1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012, 2013, 2014, 2016 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))
417 by_iter = xcalloc (n_by, sizeof *by_iter);
418 proc->pivots = xnrealloc (proc->pivots,
419 proc->n_pivots + nx, sizeof *proc->pivots);
420 for (i = 0; i < nx; i++)
422 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
426 pt->weight_format = proc->weight_format;
429 pt->vars = xmalloc (n_by * sizeof *pt->vars);
431 pt->const_vars = NULL;
432 pt->const_values = NULL;
434 for (j = 0; j < n_by; j++)
435 pt->vars[j] = by[j][by_iter[j]];
437 for (j = n_by - 1; j >= 0; j--)
439 if (++by_iter[j] < by_nvar[j])
448 /* All return paths lead here. */
449 for (i = 0; i < n_by; i++)
454 const_var_set_destroy (var_set);
459 /* Parses the VARIABLES subcommand. */
461 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
462 struct cmd_crosstabs *cmd UNUSED, void *proc_)
464 struct crosstabs_proc *proc = proc_;
467 msg (SE, _("%s must be specified before %s."), "VARIABLES", "TABLES");
471 lex_match (lexer, T_EQUALS);
475 size_t orig_nv = proc->n_variables;
480 if (!parse_variables_const (lexer, dataset_dict (ds),
481 &proc->variables, &proc->n_variables,
482 (PV_APPEND | PV_NUMERIC
483 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
486 if (!lex_force_match (lexer, T_LPAREN))
489 if (!lex_force_int (lexer))
491 min = lex_integer (lexer);
494 lex_match (lexer, T_COMMA);
496 if (!lex_force_int (lexer))
498 max = lex_integer (lexer);
501 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
507 if (!lex_force_match (lexer, T_RPAREN))
510 for (i = orig_nv; i < proc->n_variables; i++)
512 const struct variable *var = proc->variables[i];
513 struct var_range *vr = xmalloc (sizeof *vr);
518 vr->count = max - min + 1;
519 hmap_insert (&proc->var_ranges, &vr->hmap_node,
520 hash_pointer (var, 0));
523 if (lex_token (lexer) == T_SLASH)
530 free (proc->variables);
531 proc->variables = NULL;
532 proc->n_variables = 0;
536 /* Data file processing. */
538 const struct var_range *
539 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
541 if (!hmap_is_empty (&proc->var_ranges))
543 const struct var_range *range;
545 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
546 hash_pointer (var, 0), &proc->var_ranges)
547 if (range->var == var)
555 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
556 enum mv_class exclude)
559 for (j = 0; j < pt->n_vars; j++)
561 const struct variable *var = pt->vars[j];
562 const struct var_range *range = get_var_range (pt->proc, var);
564 if (var_is_value_missing (var, case_data (c, var), exclude))
569 double num = case_num (c, var);
570 if (num < range->min || num >= range->max + 1.)
578 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
586 for (j = 0; j < pt->n_vars; j++)
588 /* Throw away fractional parts of values. */
589 hash = hash_int (case_num (c, pt->vars[j]), hash);
592 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &pt->data)
594 for (j = 0; j < pt->n_vars; j++)
595 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
598 /* Found an existing entry. */
605 /* No existing entry. Create a new one. */
606 te = xmalloc (table_entry_size (pt->n_vars));
608 for (j = 0; j < pt->n_vars; j++)
609 te->values[j].f = (int) case_num (c, pt->vars[j]);
610 hmap_insert (&pt->data, &te->node, hash);
614 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
622 for (j = 0; j < pt->n_vars; j++)
624 const struct variable *var = pt->vars[j];
625 hash = value_hash (case_data (c, var), var_get_width (var), hash);
628 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &pt->data)
630 for (j = 0; j < pt->n_vars; j++)
632 const struct variable *var = pt->vars[j];
633 if (!value_equal (case_data (c, var), &te->values[j],
634 var_get_width (var)))
638 /* Found an existing entry. */
645 /* No existing entry. Create a new one. */
646 te = xmalloc (table_entry_size (pt->n_vars));
648 for (j = 0; j < pt->n_vars; j++)
650 const struct variable *var = pt->vars[j];
651 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
653 hmap_insert (&pt->data, &te->node, hash);
656 /* Post-data reading calculations. */
658 static int compare_table_entry_vars_3way (const struct freq *a,
659 const struct freq *b,
660 const struct pivot_table *pt,
662 static int compare_table_entry_3way (const void *ap_, const void *bp_,
664 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
667 static void enum_var_values (const struct pivot_table *, int var_idx,
668 union value **valuesp, int *n_values, bool descending);
669 static void output_pivot_table (struct crosstabs_proc *,
670 struct pivot_table *);
671 static void make_pivot_table_subset (struct pivot_table *pt,
672 size_t row0, size_t row1,
673 struct pivot_table *subset);
674 static void make_summary_table (struct crosstabs_proc *);
