crosstab (pt, &row0, &row1))
912 struct pivot_table x;
913 int first_difference;
915 make_pivot_table_subset (pt, row0, row1, &x);
917 /* Find all the row variable values. */
918 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
920 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
923 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
924 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
925 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
927 /* Allocate table space for the matrix. */
929 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
930 tab_realloc (table, -1,
931 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
932 tab_nr (table) * pt->n_entries / x.n_entries));
936 /* Find the first variable that differs from the last subtable. */
937 first_difference = find_first_difference (pt, row0);
940 display_dimensions (proc, &x, table, first_difference);
941 display_crosstabulation (proc, &x, table);
944 if (proc->exclude == MV_NEVER)
949 display_dimensions (proc, &x, chisq, first_difference);
950 display_chisq (&x, chisq, &showed_fisher);
954 display_dimensions (proc, &x, sym, first_difference);
955 display_symmetric (proc, &x, sym);
959 display_dimensions (proc, &x, risk, first_difference);
960 display_risk (&x, risk);
964 display_dimensions (proc, &x, direct, first_difference);
965 display_directional (proc, &x, direct);
968 /* Free the parts of x that are not owned by pt. In
969 particular we must not free x.cols, which is the same as
970 pt->cols, which is freed at the end of this function. */
978 submit (NULL, table);
983 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
995 build_matrix (struct pivot_table *x)
997 const int col_var_width = var_get_width (x->vars[COL_VAR]);
998 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1001 struct table_entry **p;
1005 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1007 const struct table_entry *te = *p;
1009 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1011 for (; col < x->n_cols; col++)
1017 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1024 if (++col >= x->n_cols)
1030 while (mp < &x->mat[x->n_cols * x->n_rows])
1032 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1034 /* Column totals, row totals, ns_rows. */
1036 for (col = 0; col < x->n_cols; col++)
1037 x->col_tot[col] = 0.0;
1038 for (row = 0; row < x->n_rows; row++)
1039 x->row_tot[row] = 0.0;
1041 for (row = 0; row < x->n_rows; row++)
1043 bool row_is_empty = true;
1044 for (col = 0; col < x->n_cols; col++)
1048 row_is_empty = false;
1049 x->col_tot[col] += *mp;
1050 x->row_tot[row] += *mp;
1057 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1061 for (col = 0; col < x->n_cols; col++)
1062 for (row = 0; row < x->n_rows; row++)
1063 if (x->mat[col + row * x->n_cols] != 0.0)
1071 for (col = 0; col < x->n_cols; col++)
1072 x->total += x->col_tot[col];
1075 static struct tab_table *
1076 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1083 static const struct tuple names[] =
1085 {CRS_CL_COUNT, N_("count")},
1086 {CRS_CL_ROW, N_("row %")},
1087 {CRS_CL_COLUMN, N_("column %")},
1088 {CRS_CL_TOTAL, N_("total %")},
1089 {CRS_CL_EXPECTED, N_("expected")},
1090 {CRS_CL_RESIDUAL, N_("residual")},
1091 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1092 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1094 const int n_names = sizeof names / sizeof *names;
1095 const struct tuple *t;
1097 struct tab_table *table;
1098 struct string title;
1099 struct pivot_table x;
1103 make_pivot_table_subset (pt, 0, 0, &x);
1105 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1106 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1107 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1109 /* First header line. */
1110 tab_joint_text (table, x.n_consts + 1, 0,
1111 (x.n_consts + 1) + (x.n_cols - 1), 0,
1112 TAB_CENTER | TAT_TITLE, var_get_name (x.vars[COL_VAR]));
1114 tab_hline (table, TAL_1, x.n_consts + 1,
1115 x.n_consts + 2 + x.n_cols - 2, 1);
1117 /* Second header line. */
1118 for (i = 2; i < x.n_consts + 2; i++)
1119 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1120 x.n_consts + 2 - i - 1, 1,
1121 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1122 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1123 var_get_name (x.vars[ROW_VAR]));
1124 for (i = 0; i < x.n_cols; i++)
1125 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1126 &x.cols[i], x.vars[COL_VAR]);
1127 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1129 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1130 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1133 ds_init_empty (&title);
1134 for (i = 0; i < x.n_consts + 2; i++)
1137 ds_put_cstr (&title, " * ");
1138 ds_put_cstr (&title, var_get_name (x.vars[i]));
1140 for (i = 0; i < pt->n_consts; i++)
1142 const struct variable *var = pt->const_vars[i];
1146 ds_put_format (&title, ", %s=", var_get_name (var));
1148 /* Insert the formatted value of the variable, then trim
1149 leading spaces in what was just inserted. */
1150 ofs = ds_length (&title);
1151 s = data_out (&pt->const_values[i], var_get_encoding (var),
1152 var_get_print_format (var));
1153 ds_put_cstr (&title, s);
1155 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1159 ds_put_cstr (&title, " [");
1161 for (t = names; t < &names[n_names]; t++)
1162 if (proc->cells & (1u << t->value))
1165 ds_put_cstr (&title, ", ");
1166 ds_put_cstr (&title, gettext (t->name));
