1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012, 2013, 2014 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 - How to calculate significance of some symmetric and directional measures?
20 - How to calculate ASE for symmetric Somers ' d?
21 - How to calculate ASE for Goodman and Kruskal's tau?
22 - How to calculate approx. T of symmetric uncertainty coefficient?
30 #include <gsl/gsl_cdf.h>
34 #include "data/case.h"
35 #include "data/casegrouper.h"
36 #include "data/casereader.h"
37 #include "data/data-out.h"
38 #include "data/dataset.h"
39 #include "data/dictionary.h"
40 #include "data/format.h"
41 #include "data/value-labels.h"
42 #include "data/variable.h"
43 #include "language/command.h"
44 #include "language/stats/freq.h"
45 #include "language/dictionary/split-file.h"
46 #include "language/lexer/lexer.h"
47 #include "language/lexer/variable-parser.h"
48 #include "libpspp/array.h"
49 #include "libpspp/assertion.h"
50 #include "libpspp/compiler.h"
51 #include "libpspp/hash-functions.h"
52 #include "libpspp/hmap.h"
53 #include "libpspp/hmapx.h"
54 #include "libpspp/message.h"
55 #include "libpspp/misc.h"
56 #include "libpspp/pool.h"
57 #include "libpspp/str.h"
58 #include "output/tab.h"
59 #include "output/chart-item.h"
60 #include "output/charts/barchart.h"
62 #include "gl/minmax.h"
63 #include "gl/xalloc.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=val:!avalue/dvalue,
80 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
102 /* Indexes into the 'vars' member of struct pivot_table and
103 struct crosstab member. */
106 ROW_VAR = 0, /* Row variable. */
107 COL_VAR = 1 /* Column variable. */
108 /* Higher indexes cause multiple tables to be output. */
111 /* A crosstabulation of 2 or more variables. */
114 struct crosstabs_proc *proc;
115 struct fmt_spec weight_format; /* Format for weight variable. */
116 double missing; /* Weight of missing cases. */
118 /* Variables (2 or more). */
120 const struct variable **vars;
122 /* Constants (0 or more). */
124 const struct variable **const_vars;
125 union value *const_values;
129 struct freq **entries;
132 /* Column values, number of columns. */
136 /* Row values, number of rows. */
140 /* Number of statistically interesting columns/rows
141 (columns/rows with data in them). */
142 int ns_cols, ns_rows;
144 /* Matrix contents. */
145 double *mat; /* Matrix proper. */
146 double *row_tot; /* Row totals. */
147 double *col_tot; /* Column totals. */
148 double total; /* Grand total. */
151 /* Integer mode variable info. */
154 struct hmap_node hmap_node; /* In struct crosstabs_proc var_ranges map. */
155 const struct variable *var; /* The variable. */
156 int min; /* Minimum value. */
157 int max; /* Maximum value + 1. */
158 int count; /* max - min. */
161 struct crosstabs_proc
163 const struct dictionary *dict;
164 enum { INTEGER, GENERAL } mode;
165 enum mv_class exclude;
169 struct fmt_spec weight_format;
171 /* Variables specifies on VARIABLES. */
172 const struct variable **variables;
174 struct hmap var_ranges;
177 struct pivot_table *pivots;
181 int n_cells; /* Number of cells requested. */
182 unsigned int cells; /* Bit k is 1 if cell k is requested. */
183 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
186 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
188 bool descending; /* True if descending sort order is requested. */
191 const struct var_range *get_var_range (const struct crosstabs_proc *,
192 const struct variable *);
194 static bool should_tabulate_case (const struct pivot_table *,
195 const struct ccase *, enum mv_class exclude);
196 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
198 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
200 static void postcalc (struct crosstabs_proc *);
201 static void submit (struct pivot_table *, struct tab_table *);
203 /* Parses and executes the CROSSTABS procedure. */
205 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
207 const struct variable *wv = dict_get_weight (dataset_dict (ds));
208 struct var_range *range, *next_range;
209 struct crosstabs_proc proc;
210 struct casegrouper *grouper;
211 struct casereader *input, *group;
212 struct cmd_crosstabs cmd;
213 struct pivot_table *pt;
218 proc.dict = dataset_dict (ds);
219 proc.bad_warn = true;
220 proc.variables = NULL;
221 proc.n_variables = 0;
222 hmap_init (&proc.var_ranges);
225 proc.descending = false;
226 proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
228 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
230 result = CMD_FAILURE;
234 proc.mode = proc.n_variables ? INTEGER : GENERAL;
235 proc.barchart = cmd.sbc_barchart > 0;
237 proc.descending = cmd.val == CRS_DVALUE;
241 proc.cells = 1u << CRS_CL_COUNT;
242 else if (cmd.a_cells[CRS_CL_ALL])
243 proc.cells = UINT_MAX;
247 for (i = 0; i < CRS_CL_count; i++)
249 proc.cells |= 1u << i;
251 proc.cells = ((1u << CRS_CL_COUNT)
253 | (1u << CRS_CL_COLUMN)
254 | (1u << CRS_CL_TOTAL));
256 proc.cells &= ((1u << CRS_CL_count) - 1);
257 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
259 for (i = 0; i < CRS_CL_count; i++)
260 if (proc.cells & (1u << i))
261 proc.a_cells[proc.n_cells++] = i;
264 if (cmd.a_statistics[CRS_ST_ALL])
265 proc.statistics = UINT_MAX;
266 else if (cmd.sbc_statistics)
271 for (i = 0; i < CRS_ST_count; i++)
272 if (cmd.a_statistics[i])
273 proc.statistics |= 1u << i;
274 if (proc.statistics == 0)
275 proc.statistics |= 1u << CRS_ST_CHISQ;
281 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
282 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
284 if (proc.mode == GENERAL && proc.exclude == MV_NEVER)
286 msg (SE, _("Missing mode %s not allowed in general mode. "
287 "Assuming %s."), "REPORT", "MISSING=TABLE");
288 proc.exclude = MV_ANY;
292 proc.pivot = cmd.pivot == CRS_PIVOT;
294 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
296 grouper = casegrouper_create_splits (input, dataset_dict (ds));
297 while (casegrouper_get_next_group (grouper, &group))
301 /* Output SPLIT FILE variables. */
302 c = casereader_peek (group, 0);
305 output_split_file_values (ds, c);
309 /* Initialize hash tables. */
310 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
311 hmap_init (&pt->data);
314 for (; (c = casereader_read (group)) != NULL; case_unref (c))
315 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
317 double weight = dict_get_case_weight (dataset_dict (ds), c,
319 if (should_tabulate_case (pt, c, proc.exclude))
321 if (proc.mode == GENERAL)
322 tabulate_general_case (pt, c, weight);
324 tabulate_integer_case (pt, c, weight);
327 pt->missing += weight;
329 casereader_destroy (group);
334 ok = casegrouper_destroy (grouper);
335 ok = proc_commit (ds) && ok;
337 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
340 free (proc.variables);
341 HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
344 hmap_delete (&proc.var_ranges, &range->hmap_node);
347 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
350 free (pt->const_vars);
351 /* We must not call value_destroy on const_values because
352 it is a wild pointer; it never pointed to anything owned