675 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
678 postcalc (struct crosstabs_proc *proc)
680 struct pivot_table *pt;
682 /* Convert hash tables into sorted arrays of entries. */
683 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
688 pt->n_entries = hmap_count (&pt->data);
689 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
691 HMAP_FOR_EACH (e, struct freq, node, &pt->data)
692 pt->entries[i++] = e;
693 hmap_destroy (&pt->data);
695 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
696 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
701 make_summary_table (proc);
703 /* Output each pivot table. */
704 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
706 if (proc->pivot || pt->n_vars == 2)
707 output_pivot_table (proc, pt);
710 size_t row0 = 0, row1 = 0;
711 while (find_crosstab (pt, &row0, &row1))
713 struct pivot_table subset;
714 make_pivot_table_subset (pt, row0, row1, &subset);
715 output_pivot_table (proc, &subset);
720 (barchart_create (pt->vars, pt->n_vars, _("Count"), false, pt->entries, pt->n_entries));
723 /* Free output and prepare for next split file. */
724 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
730 /* Free the members that were allocated in this function(and the values
731 owned by the entries.
733 The other pointer members are either both allocated and destroyed at a
734 lower level (in output_pivot_table), or both allocated and destroyed
735 at a higher level (in crs_custom_tables and free_proc,
737 for (i = 0; i < pt->n_vars; i++)
739 int width = var_get_width (pt->vars[i]);
740 if (value_needs_init (width))
744 for (j = 0; j < pt->n_entries; j++)
745 value_destroy (&pt->entries[j]->values[i], width);
749 for (i = 0; i < pt->n_entries; i++)
750 free (pt->entries[i]);
756 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
757 struct pivot_table *subset)
762 assert (pt->n_consts == 0);
763 subset->missing = pt->missing;
765 subset->vars = pt->vars;
766 subset->n_consts = pt->n_vars - 2;
767 subset->const_vars = pt->vars + 2;
768 subset->const_values = &pt->entries[row0]->values[2];
770 subset->entries = &pt->entries[row0];
771 subset->n_entries = row1 - row0;
775 compare_table_entry_var_3way (const struct freq *a,
776 const struct freq *b,
777 const struct pivot_table *pt,
780 return value_compare_3way (&a->values[idx], &b->values[idx],
781 var_get_width (pt->vars[idx]));
785 compare_table_entry_vars_3way (const struct freq *a,
786 const struct freq *b,
787 const struct pivot_table *pt,
792 for (i = idx1 - 1; i >= idx0; i--)
794 int cmp = compare_table_entry_var_3way (a, b, pt, i);
801 /* Compare the struct freq at *AP to the one at *BP and
802 return a strcmp()-type result. */
804 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
806 const struct freq *const *ap = ap_;
807 const struct freq *const *bp = bp_;
808 const struct freq *a = *ap;
809 const struct freq *b = *bp;
810 const struct pivot_table *pt = pt_;
813 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
817 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
821 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
824 /* Inverted version of compare_table_entry_3way */
826 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *pt_)
828 return -compare_table_entry_3way (ap_, bp_, pt_);
832 find_first_difference (const struct pivot_table *pt, size_t row)
835 return pt->n_vars - 1;
838 const struct freq *a = pt->entries[row];
839 const struct freq *b = pt->entries[row - 1];
842 for (col = pt->n_vars - 1; col >= 0; col--)
843 if (compare_table_entry_var_3way (a, b, pt, col))
849 /* Output a table summarizing the cases processed. */
851 make_summary_table (struct crosstabs_proc *proc)
853 struct tab_table *summary;
854 struct pivot_table *pt;
858 summary = tab_create (7, 3 + proc->n_pivots);
859 tab_set_format (summary, RC_WEIGHT, &proc->weight_format);
860 tab_title (summary, _("Summary."));
861 tab_headers (summary, 1, 0, 3, 0);
862 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
863 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
864 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
865 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
866 tab_hline (summary, TAL_1, 1, 6, 1);
867 tab_hline (summary, TAL_1, 1, 6, 2);
868 tab_vline (summary, TAL_1, 3, 1, 1);
869 tab_vline (summary, TAL_1, 5, 1, 1);
870 for (i = 0; i < 3; i++)
872 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
873 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
875 tab_offset (summary, 0, 3);
877 ds_init_empty (&name);
878 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
884 tab_hline (summary, TAL_1, 0, 6, 0);
887 for (i = 0; i < pt->n_vars; i++)
890 ds_put_cstr (&name, " * ");
891 ds_put_cstr (&name, var_to_string (pt->vars[i]));
893 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