1168 ds_put_cstr (&title, "].");
1170 tab_title (table, "%s", ds_cstr (&title));
1171 ds_destroy (&title);
1173 tab_offset (table, 0, 2);
1177 static struct tab_table *
1178 create_chisq_table (struct pivot_table *pt)
1180 struct tab_table *chisq;
1182 chisq = tab_create (6 + (pt->n_vars - 2),
1183 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1184 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1186 tab_title (chisq, _("Chi-square tests."));
1188 tab_offset (chisq, pt->n_vars - 2, 0);
1189 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1190 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1191 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1192 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1193 _("Asymp. Sig. (2-sided)"));
1194 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1195 _("Exact Sig. (2-sided)"));
1196 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1197 _("Exact Sig. (1-sided)"));
1198 tab_offset (chisq, 0, 1);
1203 /* Symmetric measures. */
1204 static struct tab_table *
1205 create_sym_table (struct pivot_table *pt)
1207 struct tab_table *sym;
1209 sym = tab_create (6 + (pt->n_vars - 2),
1210 pt->n_entries / pt->n_cols * 7 + 10);
1211 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1212 tab_title (sym, _("Symmetric measures."));
1214 tab_offset (sym, pt->n_vars - 2, 0);
1215 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1216 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1217 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1218 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1219 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1220 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1221 tab_offset (sym, 0, 1);
1226 /* Risk estimate. */
1227 static struct tab_table *
1228 create_risk_table (struct pivot_table *pt)
1230 struct tab_table *risk;
1232 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1233 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1234 tab_title (risk, _("Risk estimate."));
1236 tab_offset (risk, pt->n_vars - 2, 0);
1237 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1238 _("95%% Confidence Interval"));
1239 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1240 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1241 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1242 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1243 tab_hline (risk, TAL_1, 2, 3, 1);
1244 tab_vline (risk, TAL_1, 2, 0, 1);
1245 tab_offset (risk, 0, 2);
1250 /* Directional measures. */
1251 static struct tab_table *
1252 create_direct_table (struct pivot_table *pt)
1254 struct tab_table *direct;
1256 direct = tab_create (7 + (pt->n_vars - 2),
1257 pt->n_entries / pt->n_cols * 7 + 10);
1258 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1259 tab_title (direct, _("Directional measures."));
1261 tab_offset (direct, pt->n_vars - 2, 0);
1262 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1263 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1264 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1265 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1266 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1267 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1268 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1269 tab_offset (direct, 0, 1);
1275 /* Delete missing rows and columns for statistical analysis when
1278 delete_missing (struct pivot_table *pt)
1282 for (r = 0; r < pt->n_rows; r++)
1283 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1285 for (c = 0; c < pt->n_cols; c++)
1286 pt->mat[c + r * pt->n_cols] = 0.;
1291 for (c = 0; c < pt->n_cols; c++)
1292 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1294 for (r = 0; r < pt->n_rows; r++)
1295 pt->mat[c + r * pt->n_cols] = 0.;
1300 /* Prepare table T for submission, and submit it. */
1302 submit (struct pivot_table *pt, struct tab_table *t)
1309 tab_resize (t, -1, 0);
1310 if (tab_nr (t) == tab_t (t))
1312 table_unref (&t->table);
1315 tab_offset (t, 0, 0);
1317 for (i = 2; i < pt->n_vars; i++)
1318 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1319 var_to_string (pt->vars[i]));
1320 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1321 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1323 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1325 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1331 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1333 size_t row0 = *row1p;
1336 if (row0 >= pt->n_entries)
1339 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1341 struct table_entry *a = pt->entries[row0];
1342 struct table_entry *b = pt->entries[row1];
1343 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1351 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1352 result. WIDTH_ points to an int which is either 0 for a
1353 numeric value or a string width for a string value. */
1355 compare_value_3way (const void *a_, const void *b_, const void *width_)
1357 const union value *a = a_;
1358 const union value *b = b_;
1359 const int *width = width_;
1361 return value_compare_3way (a, b, *width);
1364 /* Given an array of ENTRY_CNT table_entry structures starting at
1365 ENTRIES, creates a sorted list of the values that the variable
1366 with index VAR_IDX takes on. The values are returned as a
1367 malloc()'d array stored in *VALUES, with the number of values
1368 stored in *VALUE_CNT.