355 The rest of the data was allocated and destroyed at a
356 lower level already. */
363 /* Parses the TABLES subcommand. */
365 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
366 struct cmd_crosstabs *cmd UNUSED, void *proc_)
368 struct crosstabs_proc *proc = proc_;
369 struct const_var_set *var_set;
371 const struct variable ***by = NULL;
373 size_t *by_nvar = NULL;
378 /* Ensure that this is a TABLES subcommand. */
379 if (!lex_match_id (lexer, "TABLES")
380 && (lex_token (lexer) != T_ID ||
381 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
382 && lex_token (lexer) != T_ALL)
384 lex_match (lexer, T_EQUALS);
386 if (proc->variables != NULL)
387 var_set = const_var_set_create_from_array (proc->variables,
390 var_set = const_var_set_create_from_dict (dataset_dict (ds));
391 assert (var_set != NULL);
395 by = xnrealloc (by, n_by + 1, sizeof *by);
396 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
397 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
398 PV_NO_DUPLICATE | PV_NO_SCRATCH))
400 if (xalloc_oversized (nx, by_nvar[n_by]))
402 msg (SE, _("Too many cross-tabulation variables or dimensions."));
408 if (!lex_match (lexer, T_BY))
412 lex_force_match (lexer, T_BY);
420 by_iter = xcalloc (n_by, sizeof *by_iter);
421 proc->pivots = xnrealloc (proc->pivots,
422 proc->n_pivots + nx, sizeof *proc->pivots);
423 for (i = 0; i < nx; i++)
425 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
429 pt->weight_format = proc->weight_format;
432 pt->vars = xmalloc (n_by * sizeof *pt->vars);
434 pt->const_vars = NULL;
435 pt->const_values = NULL;
437 for (j = 0; j < n_by; j++)
438 pt->vars[j] = by[j][by_iter[j]];
440 for (j = n_by - 1; j >= 0; j--)
442 if (++by_iter[j] < by_nvar[j])
451 /* All return paths lead here. */
452 for (i = 0; i < n_by; i++)
457 const_var_set_destroy (var_set);
462 /* Parses the VARIABLES subcommand. */
464 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
465 struct cmd_crosstabs *cmd UNUSED, void *proc_)
467 struct crosstabs_proc *proc = proc_;
470 msg (SE, _("%s must be specified before %s."), "VARIABLES", "TABLES");
474 lex_match (lexer, T_EQUALS);
478 size_t orig_nv = proc->n_variables;
483 if (!parse_variables_const (lexer, dataset_dict (ds),
484 &proc->variables, &proc->n_variables,
485 (PV_APPEND | PV_NUMERIC
486 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
489 if (!lex_force_match (lexer, T_LPAREN))
492 if (!lex_force_int (lexer))
494 min = lex_integer (lexer);
497 lex_match (lexer, T_COMMA);
499 if (!lex_force_int (lexer))
501 max = lex_integer (lexer);
504 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
510 if (!lex_force_match (lexer, T_RPAREN))
513 for (i = orig_nv; i < proc->n_variables; i++)
515 const struct variable *var = proc->variables[i];
516 struct var_range *vr = xmalloc (sizeof *vr);
521 vr->count = max - min + 1;
522 hmap_insert (&proc->var_ranges, &vr->hmap_node,
523 hash_pointer (var, 0));
526 if (lex_token (lexer) == T_SLASH)
533 free (proc->variables);
534 proc->variables = NULL;
535 proc->n_variables = 0;
539 /* Data file processing. */
541 const struct var_range *
542 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
544 if (!hmap_is_empty (&proc->var_ranges))
546 const struct var_range *range;
548 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
549 hash_pointer (var, 0), &proc->var_ranges)
550 if (range->var == var)
558 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
559 enum mv_class exclude)
562 for (j = 0; j < pt->n_vars; j++)
564 const struct variable *var = pt->vars[j];
565 const struct var_range *range = get_var_range (pt->proc, var);
567 if (var_is_value_missing (var, case_data (c, var), exclude))
572 double num = case_num (c, var);
573 if (num < range->min || num > range->max)
581 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
589 for (j = 0; j < pt->n_vars; j++)
591 /* Throw away fractional parts of values. */
592 hash = hash_int (case_num (c, pt->vars[j]), hash);
595 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &pt->data)
597 for (j = 0; j < pt->n_vars; j++)
598 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
601 /* Found an existing entry. */
608 /* No existing entry. Create a new one. */
609 te = xmalloc (table_entry_size (pt->n_vars));
611 for (j = 0; j < pt->n_vars; j++)
612 te->values[j].f = (int) case_num (c, pt->vars[j]);
613 hmap_insert (&pt->data, &te->node, hash);
617 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
625 for (j = 0; j < pt->n_vars; j++)
627 const struct variable *var = pt->vars[j];
628 hash = value_hash (case_data (c, var), var_get_width (var), hash);
631 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &pt->data)
633 for (j = 0; j < pt->n_vars; j++)
635 const struct variable *var = pt->vars[j];
636 if (!value_equal (case_data (c, var), &te->values[j],
637 var_get_width (var)))
641 /* Found an existing entry. */
648 /* No existing entry. Create a new one. */
649 te = xmalloc (table_entry_size (pt->n_vars));
651 for (j = 0; j < pt->n_vars; j++)
653 const struct variable *var = pt->vars[j];
654 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
656 hmap_insert (&pt->data, &te->node, hash);
659 /* Post-data reading calculations. */
661 static int compare_table_entry_vars_3way (const struct freq *a,
662 const struct freq *b,
663 const struct pivot_table *pt,
665 static int compare_table_entry_3way (const void *ap_, const void *bp_,
667 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
670 static void enum_var_values (const struct pivot_table *, int var_idx,
671 union value **valuesp, int *n_values, bool descending);
672 static void output_pivot_table (struct crosstabs_proc *,
673 struct pivot_table *);
674 static void make_pivot_table_subset (struct pivot_table *pt,
675 size_t row0, size_t row1,
676 struct pivot_table *subset);
677 static void make_summary_table (struct crosstabs_proc *);
678 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
681 postcalc (struct crosstabs_proc *proc)
683 struct pivot_table *pt;
685 /* Convert hash tables into sorted arrays of entries. */
686 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
691 pt->n_entries = hmap_count (&pt->data);
692 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
694 HMAP_FOR_EACH (e, struct freq, node, &pt->data)
695 pt->entries[i++] = e;
696 hmap_destroy (&pt->data);
698 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
699 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
704 make_summary_table (proc);
706 /* Output each pivot table. */
707 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
709 if (proc->pivot || pt->n_vars == 2)
710 output_pivot_table (proc, pt);
713 size_t row0 = 0, row1 = 0;
714 while (find_crosstab (pt, &row0, &row1))
716 struct pivot_table subset;
717 make_pivot_table_subset (pt, row0, row1, &subset);
718 output_pivot_table (proc, &subset);
723 (barchart_create (pt->vars, pt->n_vars, _("Count"), pt->entries, pt->n_entries));
726 /* Free output and prepare for next split file. */
727 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
733 /* Free the members that were allocated in this function(and the values
734 owned by the entries.