896 for (i = 0; i < pt->n_entries; i++)
897 valid += pt->entries[i]->count;
902 for (i = 0; i < 3; i++)
904 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i], NULL, RC_WEIGHT);
905 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
909 tab_next_row (summary);
913 submit (NULL, summary);
918 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
919 struct pivot_table *);
920 static struct tab_table *create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *);
921 static struct tab_table *create_sym_table (struct crosstabs_proc *proc, struct pivot_table *);
922 static struct tab_table *create_risk_table (struct crosstabs_proc *proc, struct pivot_table *);
923 static struct tab_table *create_direct_table (struct crosstabs_proc *proc, struct pivot_table *);
924 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
925 struct tab_table *, int first_difference);
926 static void display_crosstabulation (struct crosstabs_proc *,
927 struct pivot_table *,
929 static void display_chisq (struct pivot_table *, struct tab_table *,
930 bool *showed_fisher);
931 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
933 static void display_risk (struct pivot_table *, struct tab_table *);
934 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
936 static void table_value_missing (struct crosstabs_proc *proc,
937 struct tab_table *table, int c, int r,
938 unsigned char opt, const union value *v,
939 const struct variable *var);
940 static void delete_missing (struct pivot_table *);
941 static void build_matrix (struct pivot_table *);
943 /* Output pivot table PT in the context of PROC. */
945 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
947 struct tab_table *table = NULL; /* Crosstabulation table. */
948 struct tab_table *chisq = NULL; /* Chi-square table. */
949 bool showed_fisher = false;
950 struct tab_table *sym = NULL; /* Symmetric measures table. */
951 struct tab_table *risk = NULL; /* Risk estimate table. */
952 struct tab_table *direct = NULL; /* Directional measures table. */
955 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols, proc->descending);
962 ds_init_cstr (&vars, var_to_string (pt->vars[0]));
963 for (i = 1; i < pt->n_vars; i++)
964 ds_put_format (&vars, " * %s", var_to_string (pt->vars[i]));
966 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
967 form "var1 * var2 * var3 * ...". */
968 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
977 table = create_crosstab_table (proc, pt);
978 if (proc->statistics & (1u << CRS_ST_CHISQ))
979 chisq = create_chisq_table (proc, pt);
980 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
981 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
982 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
983 | (1u << CRS_ST_KAPPA)))
984 sym = create_sym_table (proc, pt);
985 if (proc->statistics & (1u << CRS_ST_RISK))
986 risk = create_risk_table (proc, pt);
987 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
988 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
989 direct = create_direct_table (proc, pt);
992 while (find_crosstab (pt, &row0, &row1))
994 struct pivot_table x;
995 int first_difference;
997 make_pivot_table_subset (pt, row0, row1, &x);
999 /* Find all the row variable values. */
1000 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows, proc->descending);
1002 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
1005 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
1006 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
1007 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
1009 /* Allocate table space for the matrix. */
1011 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
1012 tab_realloc (table, -1,
1013 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
1014 tab_nr (table) * pt->n_entries / x.n_entries));
1018 /* Find the first variable that differs from the last subtable. */
1019 first_difference = find_first_difference (pt, row0);
1022 display_dimensions (proc, &x, table, first_difference);
1023 display_crosstabulation (proc, &x, table);
1026 if (proc->exclude == MV_NEVER)
1027 delete_missing (&x);
1031 display_dimensions (proc, &x, chisq, first_difference);
1032 display_chisq (&x, chisq, &showed_fisher);
1036 display_dimensions (proc, &x, sym, first_difference);
1037 display_symmetric (proc, &x, sym);
1041 display_dimensions (proc, &x, risk, first_difference);
1042 display_risk (&x, risk);
1046 display_dimensions (proc, &x, direct, first_difference);
1047 display_directional (proc, &x, direct);
1050 /* Free the parts of x that are not owned by pt. In
1051 particular we must not free x.cols, which is the same as
1052 pt->cols, which is freed at the end of this function. */
1060 submit (NULL, table);
1065 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1071 submit (pt, direct);