1371 enum_var_values (const struct pivot_table *pt, int var_idx,
1372 union value **valuesp, int *n_values)
1374 const struct variable *var = pt->vars[var_idx];
1375 struct var_range *range = get_var_range (var);
1376 union value *values;
1381 values = *valuesp = xnmalloc (range->count, sizeof *values);
1382 *n_values = range->count;
1383 for (i = 0; i < range->count; i++)
1384 values[i].f = range->min + i;
1388 int width = var_get_width (var);
1389 struct hmapx_node *node;
1390 const union value *iter;
1394 for (i = 0; i < pt->n_entries; i++)
1396 const struct table_entry *te = pt->entries[i];
1397 const union value *value = &te->values[var_idx];
1398 size_t hash = value_hash (value, width, 0);
1400 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1401 if (value_equal (iter, value, width))
1404 hmapx_insert (&set, (union value *) value, hash);
1409 *n_values = hmapx_count (&set);
1410 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1412 HMAPX_FOR_EACH (iter, node, &set)
1413 values[i++] = *iter;
1414 hmapx_destroy (&set);
1416 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1420 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1421 from V, displayed with print format spec from variable VAR. When
1422 in REPORT missing-value mode, missing values have an M appended. */
1424 table_value_missing (struct crosstabs_proc *proc,
1425 struct tab_table *table, int c, int r, unsigned char opt,
1426 const union value *v, const struct variable *var)
1428 const char *label = var_lookup_value_label (var, v);
1430 tab_text (table, c, r, TAB_LEFT, label);
1433 const struct fmt_spec *print = var_get_print_format (var);
1434 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1436 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1437 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1441 tab_value (table, c, r, opt, v, proc->dict, print);
1445 /* Draws a line across TABLE at the current row to indicate the most
1446 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1447 that changed, and puts the values that changed into the table. TB
1448 and PT must be the corresponding table_entry and crosstab,
1451 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1452 struct tab_table *table, int first_difference)
1454 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1456 for (; first_difference >= 2; first_difference--)
1457 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1458 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1459 pt->vars[first_difference]);
1462 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1463 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1464 additionally suffixed with a letter `M'. */
1466 format_cell_entry (struct tab_table *table, int c, int r, double value,
1467 char suffix, bool mark_missing, const struct dictionary *dict)
1469 const struct fmt_spec f = {FMT_F, 10, 1};
1476 s = data_out (&v, dict_get_encoding (dict), &f);
1480 suffixes[suffix_len++] = suffix;
1482 suffixes[suffix_len++] = 'M';
1483 suffixes[suffix_len] = '\0';
1485 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1486 s + strspn (s, " "), suffixes);
1489 /* Displays the crosstabulation table. */
1491 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1492 struct tab_table *table)
1498 for (r = 0; r < pt->n_rows; r++)
1499 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1500 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1503 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1504 TAB_LEFT, _("Total"));
1506 /* Put in the actual cells. */
1508 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1509 for (r = 0; r < pt->n_rows; r++)
1511 if (proc->n_cells > 1)
1512 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1513 for (c = 0; c < pt->n_cols; c++)
1515 bool mark_missing = false;
1516 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1517 if (proc->exclude == MV_NEVER
1518 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1519 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1521 mark_missing = true;
1522 for (i = 0; i < proc->n_cells; i++)
1527 switch (proc->a_cells[i])
1533 v = *mp / pt->row_tot[r] * 100.;
1537 v = *mp / pt->col_tot[c] * 100.;
1541 v = *mp / pt->total * 100.;
1544 case CRS_CL_EXPECTED:
1547 case CRS_CL_RESIDUAL:
1548 v = *mp - expected_value;
1550 case CRS_CL_SRESIDUAL:
1551 v = (*mp - expected_value) / sqrt (expected_value);
1553 case CRS_CL_ASRESIDUAL:
1554 v = ((*mp - expected_value)
1555 / sqrt (expected_value
1556 * (1. - pt->row_tot[r] / pt->total)
1557 * (1. - pt->col_tot[c] / pt->total)));
1562 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1568 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1572 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1573 for (r = 0; r < pt->n_rows; r++)
1575 bool mark_missing = false;
1577 if (proc->exclude == MV_NEVER
1578 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1579 mark_missing = true;
1581 for (i = 0; i < proc->n_cells; i++)
1586 switch (proc->a_cells[i])
1596 v = pt->row_tot[r] / pt->total * 100.;
1600 v = pt->row_tot[r] / pt->total * 100.;
1603 case CRS_CL_EXPECTED:
1604 case CRS_CL_RESIDUAL:
1605 case CRS_CL_SRESIDUAL:
1606 case CRS_CL_ASRESIDUAL:
1613 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1614 tab_next_row (table);
1618 /* Column totals, grand total. */
1620 if (proc->n_cells > 1)
1621 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1622 for (c = 0; c <= pt->n_cols; c++)
1624 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1625 bool mark_missing = false;
1628 if (proc->exclude == MV_NEVER && c < pt->n_cols
1629 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1630 mark_missing = true;
1632 for (i = 0; i < proc->n_cells; i++)
1637 switch (proc->a_cells[i])
1643 v = ct / pt->total * 100.;
1651 v = ct / pt->total * 100.;