736 The other pointer members are either both allocated and destroyed at a
737 lower level (in output_pivot_table), or both allocated and destroyed
738 at a higher level (in crs_custom_tables and free_proc,
740 for (i = 0; i < pt->n_vars; i++)
742 int width = var_get_width (pt->vars[i]);
743 if (value_needs_init (width))
747 for (j = 0; j < pt->n_entries; j++)
748 value_destroy (&pt->entries[j]->values[i], width);
752 for (i = 0; i < pt->n_entries; i++)
753 free (pt->entries[i]);
759 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
760 struct pivot_table *subset)
765 assert (pt->n_consts == 0);
766 subset->missing = pt->missing;
768 subset->vars = pt->vars;
769 subset->n_consts = pt->n_vars - 2;
770 subset->const_vars = pt->vars + 2;
771 subset->const_values = &pt->entries[row0]->values[2];
773 subset->entries = &pt->entries[row0];
774 subset->n_entries = row1 - row0;
778 compare_table_entry_var_3way (const struct freq *a,
779 const struct freq *b,
780 const struct pivot_table *pt,
783 return value_compare_3way (&a->values[idx], &b->values[idx],
784 var_get_width (pt->vars[idx]));
788 compare_table_entry_vars_3way (const struct freq *a,
789 const struct freq *b,
790 const struct pivot_table *pt,
795 for (i = idx1 - 1; i >= idx0; i--)
797 int cmp = compare_table_entry_var_3way (a, b, pt, i);
804 /* Compare the struct freq at *AP to the one at *BP and
805 return a strcmp()-type result. */
807 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
809 const struct freq *const *ap = ap_;
810 const struct freq *const *bp = bp_;
811 const struct freq *a = *ap;
812 const struct freq *b = *bp;
813 const struct pivot_table *pt = pt_;
816 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
820 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
824 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
827 /* Inverted version of compare_table_entry_3way */
829 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *pt_)
831 return -compare_table_entry_3way (ap_, bp_, pt_);
835 find_first_difference (const struct pivot_table *pt, size_t row)
838 return pt->n_vars - 1;
841 const struct freq *a = pt->entries[row];
842 const struct freq *b = pt->entries[row - 1];
845 for (col = pt->n_vars - 1; col >= 0; col--)
846 if (compare_table_entry_var_3way (a, b, pt, col))
852 /* Output a table summarizing the cases processed. */
854 make_summary_table (struct crosstabs_proc *proc)
856 struct tab_table *summary;
857 struct pivot_table *pt;
861 summary = tab_create (7, 3 + proc->n_pivots);
862 tab_set_format (summary, RC_WEIGHT, &proc->weight_format);
863 tab_title (summary, _("Summary."));
864 tab_headers (summary, 1, 0, 3, 0);
865 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
866 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
867 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
868 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
869 tab_hline (summary, TAL_1, 1, 6, 1);
870 tab_hline (summary, TAL_1, 1, 6, 2);
871 tab_vline (summary, TAL_1, 3, 1, 1);
872 tab_vline (summary, TAL_1, 5, 1, 1);
873 for (i = 0; i < 3; i++)
875 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
876 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
878 tab_offset (summary, 0, 3);
880 ds_init_empty (&name);
881 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
887 tab_hline (summary, TAL_1, 0, 6, 0);
890 for (i = 0; i < pt->n_vars; i++)
893 ds_put_cstr (&name, " * ");
894 ds_put_cstr (&name, var_to_string (pt->vars[i]));
896 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
899 for (i = 0; i < pt->n_entries; i++)
900 valid += pt->entries[i]->count;
905 for (i = 0; i < 3; i++)
907 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i], NULL, RC_WEIGHT);
908 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
912 tab_next_row (summary);
916 submit (NULL, summary);
921 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
922 struct pivot_table *);
923 static struct tab_table *create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *);
924 static struct tab_table *create_sym_table (struct crosstabs_proc *proc, struct pivot_table *);
925 static struct tab_table *create_risk_table (struct crosstabs_proc *proc, struct pivot_table *);
926 static struct tab_table *create_direct_table (struct crosstabs_proc *proc, struct pivot_table *);
927 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
928 struct tab_table *, int first_difference);
929 static void display_crosstabulation (struct crosstabs_proc *,
930 struct pivot_table *,
932 static void display_chisq (struct pivot_table *, struct tab_table *,
933 bool *showed_fisher);
934 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
936 static void display_risk (struct pivot_table *, struct tab_table *);
937 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
939 static void table_value_missing (struct crosstabs_proc *proc,
940 struct tab_table *table, int c, int r,
941 unsigned char opt, const union value *v,
942 const struct variable *var);
943 static void delete_missing (struct pivot_table *);
944 static void build_matrix (struct pivot_table *);
946 /* Output pivot table PT in the context of PROC. */
948 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
950 struct tab_table *table = NULL; /* Crosstabulation table. */
951 struct tab_table *chisq = NULL; /* Chi-square table. */
952 bool showed_fisher = false;
953 struct tab_table *sym = NULL; /* Symmetric measures table. */
954 struct tab_table *risk = NULL; /* Risk estimate table. */
955 struct tab_table *direct = NULL; /* Directional measures table. */
958 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols, proc->descending);
965 ds_init_cstr (&vars, var_to_string (pt->vars[0]));
966 for (i = 1; i < pt->n_vars; i++)
967 ds_put_format (&vars, " * %s", var_to_string (pt->vars[i]));
969 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
970 form "var1 * var2 * var3 * ...". */
971 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
980 table = create_crosstab_table (proc, pt);
981 if (proc->statistics & (1u << CRS_ST_CHISQ))
982 chisq = create_chisq_table (proc, pt);
983 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
984 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
985 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
986 | (1u << CRS_ST_KAPPA)))
987 sym = create_sym_table (proc, pt);
988 if (proc->statistics & (1u << CRS_ST_RISK))
989 risk = create_risk_table (proc, pt);
990 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
991 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
992 direct = create_direct_table (proc, pt);
995 while (find_crosstab (pt, &row0, &row1))
997 struct pivot_table x;
998 int first_difference;
1000 make_pivot_table_subset (pt, row0, row1, &x);
1002 /* Find all the row variable values. */
1003 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows, proc->descending);
1005 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
1008 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
1009 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
1010 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
1012 /* Allocate table space for the matrix. */
1014 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
1015 tab_realloc (table, -1,
1016 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
1017 tab_nr (table) * pt->n_entries / x.n_entries));
1021 /* Find the first variable that differs from the last subtable. */
1022 first_difference = find_first_difference (pt, row0);
1025 display_dimensions (proc, &x, table, first_difference);
1026 display_crosstabulation (proc, &x, table);
1029 if (proc->exclude == MV_NEVER)
1030 delete_missing (&x);
1034 display_dimensions (proc, &x, chisq, first_difference);
1035 display_chisq (&x, chisq, &showed_fisher);
1039 display_dimensions (proc, &x, sym, first_difference);
1040 display_symmetric (proc, &x, sym);
1044 display_dimensions (proc, &x, risk, first_difference);
1045 display_risk (&x, risk);
1049 display_dimensions (proc, &x, direct, first_difference);
1050 display_directional (proc, &x, direct);
1053 /* Free the parts of x that are not owned by pt. In
1054 particular we must not free x.cols, which is the same as
1055 pt->cols, which is freed at the end of this function. */
1063 submit (NULL, table);
1068 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1074 submit (pt, direct);
1080 build_matrix (struct pivot_table *x)
1082 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1083 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1090 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1092 const struct freq *te = *p;
1094 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1096 for (; col < x->n_cols; col++)
1102 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1109 if (++col >= x->n_cols)
1115 while (mp < &x->mat[x->n_cols * x->n_rows])
1117 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1119 /* Column totals, row totals, ns_rows. */
1121 for (col = 0; col < x->n_cols; col++)