1077 build_matrix (struct pivot_table *x)
1079 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1080 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1087 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1089 const struct freq *te = *p;
1091 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1093 for (; col < x->n_cols; col++)
1099 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1106 if (++col >= x->n_cols)
1112 while (mp < &x->mat[x->n_cols * x->n_rows])
1114 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1116 /* Column totals, row totals, ns_rows. */
1118 for (col = 0; col < x->n_cols; col++)
1119 x->col_tot[col] = 0.0;
1120 for (row = 0; row < x->n_rows; row++)
1121 x->row_tot[row] = 0.0;
1123 for (row = 0; row < x->n_rows; row++)
1125 bool row_is_empty = true;
1126 for (col = 0; col < x->n_cols; col++)
1130 row_is_empty = false;
1131 x->col_tot[col] += *mp;
1132 x->row_tot[row] += *mp;
1139 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1143 for (col = 0; col < x->n_cols; col++)
1144 for (row = 0; row < x->n_rows; row++)
1145 if (x->mat[col + row * x->n_cols] != 0.0)
1153 for (col = 0; col < x->n_cols; col++)
1154 x->total += x->col_tot[col];
1157 static struct tab_table *
1158 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1165 static const struct tuple names[] =
1167 {CRS_CL_COUNT, N_("count")},
1168 {CRS_CL_ROW, N_("row %")},
1169 {CRS_CL_COLUMN, N_("column %")},
1170 {CRS_CL_TOTAL, N_("total %")},
1171 {CRS_CL_EXPECTED, N_("expected")},
1172 {CRS_CL_RESIDUAL, N_("residual")},
1173 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1174 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1176 const int n_names = sizeof names / sizeof *names;
1177 const struct tuple *t;
1179 struct tab_table *table;
1180 struct string title;
1181 struct pivot_table x;
1185 make_pivot_table_subset (pt, 0, 0, &x);
1187 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1188 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1189 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1190 tab_set_format (table, RC_WEIGHT, &proc->weight_format);
1192 /* First header line. */
1193 tab_joint_text (table, x.n_consts + 1, 0,
1194 (x.n_consts + 1) + (x.n_cols - 1), 0,
1195 TAB_CENTER | TAT_TITLE, var_to_string (x.vars[COL_VAR]));
1197 tab_hline (table, TAL_1, x.n_consts + 1,
1198 x.n_consts + 2 + x.n_cols - 2, 1);
1200 /* Second header line. */
1201 for (i = 2; i < x.n_consts + 2; i++)
1202 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1203 x.n_consts + 2 - i - 1, 1,
1204 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1205 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1206 var_to_string (x.vars[ROW_VAR]));
1207 for (i = 0; i < x.n_cols; i++)
1208 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1209 &x.cols[i], x.vars[COL_VAR]);
1210 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1212 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1213 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1216 ds_init_empty (&title);
1217 for (i = 0; i < x.n_consts + 2; i++)
1220 ds_put_cstr (&title, " * ");
1221 ds_put_cstr (&title, var_to_string (x.vars[i]));
1223 for (i = 0; i < pt->n_consts; i++)
1225 const struct variable *var = pt->const_vars[i];
1228 ds_put_format (&title, ", %s=", var_to_string (var));
1230 /* Insert the formatted value of VAR without any leading spaces. */
1231 s = data_out (&pt->const_values[i], var_get_encoding (var),
1232 var_get_print_format (var));
1233 ds_put_cstr (&title, s + strspn (s, " "));
1237 ds_put_cstr (&title, " [");
1239 for (t = names; t < &names[n_names]; t++)
1240 if (proc->cells & (1u << t->value))
1243 ds_put_cstr (&title, ", ");
1244 ds_put_cstr (&title, gettext (t->name));
1246 ds_put_cstr (&title, "].");
1248 tab_title (table, "%s", ds_cstr (&title));
1249 ds_destroy (&title);
1251 tab_offset (table, 0, 2);
1255 static struct tab_table *
1256 create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1258 struct tab_table *chisq;
1260 chisq = tab_create (6 + (pt->n_vars - 2),
1261 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1262 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1263 tab_set_format (chisq, RC_WEIGHT, &proc->weight_format);
1265 tab_title (chisq, _("Chi-square tests."));
1267 tab_offset (chisq, pt->n_vars - 2, 0);
1268 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1269 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1270 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1271 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1272 _("Asymp. Sig. (2-tailed)"));
1273 tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1274 _("Exact Sig. (%d-tailed)"), 2);
1275 tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1276 _("Exact Sig. (%d-tailed)"), 1);
1277 tab_offset (chisq, 0, 1);