1654 case CRS_CL_EXPECTED:
1655 case CRS_CL_RESIDUAL:
1656 case CRS_CL_SRESIDUAL:
1657 case CRS_CL_ASRESIDUAL:
1663 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1668 tab_offset (table, -1, tab_row (table) + last_row);
1669 tab_offset (table, 0, -1);
1672 static void calc_r (struct pivot_table *,
1673 double *PT, double *Y, double *, double *, double *);
1674 static void calc_chisq (struct pivot_table *,
1675 double[N_CHISQ], int[N_CHISQ], double *, double *);
1677 /* Display chi-square statistics. */
1679 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1680 bool *showed_fisher)
1682 static const char *chisq_stats[N_CHISQ] =
1684 N_("Pearson Chi-Square"),
1685 N_("Likelihood Ratio"),
1686 N_("Fisher's Exact Test"),
1687 N_("Continuity Correction"),
1688 N_("Linear-by-Linear Association"),
1690 double chisq_v[N_CHISQ];
1691 double fisher1, fisher2;
1696 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1698 tab_offset (chisq, pt->n_vars - 2, -1);
1700 for (i = 0; i < N_CHISQ; i++)
1702 if ((i != 2 && chisq_v[i] == SYSMIS)
1703 || (i == 2 && fisher1 == SYSMIS))
1706 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1709 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1710 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1711 tab_double (chisq, 3, 0, TAB_RIGHT,
1712 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1716 *showed_fisher = true;
1717 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1718 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1720 tab_next_row (chisq);
1723 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1724 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1725 tab_next_row (chisq);
1727 tab_offset (chisq, 0, -1);
1730 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1731 double[N_SYMMETRIC], double[N_SYMMETRIC],
1732 double[N_SYMMETRIC],
1733 double[3], double[3], double[3]);
1735 /* Display symmetric measures. */
1737 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1738 struct tab_table *sym)
1740 static const char *categories[] =
1742 N_("Nominal by Nominal"),
1743 N_("Ordinal by Ordinal"),
1744 N_("Interval by Interval"),
1745 N_("Measure of Agreement"),
1748 static const char *stats[N_SYMMETRIC] =
1752 N_("Contingency Coefficient"),
1753 N_("Kendall's tau-b"),
1754 N_("Kendall's tau-c"),
1756 N_("Spearman Correlation"),
1761 static const int stats_categories[N_SYMMETRIC] =
1763 0, 0, 0, 1, 1, 1, 1, 2, 3,
1767 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1768 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1771 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1772 somers_d_v, somers_d_ase, somers_d_t))
1775 tab_offset (sym, pt->n_vars - 2, -1);
1777 for (i = 0; i < N_SYMMETRIC; i++)
1779 if (sym_v[i] == SYSMIS)
1782 if (stats_categories[i] != last_cat)
1784 last_cat = stats_categories[i];
1785 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1788 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1789 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1790 if (sym_ase[i] != SYSMIS)
1791 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1792 if (sym_t[i] != SYSMIS)
1793 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1794 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1798 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1799 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1802 tab_offset (sym, 0, -1);
1805 static int calc_risk (struct pivot_table *,
1806 double[], double[], double[], union value *);
1808 /* Display risk estimate. */
1810 display_risk (struct pivot_table *pt, struct tab_table *risk)
1813 double risk_v[3], lower[3], upper[3];
1817 if (!calc_risk (pt, risk_v, upper, lower, c))
1820 tab_offset (risk, pt->n_vars - 2, -1);
1822 for (i = 0; i < 3; i++)
1824 const struct variable *cv = pt->vars[COL_VAR];
1825 const struct variable *rv = pt->vars[ROW_VAR];
1826 int cvw = var_get_width (cv);
1827 int rvw = var_get_width (rv);
1829 if (risk_v[i] == SYSMIS)
1835 if (var_is_numeric (cv))
1836 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1837 var_get_name (cv), c[0].f, c[1].f);
1839 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1841 cvw, value_str (&c[0], cvw),
1842 cvw, value_str (&c[1], cvw));
1846 if (var_is_numeric (rv))
1847 sprintf (buf, _("For cohort %s = %g"),
1848 var_get_name (rv), pt->rows[i - 1].f);
1850 sprintf (buf, _("For cohort %s = %.*s"),
1852 rvw, value_str (&pt->rows[i - 1], rvw));
1856 tab_text (risk, 0, 0, TAB_LEFT, buf);
1857 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1858 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1859 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1860 tab_next_row (risk);
1863 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1864 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1865 tab_next_row (risk);
1867 tab_offset (risk, 0, -1);
1870 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1871 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1872 double[N_DIRECTIONAL]);
1874 /* Display directional measures. */
1876 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1877 struct tab_table *direct)
1879 static const char *categories[] =
1881 N_("Nominal by Nominal"),
1882 N_("Ordinal by Ordinal"),
1883 N_("Nominal by Interval"),
1886 static const char *stats[] =
1889 N_("Goodman and Kruskal tau"),
1890 N_("Uncertainty Coefficient"),
1895 static const char *types[] =
1902 static const int stats_categories[N_DIRECTIONAL] =
1904 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1907 static const int stats_stats[N_DIRECTIONAL] =
1909 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1912 static const int stats_types[N_DIRECTIONAL] =
1914 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
1917 static const int *stats_lookup[] =
1924 static const char **stats_names[] =