1122 x->col_tot[col] = 0.0;
1123 for (row = 0; row < x->n_rows; row++)
1124 x->row_tot[row] = 0.0;
1126 for (row = 0; row < x->n_rows; row++)
1128 bool row_is_empty = true;
1129 for (col = 0; col < x->n_cols; col++)
1133 row_is_empty = false;
1134 x->col_tot[col] += *mp;
1135 x->row_tot[row] += *mp;
1142 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1146 for (col = 0; col < x->n_cols; col++)
1147 for (row = 0; row < x->n_rows; row++)
1148 if (x->mat[col + row * x->n_cols] != 0.0)
1156 for (col = 0; col < x->n_cols; col++)
1157 x->total += x->col_tot[col];
1160 static struct tab_table *
1161 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1168 static const struct tuple names[] =
1170 {CRS_CL_COUNT, N_("count")},
1171 {CRS_CL_ROW, N_("row %")},
1172 {CRS_CL_COLUMN, N_("column %")},
1173 {CRS_CL_TOTAL, N_("total %")},
1174 {CRS_CL_EXPECTED, N_("expected")},
1175 {CRS_CL_RESIDUAL, N_("residual")},
1176 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1177 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1179 const int n_names = sizeof names / sizeof *names;
1180 const struct tuple *t;
1182 struct tab_table *table;
1183 struct string title;
1184 struct pivot_table x;
1188 make_pivot_table_subset (pt, 0, 0, &x);
1190 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1191 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1192 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1193 tab_set_format (table, RC_WEIGHT, &proc->weight_format);
1195 /* First header line. */
1196 tab_joint_text (table, x.n_consts + 1, 0,
1197 (x.n_consts + 1) + (x.n_cols - 1), 0,
1198 TAB_CENTER | TAT_TITLE, var_to_string (x.vars[COL_VAR]));
1200 tab_hline (table, TAL_1, x.n_consts + 1,
1201 x.n_consts + 2 + x.n_cols - 2, 1);
1203 /* Second header line. */
1204 for (i = 2; i < x.n_consts + 2; i++)
1205 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1206 x.n_consts + 2 - i - 1, 1,
1207 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1208 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1209 var_to_string (x.vars[ROW_VAR]));
1210 for (i = 0; i < x.n_cols; i++)
1211 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1212 &x.cols[i], x.vars[COL_VAR]);
1213 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1215 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1216 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1219 ds_init_empty (&title);
1220 for (i = 0; i < x.n_consts + 2; i++)
1223 ds_put_cstr (&title, " * ");
1224 ds_put_cstr (&title, var_to_string (x.vars[i]));
1226 for (i = 0; i < pt->n_consts; i++)
1228 const struct variable *var = pt->const_vars[i];
1231 ds_put_format (&title, ", %s=", var_to_string (var));
1233 /* Insert the formatted value of VAR without any leading spaces. */
1234 s = data_out (&pt->const_values[i], var_get_encoding (var),
1235 var_get_print_format (var));
1236 ds_put_cstr (&title, s + strspn (s, " "));
1240 ds_put_cstr (&title, " [");
1242 for (t = names; t < &names[n_names]; t++)
1243 if (proc->cells & (1u << t->value))
1246 ds_put_cstr (&title, ", ");
1247 ds_put_cstr (&title, gettext (t->name));
1249 ds_put_cstr (&title, "].");
1251 tab_title (table, "%s", ds_cstr (&title));
1252 ds_destroy (&title);
1254 tab_offset (table, 0, 2);
1258 static struct tab_table *
1259 create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1261 struct tab_table *chisq;
1263 chisq = tab_create (6 + (pt->n_vars - 2),
1264 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1265 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1266 tab_set_format (chisq, RC_WEIGHT, &proc->weight_format);
1268 tab_title (chisq, _("Chi-square tests."));
1270 tab_offset (chisq, pt->n_vars - 2, 0);
1271 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1272 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1273 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1274 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1275 _("Asymp. Sig. (2-tailed)"));
1276 tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1277 _("Exact Sig. (%d-tailed)"), 2);
1278 tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1279 _("Exact Sig. (%d-tailed)"), 1);
1280 tab_offset (chisq, 0, 1);
1285 /* Symmetric measures. */
1286 static struct tab_table *
1287 create_sym_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1289 struct tab_table *sym;
1291 sym = tab_create (6 + (pt->n_vars - 2),
1292 pt->n_entries / pt->n_cols * 7 + 10);
1294 tab_set_format (sym, RC_WEIGHT, &proc->weight_format);
1296 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1297 tab_title (sym, _("Symmetric measures."));
1299 tab_offset (sym, pt->n_vars - 2, 0);
1300 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1301 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1302 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1303 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1304 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1305 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1306 tab_offset (sym, 0, 1);
1311 /* Risk estimate. */
1312 static struct tab_table *
1313 create_risk_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1315 struct tab_table *risk;
1317 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1318 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1319 tab_title (risk, _("Risk estimate."));
1320 tab_set_format (risk, RC_WEIGHT, &proc->weight_format);
1322 tab_offset (risk, pt->n_vars - 2, 0);
1323 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1324 _("95%% Confidence Interval"));
1325 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1326 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1327 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1328 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1329 tab_hline (risk, TAL_1, 2, 3, 1);
1330 tab_vline (risk, TAL_1, 2, 0, 1);
1331 tab_offset (risk, 0, 2);
1336 /* Directional measures. */
1337 static struct tab_table *
1338 create_direct_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1340 struct tab_table *direct;
1342 direct = tab_create (7 + (pt->n_vars - 2),
1343 pt->n_entries / pt->n_cols * 7 + 10);
1344 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1345 tab_title (direct, _("Directional measures."));
1346 tab_set_format (direct, RC_WEIGHT, &proc->weight_format);
1348 tab_offset (direct, pt->n_vars - 2, 0);
1349 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1350 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1351 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1352 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1353 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1354 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1355 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1356 tab_offset (direct, 0, 1);
1362 /* Delete missing rows and columns for statistical analysis when
1365 delete_missing (struct pivot_table *pt)
1369 for (r = 0; r < pt->n_rows; r++)
1370 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1372 for (c = 0; c < pt->n_cols; c++)
1373 pt->mat[c + r * pt->n_cols] = 0.;
1378 for (c = 0; c < pt->n_cols; c++)
1379 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1381 for (r = 0; r < pt->n_rows; r++)
1382 pt->mat[c + r * pt->n_cols] = 0.;
1387 /* Prepare table T for submission, and submit it. */
1389 submit (struct pivot_table *pt, struct tab_table *t)
1396 tab_resize (t, -1, 0);
1397 if (tab_nr (t) == tab_t (t))
1399 table_unref (&t->table);
1402 tab_offset (t, 0, 0);
1404 for (i = 2; i < pt->n_vars; i++)
1405 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1406 var_to_string (pt->vars[i]));
1407 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1408 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1410 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1412 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1418 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1420 size_t row0 = *row1p;
1423 if (row0 >= pt->n_entries)
1426 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1428 struct freq *a = pt->entries[row0];
1429 struct freq *b = pt->entries[row1];
1430 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1438 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1439 result. WIDTH_ points to an int which is either 0 for a
1440 numeric value or a string width for a string value. */
1442 compare_value_3way (const void *a_, const void *b_, const void *width_)
1444 const union value *a = a_;
1445 const union value *b = b_;
1446 const int *width = width_;
1448 return value_compare_3way (a, b, *width);
1451 /* Inverted version of the above */
1453 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1455 return -compare_value_3way (a_, b_, width_);
1459 /* Given an array of ENTRY_CNT table_entry structures starting at
1460 ENTRIES, creates a sorted list of the values that the variable
1461 with index VAR_IDX takes on. The values are returned as a
1462 malloc()'d array stored in *VALUES, with the number of values
1463 stored in *VALUE_CNT.