1282 /* Symmetric measures. */
1283 static struct tab_table *
1284 create_sym_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1286 struct tab_table *sym;
1288 sym = tab_create (6 + (pt->n_vars - 2),
1289 pt->n_entries / pt->n_cols * 7 + 10);
1291 tab_set_format (sym, RC_WEIGHT, &proc->weight_format);
1293 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1294 tab_title (sym, _("Symmetric measures."));
1296 tab_offset (sym, pt->n_vars - 2, 0);
1297 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1298 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1299 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1300 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1301 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1302 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1303 tab_offset (sym, 0, 1);
1308 /* Risk estimate. */
1309 static struct tab_table *
1310 create_risk_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1312 struct tab_table *risk;
1314 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1315 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1316 tab_title (risk, _("Risk estimate."));
1317 tab_set_format (risk, RC_WEIGHT, &proc->weight_format);
1319 tab_offset (risk, pt->n_vars - 2, 0);
1320 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1321 _("95%% Confidence Interval"));
1322 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1323 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1324 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1325 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1326 tab_hline (risk, TAL_1, 2, 3, 1);
1327 tab_vline (risk, TAL_1, 2, 0, 1);
1328 tab_offset (risk, 0, 2);
1333 /* Directional measures. */
1334 static struct tab_table *
1335 create_direct_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1337 struct tab_table *direct;
1339 direct = tab_create (7 + (pt->n_vars - 2),
1340 pt->n_entries / pt->n_cols * 7 + 10);
1341 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1342 tab_title (direct, _("Directional measures."));
1343 tab_set_format (direct, RC_WEIGHT, &proc->weight_format);
1345 tab_offset (direct, pt->n_vars - 2, 0);
1346 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1347 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1348 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1349 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1350 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1351 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1352 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1353 tab_offset (direct, 0, 1);
1359 /* Delete missing rows and columns for statistical analysis when
1362 delete_missing (struct pivot_table *pt)
1366 for (r = 0; r < pt->n_rows; r++)
1367 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1369 for (c = 0; c < pt->n_cols; c++)
1370 pt->mat[c + r * pt->n_cols] = 0.;
1375 for (c = 0; c < pt->n_cols; c++)
1376 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1378 for (r = 0; r < pt->n_rows; r++)
1379 pt->mat[c + r * pt->n_cols] = 0.;
1384 /* Prepare table T for submission, and submit it. */
1386 submit (struct pivot_table *pt, struct tab_table *t)
1393 tab_resize (t, -1, 0);
1394 if (tab_nr (t) == tab_t (t))
1396 table_unref (&t->table);
1399 tab_offset (t, 0, 0);
1401 for (i = 2; i < pt->n_vars; i++)
1402 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1403 var_to_string (pt->vars[i]));
1404 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1405 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1407 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1409 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1415 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1417 size_t row0 = *row1p;
1420 if (row0 >= pt->n_entries)
1423 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1425 struct freq *a = pt->entries[row0];
1426 struct freq *b = pt->entries[row1];
1427 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1435 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1436 result. WIDTH_ points to an int which is either 0 for a
1437 numeric value or a string width for a string value. */
1439 compare_value_3way (const void *a_, const void *b_, const void *width_)
1441 const union value *a = a_;
1442 const union value *b = b_;
1443 const int *width = width_;
1445 return value_compare_3way (a, b, *width);
1448 /* Inverted version of the above */
1450 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1452 return -compare_value_3way (a_, b_, width_);
1456 /* Given an array of ENTRY_CNT table_entry structures starting at
1457 ENTRIES, creates a sorted list of the values that the variable
1458 with index VAR_IDX takes on. The values are returned as a
1459 malloc()'d array stored in *VALUES, with the number of values
1460 stored in *VALUE_CNT.