1936 double direct_v[N_DIRECTIONAL];
1937 double direct_ase[N_DIRECTIONAL];
1938 double direct_t[N_DIRECTIONAL];
1942 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
1945 tab_offset (direct, pt->n_vars - 2, -1);
1947 for (i = 0; i < N_DIRECTIONAL; i++)
1949 if (direct_v[i] == SYSMIS)
1955 for (j = 0; j < 3; j++)
1956 if (last[j] != stats_lookup[j][i])
1959 tab_hline (direct, TAL_1, j, 6, 0);
1964 int k = last[j] = stats_lookup[j][i];
1969 string = var_get_name (pt->vars[0]);
1971 string = var_get_name (pt->vars[1]);
1973 tab_text_format (direct, j, 0, TAB_LEFT,
1974 gettext (stats_names[j][k]), string);
1979 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
1980 if (direct_ase[i] != SYSMIS)
1981 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
1982 if (direct_t[i] != SYSMIS)
1983 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
1984 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
1985 tab_next_row (direct);
1988 tab_offset (direct, 0, -1);
1991 /* Statistical calculations. */
1993 /* Returns the value of the gamma (factorial) function for an integer
1996 gamma_int (double pt)
2001 for (i = 2; i < pt; i++)
2006 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2008 static inline double
2009 Pr (int a, int b, int c, int d)
2011 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2012 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2013 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2014 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2015 / gamma_int (a + b + c + d + 1.));
2018 /* Swap the contents of A and B. */
2020 swap (int *a, int *b)
2027 /* Calculate significance for Fisher's exact test as specified in
2028 _SPSS Statistical Algorithms_, Appendix 5. */
2030 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2034 if (MIN (c, d) < MIN (a, b))
2035 swap (&a, &c), swap (&b, &d);
2036 if (MIN (b, d) < MIN (a, c))
2037 swap (&a, &b), swap (&c, &d);
2041 swap (&a, &b), swap (&c, &d);
2043 swap (&a, &c), swap (&b, &d);
2047 for (pt = 0; pt <= a; pt++)
2048 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2050 *fisher2 = *fisher1;
2051 for (pt = 1; pt <= b; pt++)
2052 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2055 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2056 columns with values COLS and N_ROWS rows with values ROWS. Values
2057 in the matrix sum to pt->total. */
2059 calc_chisq (struct pivot_table *pt,
2060 double chisq[N_CHISQ], int df[N_CHISQ],
2061 double *fisher1, double *fisher2)
2065 chisq[0] = chisq[1] = 0.;
2066 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2067 *fisher1 = *fisher2 = SYSMIS;
2069 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2071 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2073 chisq[0] = chisq[1] = SYSMIS;
2077 for (r = 0; r < pt->n_rows; r++)
2078 for (c = 0; c < pt->n_cols; c++)
2080 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2081 const double freq = pt->mat[pt->n_cols * r + c];
2082 const double residual = freq - expected;
2084 chisq[0] += residual * residual / expected;
2086 chisq[1] += freq * log (expected / freq);
2097 /* Calculate Yates and Fisher exact test. */
2098 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2100 double f11, f12, f21, f22;
2106 for (i = j = 0; i < pt->n_cols; i++)
2107 if (pt->col_tot[i] != 0.)
2116 f11 = pt->mat[nz_cols[0]];
2117 f12 = pt->mat[nz_cols[1]];
2118 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2119 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2124 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2127 chisq[3] = (pt->total * pow2 (pt_)
2128 / (f11 + f12) / (f21 + f22)
2129 / (f11 + f21) / (f12 + f22));
2137 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2138 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2141 /* Calculate Mantel-Haenszel. */
2142 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2144 double r, ase_0, ase_1;
2145 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2147 chisq[4] = (pt->total - 1.) * r * r;
2152 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2153 ASE_1, and ase_0 into ASE_0. The row and column values must be
2154 passed in PT and Y. */
2156 calc_r (struct pivot_table *pt,
2157 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2159 double SX, SY, S, T;
2161 double sum_XYf, sum_X2Y2f;
2162 double sum_Xr, sum_X2r;
2163 double sum_Yc, sum_Y2c;
2166 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2167 for (j = 0; j < pt->n_cols; j++)
2169 double fij = pt->mat[j + i * pt->n_cols];
2170 double product = PT[i] * Y[j];
2171 double temp = fij * product;
2173 sum_X2Y2f += temp * product;
2176 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2178 sum_Xr += PT[i] * pt->row_tot[i];
2179 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2181 Xbar = sum_Xr / pt->total;
2183 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2185 sum_Yc += Y[i] * pt->col_tot[i];
2186 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2188 Ybar = sum_Yc / pt->total;
2190 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2191 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2192 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2195 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2200 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2201 for (j = 0; j < pt->n_cols; j++)
2203 double Xresid, Yresid;
2206 Xresid = PT[i] - Xbar;
2207 Yresid = Y[j] - Ybar;
2208 temp = (T * Xresid * Yresid
2210 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2211 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2216 *ase_1 = sqrt (s) / (T * T);
2220 /* Calculate symmetric statistics and their asymptotic standard
2221 errors. Returns 0 if none could be calculated. */
2223 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2224 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2225 double t[N_SYMMETRIC],