1465 The caller must eventually free *VALUES, but each pointer in *VALUES points
1466 to existing data not owned by *VALUES itself. */
1468 enum_var_values (const struct pivot_table *pt, int var_idx,
1469 union value **valuesp, int *n_values, bool descending)
1471 const struct variable *var = pt->vars[var_idx];
1472 const struct var_range *range = get_var_range (pt->proc, var);
1473 union value *values;
1478 values = *valuesp = xnmalloc (range->count, sizeof *values);
1479 *n_values = range->count;
1480 for (i = 0; i < range->count; i++)
1481 values[i].f = range->min + i;
1485 int width = var_get_width (var);
1486 struct hmapx_node *node;
1487 const union value *iter;
1491 for (i = 0; i < pt->n_entries; i++)
1493 const struct freq *te = pt->entries[i];
1494 const union value *value = &te->values[var_idx];
1495 size_t hash = value_hash (value, width, 0);
1497 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1498 if (value_equal (iter, value, width))
1501 hmapx_insert (&set, (union value *) value, hash);
1506 *n_values = hmapx_count (&set);
1507 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1509 HMAPX_FOR_EACH (iter, node, &set)
1510 values[i++] = *iter;
1511 hmapx_destroy (&set);
1513 sort (values, *n_values, sizeof *values,
1514 descending ? compare_value_3way_inv : compare_value_3way,
1519 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1520 from V, displayed with print format spec from variable VAR. When
1521 in REPORT missing-value mode, missing values have an M appended. */
1523 table_value_missing (struct crosstabs_proc *proc,
1524 struct tab_table *table, int c, int r, unsigned char opt,
1525 const union value *v, const struct variable *var)
1527 const char *label = var_lookup_value_label (var, v);
1529 tab_text (table, c, r, TAB_LEFT, label);
1532 const struct fmt_spec *print = var_get_print_format (var);
1533 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1535 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1536 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1540 tab_value (table, c, r, opt, v, var, print);
1544 /* Draws a line across TABLE at the current row to indicate the most
1545 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1546 that changed, and puts the values that changed into the table. TB
1547 and PT must be the corresponding table_entry and crosstab,
1550 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1551 struct tab_table *table, int first_difference)
1553 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1555 for (; first_difference >= 2; first_difference--)
1556 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1557 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1558 pt->vars[first_difference]);
1561 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1562 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1563 additionally suffixed with a letter `M'. */
1565 format_cell_entry (struct tab_table *table, int c, int r, double value,
1566 char suffix, bool mark_missing, const struct dictionary *dict)
1574 s = data_out (&v, dict_get_encoding (dict), settings_get_format ());
1578 suffixes[suffix_len++] = suffix;
1580 suffixes[suffix_len++] = 'M';
1581 suffixes[suffix_len] = '\0';
1583 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1584 s + strspn (s, " "), suffixes);
1589 /* Displays the crosstabulation table. */
1591 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1592 struct tab_table *table)
1598 for (r = 0; r < pt->n_rows; r++)
1599 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1600 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1603 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1604 TAB_LEFT, _("Total"));
1606 /* Put in the actual cells. */
1608 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1609 for (r = 0; r < pt->n_rows; r++)
1611 if (proc->n_cells > 1)
1612 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1613 for (c = 0; c < pt->n_cols; c++)
1615 bool mark_missing = false;
1616 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1617 if (proc->exclude == MV_NEVER
1618 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1619 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1621 mark_missing = true;
1622 for (i = 0; i < proc->n_cells; i++)
1627 switch (proc->a_cells[i])
1633 v = *mp / pt->row_tot[r] * 100.;
1637 v = *mp / pt->col_tot[c] * 100.;
1641 v = *mp / pt->total * 100.;
1644 case CRS_CL_EXPECTED:
1647 case CRS_CL_RESIDUAL:
1648 v = *mp - expected_value;
1650 case CRS_CL_SRESIDUAL:
1651 v = (*mp - expected_value) / sqrt (expected_value);
1653 case CRS_CL_ASRESIDUAL:
1654 v = ((*mp - expected_value)
1655 / sqrt (expected_value
1656 * (1. - pt->row_tot[r] / pt->total)
1657 * (1. - pt->col_tot[c] / pt->total)));
1662 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1668 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1672 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1673 for (r = 0; r < pt->n_rows; r++)
1675 bool mark_missing = false;
1677 if (proc->exclude == MV_NEVER
1678 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1679 mark_missing = true;
1681 for (i = 0; i < proc->n_cells; i++)
1686 switch (proc->a_cells[i])
1696 v = pt->row_tot[r] / pt->total * 100.;
1700 v = pt->row_tot[r] / pt->total * 100.;
1703 case CRS_CL_EXPECTED:
1704 case CRS_CL_RESIDUAL:
1705 case CRS_CL_SRESIDUAL:
1706 case CRS_CL_ASRESIDUAL:
1713 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1714 tab_next_row (table);
1718 /* Column totals, grand total. */
1720 if (proc->n_cells > 1)
1721 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1722 for (c = 0; c <= pt->n_cols; c++)
1724 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1725 bool mark_missing = false;
1728 if (proc->exclude == MV_NEVER && c < pt->n_cols
1729 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1730 mark_missing = true;
1732 for (i = 0; i < proc->n_cells; i++)
1737 switch (proc->a_cells[i])
1743 v = ct / pt->total * 100.;
1751 v = ct / pt->total * 100.;
1754 case CRS_CL_EXPECTED:
1755 case CRS_CL_RESIDUAL:
1756 case CRS_CL_SRESIDUAL:
1757 case CRS_CL_ASRESIDUAL:
1763 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1768 tab_offset (table, -1, tab_row (table) + last_row);
1769 tab_offset (table, 0, -1);
1772 static void calc_r (struct pivot_table *,
1773 double *PT, double *Y, double *, double *, double *);
1774 static void calc_chisq (struct pivot_table *,
1775 double[N_CHISQ], int[N_CHISQ], double *, double *);
1777 /* Display chi-square statistics. */
1779 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1780 bool *showed_fisher)
1782 static const char *chisq_stats[N_CHISQ] =
1784 N_("Pearson Chi-Square"),
1785 N_("Likelihood Ratio"),
1786 N_("Fisher's Exact Test"),
1787 N_("Continuity Correction"),
1788 N_("Linear-by-Linear Association"),
1790 double chisq_v[N_CHISQ];
1791 double fisher1, fisher2;
1796 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1798 tab_offset (chisq, pt->n_consts + pt->n_vars - 2, -1);
1800 for (i = 0; i < N_CHISQ; i++)
1802 if ((i != 2 && chisq_v[i] == SYSMIS)
1803 || (i == 2 && fisher1 == SYSMIS))
1806 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1809 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL, RC_OTHER);
1810 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], NULL, RC_WEIGHT);
1811 tab_double (chisq, 3, 0, TAB_RIGHT,
1812 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL, RC_PVALUE);
1816 *showed_fisher = true;
1817 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL, RC_PVALUE);
1818 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL, RC_PVALUE);
1820 tab_next_row (chisq);
1823 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1824 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1825 tab_next_row (chisq);