2226 double somers_d_v[3], double somers_d_ase[3],
2227 double somers_d_t[3])
2231 q = MIN (pt->ns_rows, pt->ns_cols);
2235 for (i = 0; i < N_SYMMETRIC; i++)
2236 v[i] = ase[i] = t[i] = SYSMIS;
2238 /* Phi, Cramer's V, contingency coefficient. */
2239 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2241 double Xp = 0.; /* Pearson chi-square. */
2244 for (r = 0; r < pt->n_rows; r++)
2245 for (c = 0; c < pt->n_cols; c++)
2247 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2248 const double freq = pt->mat[pt->n_cols * r + c];
2249 const double residual = freq - expected;
2251 Xp += residual * residual / expected;
2254 if (proc->statistics & (1u << CRS_ST_PHI))
2256 v[0] = sqrt (Xp / pt->total);
2257 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2259 if (proc->statistics & (1u << CRS_ST_CC))
2260 v[2] = sqrt (Xp / (Xp + pt->total));
2263 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2264 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2269 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2273 Dr = Dc = pow2 (pt->total);
2274 for (r = 0; r < pt->n_rows; r++)
2275 Dr -= pow2 (pt->row_tot[r]);
2276 for (c = 0; c < pt->n_cols; c++)
2277 Dc -= pow2 (pt->col_tot[c]);
2279 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2280 for (c = 0; c < pt->n_cols; c++)
2284 for (r = 0; r < pt->n_rows; r++)
2285 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2294 for (i = 0; i < pt->n_rows; i++)
2298 for (j = 1; j < pt->n_cols; j++)
2299 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2302 for (j = 1; j < pt->n_cols; j++)
2303 Dij += cum[j + (i - 1) * pt->n_cols];
2307 double fij = pt->mat[j + i * pt->n_cols];
2311 if (++j == pt->n_cols)
2313 assert (j < pt->n_cols);
2315 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2316 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2320 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2321 Dij -= cum[j + (i - 1) * pt->n_cols];
2327 if (proc->statistics & (1u << CRS_ST_BTAU))
2328 v[3] = (P - Q) / sqrt (Dr * Dc);
2329 if (proc->statistics & (1u << CRS_ST_CTAU))
2330 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2331 if (proc->statistics & (1u << CRS_ST_GAMMA))
2332 v[5] = (P - Q) / (P + Q);
2334 /* ASE for tau-b, tau-c, gamma. Calculations could be
2335 eliminated here, at expense of memory. */
2340 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2341 for (i = 0; i < pt->n_rows; i++)
2345 for (j = 1; j < pt->n_cols; j++)
2346 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2349 for (j = 1; j < pt->n_cols; j++)
2350 Dij += cum[j + (i - 1) * pt->n_cols];
2354 double fij = pt->mat[j + i * pt->n_cols];
2356 if (proc->statistics & (1u << CRS_ST_BTAU))
2358 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2359 + v[3] * (pt->row_tot[i] * Dc
2360 + pt->col_tot[j] * Dr));
2361 btau_cum += fij * temp * temp;
2365 const double temp = Cij - Dij;
2366 ctau_cum += fij * temp * temp;
2369 if (proc->statistics & (1u << CRS_ST_GAMMA))
2371 const double temp = Q * Cij - P * Dij;
2372 gamma_cum += fij * temp * temp;
2375 if (proc->statistics & (1u << CRS_ST_D))
2377 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2378 - (P - Q) * (pt->total - pt->row_tot[i]));
2379 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2380 - (Q - P) * (pt->total - pt->col_tot[j]));
2383 if (++j == pt->n_cols)
2385 assert (j < pt->n_cols);
2387 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2388 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2392 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2393 Dij -= cum[j + (i - 1) * pt->n_cols];
2399 btau_var = ((btau_cum
2400 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2402 if (proc->statistics & (1u << CRS_ST_BTAU))
2404 ase[3] = sqrt (btau_var);
2405 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2408 if (proc->statistics & (1u << CRS_ST_CTAU))
2410 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2411 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2412 t[4] = v[4] / ase[4];
2414 if (proc->statistics & (1u << CRS_ST_GAMMA))
2416 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2417 t[5] = v[5] / (2. / (P + Q)
2418 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2420 if (proc->statistics & (1u << CRS_ST_D))
2422 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2423 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2424 somers_d_t[0] = (somers_d_v[0]
2426 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2427 somers_d_v[1] = (P - Q) / Dc;
2428 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2429 somers_d_t[1] = (somers_d_v[1]
2431 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2432 somers_d_v[2] = (P - Q) / Dr;
2433 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2434 somers_d_t[2] = (somers_d_v[2]
2436 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2442 /* Spearman correlation, Pearson's r. */
2443 if (proc->statistics & (1u << CRS_ST_CORR))
2445 double *R = xmalloc (sizeof *R * pt->n_rows);
2446 double *C = xmalloc (sizeof *C * pt->n_cols);
2449 double y, t, c = 0., s = 0.;
2454 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2455 y = pt->row_tot[i] - c;
2459 if (++i == pt->n_rows)
2461 assert (i < pt->n_rows);
2466 double y, t, c = 0., s = 0.;
2471 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2472 y = pt->col_tot[j] - c;
2476 if (++j == pt->n_cols)
2478 assert (j < pt->n_cols);
2482 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2488 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2492 /* Cohen's kappa. */
2493 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2495 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2498 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2499 i < pt->ns_rows; i++, j++)
2503 while (pt->col_tot[j] == 0.)