1827 tab_offset (chisq, 0, -1);
1830 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1831 double[N_SYMMETRIC], double[N_SYMMETRIC],
1832 double[N_SYMMETRIC],
1833 double[3], double[3], double[3]);
1835 /* Display symmetric measures. */
1837 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1838 struct tab_table *sym)
1840 static const char *categories[] =
1842 N_("Nominal by Nominal"),
1843 N_("Ordinal by Ordinal"),
1844 N_("Interval by Interval"),
1845 N_("Measure of Agreement"),
1848 static const char *stats[N_SYMMETRIC] =
1852 N_("Contingency Coefficient"),
1853 N_("Kendall's tau-b"),
1854 N_("Kendall's tau-c"),
1856 N_("Spearman Correlation"),
1861 static const int stats_categories[N_SYMMETRIC] =
1863 0, 0, 0, 1, 1, 1, 1, 2, 3,
1867 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1868 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1871 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1872 somers_d_v, somers_d_ase, somers_d_t))
1875 tab_offset (sym, pt->n_consts + pt->n_vars - 2, -1);
1877 for (i = 0; i < N_SYMMETRIC; i++)
1879 if (sym_v[i] == SYSMIS)
1882 if (stats_categories[i] != last_cat)
1884 last_cat = stats_categories[i];
1885 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1888 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1889 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL, RC_OTHER);
1890 if (sym_ase[i] != SYSMIS)
1891 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL, RC_OTHER);
1892 if (sym_t[i] != SYSMIS)
1893 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL, RC_OTHER);
1894 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL, RC_PVALUE);*/
1898 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1899 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1902 tab_offset (sym, 0, -1);
1905 static int calc_risk (struct pivot_table *,
1906 double[], double[], double[], union value *);
1908 /* Display risk estimate. */
1910 display_risk (struct pivot_table *pt, struct tab_table *risk)
1913 double risk_v[3], lower[3], upper[3];
1917 if (!calc_risk (pt, risk_v, upper, lower, c))
1920 tab_offset (risk, pt->n_consts + pt->n_vars - 2, -1);
1922 for (i = 0; i < 3; i++)
1924 const struct variable *cv = pt->vars[COL_VAR];
1925 const struct variable *rv = pt->vars[ROW_VAR];
1926 int cvw = var_get_width (cv);
1927 int rvw = var_get_width (rv);
1929 if (risk_v[i] == SYSMIS)
1935 if (var_is_numeric (cv))
1936 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1937 var_to_string (cv), c[0].f, c[1].f);
1939 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1941 cvw, value_str (&c[0], cvw),
1942 cvw, value_str (&c[1], cvw));
1946 if (var_is_numeric (rv))
1947 sprintf (buf, _("For cohort %s = %.*g"),
1948 var_to_string (rv), DBL_DIG + 1, pt->rows[i - 1].f);
1950 sprintf (buf, _("For cohort %s = %.*s"),
1952 rvw, value_str (&pt->rows[i - 1], rvw));
1956 tab_text (risk, 0, 0, TAB_LEFT, buf);
1957 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL, RC_OTHER);
1958 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL, RC_OTHER);
1959 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL, RC_OTHER);
1960 tab_next_row (risk);
1963 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1964 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1965 tab_next_row (risk);
1967 tab_offset (risk, 0, -1);
1970 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1971 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1972 double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
1974 /* Display directional measures. */
1976 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1977 struct tab_table *direct)
1979 static const char *categories[] =
1981 N_("Nominal by Nominal"),
1982 N_("Ordinal by Ordinal"),
1983 N_("Nominal by Interval"),
1986 static const char *stats[] =
1989 N_("Goodman and Kruskal tau"),
1990 N_("Uncertainty Coefficient"),
1995 static const char *types[] =
2002 static const int stats_categories[N_DIRECTIONAL] =
2004 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
2007 static const int stats_stats[N_DIRECTIONAL] =
2009 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2012 static const int stats_types[N_DIRECTIONAL] =
2014 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2017 static const int *stats_lookup[] =
2024 static const char **stats_names[] =
2036 double direct_v[N_DIRECTIONAL];
2037 double direct_ase[N_DIRECTIONAL];
2038 double direct_t[N_DIRECTIONAL];
2039 double sig[N_DIRECTIONAL];
2043 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t, sig))
2046 tab_offset (direct, pt->n_consts + pt->n_vars - 2, -1);
2048 for (i = 0; i < N_DIRECTIONAL; i++)
2050 if (direct_v[i] == SYSMIS)
2056 for (j = 0; j < 3; j++)
2057 if (last[j] != stats_lookup[j][i])
2060 tab_hline (direct, TAL_1, j, 6, 0);
2065 int k = last[j] = stats_lookup[j][i];
2070 string = var_to_string (pt->vars[0]);
2072 string = var_to_string (pt->vars[1]);
2074 tab_text_format (direct, j, 0, TAB_LEFT,
2075 gettext (stats_names[j][k]), string);
2080 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL, RC_OTHER);
2081 if (direct_ase[i] != SYSMIS)
2082 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL, RC_OTHER);
2083 if (direct_t[i] != SYSMIS)
2084 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL, RC_OTHER);
2085 tab_double (direct, 6, 0, TAB_RIGHT, sig[i], NULL, RC_PVALUE);
2086 tab_next_row (direct);
2089 tab_offset (direct, 0, -1);
2092 /* Statistical calculations. */
2094 /* Returns the value of the logarithm of gamma (factorial) function for an integer
2097 log_gamma_int (double pt)
2102 for (i = 2; i < pt; i++)
2108 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2110 static inline double
2111 Pr (int a, int b, int c, int d)
2113 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
2114 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
2115 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
2116 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
2117 - log_gamma_int (a + b + c + d + 1.));
2120 /* Swap the contents of A and B. */
2122 swap (int *a, int *b)
2129 /* Calculate significance for Fisher's exact test as specified in
2130 _SPSS Statistical Algorithms_, Appendix 5. */
2132 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2137 if (MIN (c, d) < MIN (a, b))
2138 swap (&a, &c), swap (&b, &d);
2139 if (MIN (b, d) < MIN (a, c))
2140 swap (&a, &b), swap (&c, &d);
2144 swap (&a, &b), swap (&c, &d);
2146 swap (&a, &c), swap (&b, &d);
2149 pn1 = Pr (a, b, c, d);
2151 for (pt = 1; pt <= a; pt++)
2153 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2156 *fisher2 = *fisher1;
2158 for (pt = 1; pt <= b; pt++)
2160 double p = Pr (a + pt, b - pt, c - pt, d + pt);
2166 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2167 columns with values COLS and N_ROWS rows with values ROWS. Values
2168 in the matrix sum to pt->total. */
2170 calc_chisq (struct pivot_table *pt,
2171 double chisq[N_CHISQ], int df[N_CHISQ],
2172 double *fisher1, double *fisher2)
2176 chisq[0] = chisq[1] = 0.;
2177 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2178 *fisher1 = *fisher2 = SYSMIS;
2180 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2182 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2184 chisq[0] = chisq[1] = SYSMIS;
2188 for (r = 0; r < pt->n_rows; r++)
2189 for (c = 0; c < pt->n_cols; c++)
2191 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2192 const double freq = pt->mat[pt->n_cols * r + c];
2193 const double residual = freq - expected;
2195 chisq[0] += residual * residual / expected;
2197 chisq[1] += freq * log (expected / freq);
2208 /* Calculate Yates and Fisher exact test. */
2209 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2211 double f11, f12, f21, f22;
2217 for (i = j = 0; i < pt->n_cols; i++)
2218 if (pt->col_tot[i] != 0.)
2227 f11 = pt->mat[nz_cols[0]];
2228 f12 = pt->mat[nz_cols[1]];
2229 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2230 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2235 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2238 chisq[3] = (pt->total * pow2 (pt_)
2239 / (f11 + f12) / (f21 + f22)
2240 / (f11 + f21) / (f12 + f22));
2248 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2251 /* Calculate Mantel-Haenszel. */
2252 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2254 double r, ase_0, ase_1;
2255 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2257 chisq[4] = (pt->total - 1.) * r * r;
2262 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2263 T, and standard error into ERROR. The row and column values must be
2264 passed in PT and Y. */
2266 calc_r (struct pivot_table *pt,
2267 double *PT, double *Y, double *r, double *t, double *error)
2269 double SX, SY, S, T;
2271 double sum_XYf, sum_X2Y2f;
2272 double sum_Xr, sum_X2r;
2273 double sum_Yc, sum_Y2c;
2276 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2277 for (j = 0; j < pt->n_cols; j++)
2279 double fij = pt->mat[j + i * pt->n_cols];
2280 double product = PT[i] * Y[j];
2281 double temp = fij * product;
2283 sum_X2Y2f += temp * product;
2286 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2288 sum_Xr += PT[i] * pt->row_tot[i];
2289 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2291 Xbar = sum_Xr / pt->total;
2293 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2295 sum_Yc += Y[i] * pt->col_tot[i];
2296 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2298 Ybar = sum_Yc / pt->total;
2300 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2301 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2302 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2305 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (pt->total - 2);
2310 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2311 for (j = 0; j < pt->n_cols; j++)
2313 double Xresid, Yresid;
2316 Xresid = PT[i] - Xbar;
2317 Yresid = Y[j] - Ybar;
2318 temp = (T * Xresid * Yresid
2320 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2321 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2326 *error = sqrt (s) / (T * T);
2330 /* Calculate symmetric statistics and their asymptotic standard
2331 errors. Returns 0 if none could be calculated. */
2333 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2334 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2335 double t[N_SYMMETRIC],
2336 double somers_d_v[3], double somers_d_ase[3],
2337 double somers_d_t[3])
2341 q = MIN (pt->ns_rows, pt->ns_cols);
2345 for (i = 0; i < N_SYMMETRIC; i++)
2346 v[i] = ase[i] = t[i] = SYSMIS;
2348 /* Phi, Cramer's V, contingency coefficient. */
2349 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2351 double Xp = 0.; /* Pearson chi-square. */
2354 for (r = 0; r < pt->n_rows; r++)
2355 for (c = 0; c < pt->n_cols; c++)
2357 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2358 const double freq = pt->mat[pt->n_cols * r + c];
2359 const double residual = freq - expected;
2361 Xp += residual * residual / expected;
2364 if (proc->statistics & (1u << CRS_ST_PHI))
2366 v[0] = sqrt (Xp / pt->total);
2367 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2369 if (proc->statistics & (1u << CRS_ST_CC))
2370 v[2] = sqrt (Xp / (Xp + pt->total));
2373 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2374 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2379 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2383 Dr = Dc = pow2 (pt->total);
2384 for (r = 0; r < pt->n_rows; r++)
2385 Dr -= pow2 (pt->row_tot[r]);
2386 for (c = 0; c < pt->n_cols; c++)
2387 Dc -= pow2 (pt->col_tot[c]);
2389 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2390 for (c = 0; c < pt->n_cols; c++)
2394 for (r = 0; r < pt->n_rows; r++)
2395 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2404 for (i = 0; i < pt->n_rows; i++)
2408 for (j = 1; j < pt->n_cols; j++)
2409 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2412 for (j = 1; j < pt->n_cols; j++)
2413 Dij += cum[j + (i - 1) * pt->n_cols];
2417 double fij = pt->mat[j + i * pt->n_cols];
2421 if (++j == pt->n_cols)
2423 assert (j < pt->n_cols);
2425 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2426 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2430 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2431 Dij -= cum[j + (i - 1) * pt->n_cols];
2437 if (proc->statistics & (1u << CRS_ST_BTAU))
2438 v[3] = (P - Q) / sqrt (Dr * Dc);
2439 if (proc->statistics & (1u << CRS_ST_CTAU))
2440 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2441 if (proc->statistics & (1u << CRS_ST_GAMMA))
2442 v[5] = (P - Q) / (P + Q);
2444 /* ASE for tau-b, tau-c, gamma. Calculations could be
2445 eliminated here, at expense of memory. */
2450 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2451 for (i = 0; i < pt->n_rows; i++)
2455 for (j = 1; j < pt->n_cols; j++)
2456 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2459 for (j = 1; j < pt->n_cols; j++)
2460 Dij += cum[j + (i - 1) * pt->n_cols];
2464 double fij = pt->mat[j + i * pt->n_cols];
2466 if (proc->statistics & (1u << CRS_ST_BTAU))
2468 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2469 + v[3] * (pt->row_tot[i] * Dc
2470 + pt->col_tot[j] * Dr));
2471 btau_cum += fij * temp * temp;
2475 const double temp = Cij - Dij;
2476 ctau_cum += fij * temp * temp;
2479 if (proc->statistics & (1u << CRS_ST_GAMMA))
2481 const double temp = Q * Cij - P * Dij;
2482 gamma_cum += fij * temp * temp;
2485 if (proc->statistics & (1u << CRS_ST_D))
2487 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2488 - (P - Q) * (pt->total - pt->row_tot[i]));
2489 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2490 - (Q - P) * (pt->total - pt->col_tot[j]));
2493 if (++j == pt->n_cols)
2495 assert (j < pt->n_cols);
2497 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2498 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2502 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2503 Dij -= cum[j + (i - 1) * pt->n_cols];
2509 btau_var = ((btau_cum
2510 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2512 if (proc->statistics & (1u << CRS_ST_BTAU))
2514 ase[3] = sqrt (btau_var);
2515 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2518 if (proc->statistics & (1u << CRS_ST_CTAU))
2520 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2521 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2522 t[4] = v[4] / ase[4];
2524 if (proc->statistics & (1u << CRS_ST_GAMMA))
2526 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2527 t[5] = v[5] / (2. / (P + Q)
2528 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2530 if (proc->statistics & (1u << CRS_ST_D))
2532 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2533 somers_d_ase[0] = SYSMIS;
2534 somers_d_t[0] = (somers_d_v[0]
2536 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2537 somers_d_v[1] = (P - Q) / Dc;
2538 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2539 somers_d_t[1] = (somers_d_v[1]
2541 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2542 somers_d_v[2] = (P - Q) / Dr;
2543 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2544 somers_d_t[2] = (somers_d_v[2]
2546 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2552 /* Spearman correlation, Pearson's r. */
2553 if (proc->statistics & (1u << CRS_ST_CORR))
2555 double *R = xmalloc (sizeof *R * pt->n_rows);
2556 double *C = xmalloc (sizeof *C * pt->n_cols);
2559 double y, t, c = 0., s = 0.;
2564 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2565 y = pt->row_tot[i] - c;
2569 if (++i == pt->n_rows)
2571 assert (i < pt->n_rows);
2576 double y, t, c = 0., s = 0.;
2581 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2582 y = pt->col_tot[j] - c;
2586 if (++j == pt->n_cols)
2588 assert (j < pt->n_cols);
2592 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2597 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2600 /* Cohen's kappa. */
2601 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2603 double ase_under_h0;
2604 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2607 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2608 i < pt->ns_rows; i++, j++)
2612 while (pt->col_tot[j] == 0.)
2615 prod = pt->row_tot[i] * pt->col_tot[j];
2616 sum = pt->row_tot[i] + pt->col_tot[j];
2618 sum_fii += pt->mat[j + i * pt->n_cols];
2620 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2621 sum_riciri_ci += prod * sum;
2623 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2624 for (j = 0; j < pt->ns_cols; j++)
2626 double sum = pt->row_tot[i] + pt->col_tot[j];
2627 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2630 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2632 ase_under_h0 = sqrt ((pow2 (pt->total) * sum_rici
2633 + sum_rici * sum_rici
2634 - pt->total * sum_riciri_ci)
2635 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2637 ase[8] = sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2638 / pow2 (pow2 (pt->total) - sum_rici))
2639 + ((2. * (pt->total - sum_fii)
2640 * (2. * sum_fii * sum_rici
2641 - pt->total * sum_fiiri_ci))
2642 / pow3 (pow2 (pt->total) - sum_rici))
2643 + (pow2 (pt->total - sum_fii)
2644 * (pt->total * sum_fijri_ci2 - 4.