2506 prod = pt->row_tot[i] * pt->col_tot[j];
2507 sum = pt->row_tot[i] + pt->col_tot[j];
2509 sum_fii += pt->mat[j + i * pt->n_cols];
2511 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2512 sum_riciri_ci += prod * sum;
2514 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2515 for (j = 0; j < pt->ns_cols; j++)
2517 double sum = pt->row_tot[i] + pt->col_tot[j];
2518 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2521 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2523 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2524 + sum_rici * sum_rici
2525 - pt->total * sum_riciri_ci)
2526 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2528 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2529 / pow2 (pow2 (pt->total) - sum_rici))
2530 + ((2. * (pt->total - sum_fii)
2531 * (2. * sum_fii * sum_rici
2532 - pt->total * sum_fiiri_ci))
2533 / cube (pow2 (pt->total) - sum_rici))
2534 + (pow2 (pt->total - sum_fii)
2535 * (pt->total * sum_fijri_ci2 - 4.
2536 * sum_rici * sum_rici)
2537 / pow4 (pow2 (pt->total) - sum_rici))));
2539 t[8] = v[8] / ase[8];
2546 /* Calculate risk estimate. */
2548 calc_risk (struct pivot_table *pt,
2549 double *value, double *upper, double *lower, union value *c)
2551 double f11, f12, f21, f22;
2557 for (i = 0; i < 3; i++)
2558 value[i] = upper[i] = lower[i] = SYSMIS;
2561 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2568 for (i = j = 0; i < pt->n_cols; i++)
2569 if (pt->col_tot[i] != 0.)
2578 f11 = pt->mat[nz_cols[0]];
2579 f12 = pt->mat[nz_cols[1]];
2580 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2581 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2583 c[0] = pt->cols[nz_cols[0]];
2584 c[1] = pt->cols[nz_cols[1]];
2587 value[0] = (f11 * f22) / (f12 * f21);
2588 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2589 lower[0] = value[0] * exp (-1.960 * v);
2590 upper[0] = value[0] * exp (1.960 * v);
2592 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2593 v = sqrt ((f12 / (f11 * (f11 + f12)))
2594 + (f22 / (f21 * (f21 + f22))));
2595 lower[1] = value[1] * exp (-1.960 * v);
2596 upper[1] = value[1] * exp (1.960 * v);
2598 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2599 v = sqrt ((f11 / (f12 * (f11 + f12)))
2600 + (f21 / (f22 * (f21 + f22))));
2601 lower[2] = value[2] * exp (-1.960 * v);
2602 upper[2] = value[2] * exp (1.960 * v);
2607 /* Calculate directional measures. */
2609 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2610 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2611 double t[N_DIRECTIONAL])
2616 for (i = 0; i < N_DIRECTIONAL; i++)
2617 v[i] = ase[i] = t[i] = SYSMIS;
2621 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2623 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2624 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2625 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2626 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2627 double sum_fim, sum_fmj;
2629 int rm_index, cm_index;
2632 /* Find maximum for each row and their sum. */
2633 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2635 double max = pt->mat[i * pt->n_cols];
2638 for (j = 1; j < pt->n_cols; j++)
2639 if (pt->mat[j + i * pt->n_cols] > max)
2641 max = pt->mat[j + i * pt->n_cols];
2645 sum_fim += fim[i] = max;
2646 fim_index[i] = index;
2649 /* Find maximum for each column. */
2650 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2652 double max = pt->mat[j];
2655 for (i = 1; i < pt->n_rows; i++)
2656 if (pt->mat[j + i * pt->n_cols] > max)
2658 max = pt->mat[j + i * pt->n_cols];
2662 sum_fmj += fmj[j] = max;
2663 fmj_index[j] = index;
2666 /* Find maximum row total. */
2667 rm = pt->row_tot[0];
2669 for (i = 1; i < pt->n_rows; i++)
2670 if (pt->row_tot[i] > rm)
2672 rm = pt->row_tot[i];
2676 /* Find maximum column total. */
2677 cm = pt->col_tot[0];
2679 for (j = 1; j < pt->n_cols; j++)
2680 if (pt->col_tot[j] > cm)
2682 cm = pt->col_tot[j];
2686 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2687 v[1] = (sum_fmj - rm) / (pt->total - rm);
2688 v[2] = (sum_fim - cm) / (pt->total - cm);
2690 /* ASE1 for Y given PT. */
2694 for (accum = 0., i = 0; i < pt->n_rows; i++)
2695 for (j = 0; j < pt->n_cols; j++)
2697 const int deltaj = j == cm_index;
2698 accum += (pt->mat[j + i * pt->n_cols]
2699 * pow2 ((j == fim_index[i])
2704 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2707 /* ASE0 for Y given PT. */
2711 for (accum = 0., i = 0; i < pt->n_rows; i++)
2712 if (cm_index != fim_index[i])
2713 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2714 + pt->mat[i * pt->n_cols + cm_index]);
2715 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2718 /* ASE1 for PT given Y. */
2722 for (accum = 0., i = 0; i < pt->n_rows; i++)
2723 for (j = 0; j < pt->n_cols; j++)
2725 const int deltaj = i == rm_index;
2726 accum += (pt->mat[j + i * pt->n_cols]