2645 * sum_rici * sum_rici)
2646 / pow4 (pow2 (pt->total) - sum_rici))));
2648 t[8] = v[8] / ase_under_h0;
2654 /* Calculate risk estimate. */
2656 calc_risk (struct pivot_table *pt,
2657 double *value, double *upper, double *lower, union value *c)
2659 double f11, f12, f21, f22;
2665 for (i = 0; i < 3; i++)
2666 value[i] = upper[i] = lower[i] = SYSMIS;
2669 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2676 for (i = j = 0; i < pt->n_cols; i++)
2677 if (pt->col_tot[i] != 0.)
2686 f11 = pt->mat[nz_cols[0]];
2687 f12 = pt->mat[nz_cols[1]];
2688 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2689 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2691 c[0] = pt->cols[nz_cols[0]];
2692 c[1] = pt->cols[nz_cols[1]];
2695 value[0] = (f11 * f22) / (f12 * f21);
2696 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2697 lower[0] = value[0] * exp (-1.960 * v);
2698 upper[0] = value[0] * exp (1.960 * v);
2700 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2701 v = sqrt ((f12 / (f11 * (f11 + f12)))
2702 + (f22 / (f21 * (f21 + f22))));
2703 lower[1] = value[1] * exp (-1.960 * v);
2704 upper[1] = value[1] * exp (1.960 * v);
2706 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2707 v = sqrt ((f11 / (f12 * (f11 + f12)))
2708 + (f21 / (f22 * (f21 + f22))));
2709 lower[2] = value[2] * exp (-1.960 * v);
2710 upper[2] = value[2] * exp (1.960 * v);
2715 /* Calculate directional measures. */
2717 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2718 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2719 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
2724 for (i = 0; i < N_DIRECTIONAL; i++)
2725 v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
2729 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2731 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2732 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2733 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2734 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2735 double sum_fim, sum_fmj;
2737 int rm_index, cm_index;
2740 /* Find maximum for each row and their sum. */
2741 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2743 double max = pt->mat[i * pt->n_cols];
2746 for (j = 1; j < pt->n_cols; j++)
2747 if (pt->mat[j + i * pt->n_cols] > max)
2749 max = pt->mat[j + i * pt->n_cols];
2753 sum_fim += fim[i] = max;
2754 fim_index[i] = index;
2757 /* Find maximum for each column. */
2758 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2760 double max = pt->mat[j];
2763 for (i = 1; i < pt->n_rows; i++)
2764 if (pt->mat[j + i * pt->n_cols] > max)
2766 max = pt->mat[j + i * pt->n_cols];
2770 sum_fmj += fmj[j] = max;
2771 fmj_index[j] = index;
2774 /* Find maximum row total. */
2775 rm = pt->row_tot[0];
2777 for (i = 1; i < pt->n_rows; i++)
2778 if (pt->row_tot[i] > rm)
2780 rm = pt->row_tot[i];
2784 /* Find maximum column total. */
2785 cm = pt->col_tot[0];
2787 for (j = 1; j < pt->n_cols; j++)
2788 if (pt->col_tot[j] > cm)
2790 cm = pt->col_tot[j];
2794 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2795 v[1] = (sum_fmj - rm) / (pt->total - rm);
2796 v[2] = (sum_fim - cm) / (pt->total - cm);
2798 /* ASE1 for Y given PT. */
2803 for (i = 0; i < pt->n_rows; i++)
2804 if (cm_index == fim_index[i])
2806 ase[2] = sqrt ((pt->total - sum_fim) * (sum_fim + cm - 2. * accum)
2807 / pow3 (pt->total - cm));
2810 /* ASE0 for Y given PT. */
2814 for (accum = 0., i = 0; i < pt->n_rows; i++)
2815 if (cm_index != fim_index[i])
2816 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2817 + pt->mat[i * pt->n_cols + cm_index]);
2818 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2821 /* ASE1 for PT given Y. */
2826 for (j = 0; j < pt->n_cols; j++)
2827 if (rm_index == fmj_index[j])
2829 ase[1] = sqrt ((pt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
2830 / pow3 (pt->total - rm));
2833 /* ASE0 for PT given Y. */
2837 for (accum = 0., j = 0; j < pt->n_cols; j++)
2838 if (rm_index != fmj_index[j])
2839 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2840 + pt->mat[j + pt->n_cols * rm_index]);
2841 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2844 /* Symmetric ASE0 and ASE1. */
2849 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2850 for (j = 0; j < pt->n_cols; j++)
2852 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2853 int temp1 = (i == rm_index) + (j == cm_index);
2854 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2855 accum1 += (pt->mat[j + i * pt->n_cols]
2856 * pow2 (temp0 + (v[0] - 1.) * temp1));
2858 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2859 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / pt->total)
2860 / (2. * pt->total - rm - cm));
2863 for (i = 0; i < 3; i++)
2864 sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
2873 double sum_fij2_ri, sum_fij2_ci;
2874 double sum_ri2, sum_cj2;
2876 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2877 for (j = 0; j < pt->n_cols; j++)
2879 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2880 sum_fij2_ri += temp / pt->row_tot[i];
2881 sum_fij2_ci += temp / pt->col_tot[j];
2884 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2885 sum_ri2 += pow2 (pt->row_tot[i]);
2887 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2888 sum_cj2 += pow2 (pt->col_tot[j]);
2890 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2891 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2895 if (proc->statistics & (1u << CRS_ST_UC))
2897 double UX, UY, UXY, P;
2898 double ase1_yx, ase1_xy, ase1_sym;
2901 for (UX = 0., i = 0; i < pt->n_rows; i++)
2902 if (pt->row_tot[i] > 0.)
2903 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2905 for (UY = 0., j = 0; j < pt->n_cols; j++)
2906 if (pt->col_tot[j] > 0.)
2907 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2909 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2910 for (j = 0; j < pt->n_cols; j++)
2912 double entry = pt->mat[j + i * pt->n_cols];
2917 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2918 UXY -= entry / pt->total * log (entry / pt->total);
2921 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2922 for (j = 0; j < pt->n_cols; j++)
2924 double entry = pt->mat[j + i * pt->n_cols];
2929 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2930 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2931 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2932 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2933 ase1_sym += entry * pow2 ((UXY
2934 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2935 - (UX + UY) * log (entry / pt->total));
2938 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2939 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2942 v[6] = (UX + UY - UXY) / UX;
2943 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2944 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2946 v[7] = (UX + UY - UXY) / UY;
2947 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2948 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2952 if (proc->statistics & (1u << CRS_ST_D))
2954 double v_dummy[N_SYMMETRIC];
2955 double ase_dummy[N_SYMMETRIC];
2956 double t_dummy[N_SYMMETRIC];
2957 double somers_d_v[3];
2958 double somers_d_ase[3];
2959 double somers_d_t[3];
2961 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2962 somers_d_v, somers_d_ase, somers_d_t))
2965 for (i = 0; i < 3; i++)
2967 v[8 + i] = somers_d_v[i];
2968 ase[8 + i] = somers_d_ase[i];
2969 t[8 + i] = somers_d_t[i];
2970 sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
2976 if (proc->statistics & (1u << CRS_ST_ETA))
2979 double sum_Xr, sum_X2r;
2983 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2985 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2986 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2988 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2990 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2994 for (cum = 0., i = 0; i < pt->n_rows; i++)
2996 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2997 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
3000 SXW -= cum * cum / pt->col_tot[j];
3002 v[11] = sqrt (1. - SXW / SX);
3006 double sum_Yc, sum_Y2c;
3010 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
3012 sum_Yc += pt->cols[i].f * pt->col_tot[i];
3013 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
3015 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3017 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3021 for (cum = 0., j = 0; j < pt->n_cols; j++)
3023 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3024 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3027 SYW -= cum * cum / pt->row_tot[i];
3029 v[12] = sqrt (1. - SYW / SY);