2727 * pow2 ((i == fmj_index[j])
2732 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2735 /* ASE0 for PT given Y. */
2739 for (accum = 0., j = 0; j < pt->n_cols; j++)
2740 if (rm_index != fmj_index[j])
2741 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2742 + pt->mat[j + pt->n_cols * rm_index]);
2743 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2746 /* Symmetric ASE0 and ASE1. */
2751 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2752 for (j = 0; j < pt->n_cols; j++)
2754 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2755 int temp1 = (i == rm_index) + (j == cm_index);
2756 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2757 accum1 += (pt->mat[j + i * pt->n_cols]
2758 * pow2 (temp0 + (v[0] - 1.) * temp1));
2760 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2761 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2762 / (2. * pt->total - rm - cm));
2771 double sum_fij2_ri, sum_fij2_ci;
2772 double sum_ri2, sum_cj2;
2774 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2775 for (j = 0; j < pt->n_cols; j++)
2777 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2778 sum_fij2_ri += temp / pt->row_tot[i];
2779 sum_fij2_ci += temp / pt->col_tot[j];
2782 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2783 sum_ri2 += pow2 (pt->row_tot[i]);
2785 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2786 sum_cj2 += pow2 (pt->col_tot[j]);
2788 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2789 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2793 if (proc->statistics & (1u << CRS_ST_UC))
2795 double UX, UY, UXY, P;
2796 double ase1_yx, ase1_xy, ase1_sym;
2799 for (UX = 0., i = 0; i < pt->n_rows; i++)
2800 if (pt->row_tot[i] > 0.)
2801 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2803 for (UY = 0., j = 0; j < pt->n_cols; j++)
2804 if (pt->col_tot[j] > 0.)
2805 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2807 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2808 for (j = 0; j < pt->n_cols; j++)
2810 double entry = pt->mat[j + i * pt->n_cols];
2815 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2816 UXY -= entry / pt->total * log (entry / pt->total);
2819 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2820 for (j = 0; j < pt->n_cols; j++)
2822 double entry = pt->mat[j + i * pt->n_cols];
2827 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2828 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2829 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2830 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2831 ase1_sym += entry * pow2 ((UXY
2832 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2833 - (UX + UY) * log (entry / pt->total));
2836 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2837 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2838 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2839 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2841 v[6] = (UX + UY - UXY) / UX;
2842 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2843 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2845 v[7] = (UX + UY - UXY) / UY;
2846 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2847 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2851 if (proc->statistics & (1u << CRS_ST_D))
2853 double v_dummy[N_SYMMETRIC];
2854 double ase_dummy[N_SYMMETRIC];
2855 double t_dummy[N_SYMMETRIC];
2856 double somers_d_v[3];
2857 double somers_d_ase[3];
2858 double somers_d_t[3];
2860 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2861 somers_d_v, somers_d_ase, somers_d_t))
2864 for (i = 0; i < 3; i++)
2866 v[8 + i] = somers_d_v[i];
2867 ase[8 + i] = somers_d_ase[i];
2868 t[8 + i] = somers_d_t[i];
2874 if (proc->statistics & (1u << CRS_ST_ETA))
2877 double sum_Xr, sum_X2r;
2881 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2883 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2884 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2886 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2888 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2892 for (cum = 0., i = 0; i < pt->n_rows; i++)
2894 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2895 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2898 SXW -= cum * cum / pt->col_tot[j];
2900 v[11] = sqrt (1. - SXW / SX);
2904 double sum_Yc, sum_Y2c;
2908 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2910 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2911 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2913 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
2915 for (SYW = 0., i = 0; i < pt->n_rows; i++)
2919 for (cum = 0., j = 0; j < pt->n_cols; j++)
2921 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
2922 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
2925 SYW -= cum * cum / pt->row_tot[i];
2927 v[12] = sqrt (1. - SYW / SY);