1462 The caller must eventually free *VALUES, but each pointer in *VALUES points
1463 to existing data not owned by *VALUES itself. */
1465 enum_var_values (const struct pivot_table *pt, int var_idx,
1466 union value **valuesp, int *n_values, bool descending)
1468 const struct variable *var = pt->vars[var_idx];
1469 const struct var_range *range = get_var_range (pt->proc, var);
1470 union value *values;
1475 values = *valuesp = xnmalloc (range->count, sizeof *values);
1476 *n_values = range->count;
1477 for (i = 0; i < range->count; i++)
1478 values[i].f = range->min + i;
1482 int width = var_get_width (var);
1483 struct hmapx_node *node;
1484 const union value *iter;
1488 for (i = 0; i < pt->n_entries; i++)
1490 const struct freq *te = pt->entries[i];
1491 const union value *value = &te->values[var_idx];
1492 size_t hash = value_hash (value, width, 0);
1494 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1495 if (value_equal (iter, value, width))
1498 hmapx_insert (&set, (union value *) value, hash);
1503 *n_values = hmapx_count (&set);
1504 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1506 HMAPX_FOR_EACH (iter, node, &set)
1507 values[i++] = *iter;
1508 hmapx_destroy (&set);
1510 sort (values, *n_values, sizeof *values,
1511 descending ? compare_value_3way_inv : compare_value_3way,
1516 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1517 from V, displayed with print format spec from variable VAR. When
1518 in REPORT missing-value mode, missing values have an M appended. */
1520 table_value_missing (struct crosstabs_proc *proc,
1521 struct tab_table *table, int c, int r, unsigned char opt,
1522 const union value *v, const struct variable *var)
1524 const char *label = var_lookup_value_label (var, v);
1526 tab_text (table, c, r, TAB_LEFT, label);
1529 const struct fmt_spec *print = var_get_print_format (var);
1530 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1532 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1533 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1537 tab_value (table, c, r, opt, v, var, print);
1541 /* Draws a line across TABLE at the current row to indicate the most
1542 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1543 that changed, and puts the values that changed into the table. TB
1544 and PT must be the corresponding table_entry and crosstab,
1547 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1548 struct tab_table *table, int first_difference)
1550 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1552 for (; first_difference >= 2; first_difference--)
1553 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1554 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1555 pt->vars[first_difference]);
1558 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1559 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1560 additionally suffixed with a letter `M'. */
1562 format_cell_entry (struct tab_table *table, int c, int r, double value,
1563 char suffix, bool mark_missing, const struct dictionary *dict)
1571 s = data_out (&v, dict_get_encoding (dict), settings_get_format ());
1575 suffixes[suffix_len++] = suffix;
1577 suffixes[suffix_len++] = 'M';
1578 suffixes[suffix_len] = '\0';
1580 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1581 s + strspn (s, " "), suffixes);
1586 /* Displays the crosstabulation table. */
1588 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1589 struct tab_table *table)
1595 for (r = 0; r < pt->n_rows; r++)
1596 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1597 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1600 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1601 TAB_LEFT, _("Total"));
1603 /* Put in the actual cells. */
1605 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1606 for (r = 0; r < pt->n_rows; r++)
1608 if (proc->n_cells > 1)
1609 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1610 for (c = 0; c < pt->n_cols; c++)
1612 bool mark_missing = false;
1613 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1614 if (proc->exclude == MV_NEVER
1615 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1616 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1618 mark_missing = true;
1619 for (i = 0; i < proc->n_cells; i++)
1624 switch (proc->a_cells[i])
1630 v = *mp / pt->row_tot[r] * 100.;
1634 v = *mp / pt->col_tot[c] * 100.;
1638 v = *mp / pt->total * 100.;
1641 case CRS_CL_EXPECTED:
1644 case CRS_CL_RESIDUAL:
1645 v = *mp - expected_value;
1647 case CRS_CL_SRESIDUAL:
1648 v = (*mp - expected_value) / sqrt (expected_value);
1650 case CRS_CL_ASRESIDUAL:
1651 v = ((*mp - expected_value)
1652 / sqrt (expected_value
1653 * (1. - pt->row_tot[r] / pt->total)
1654 * (1. - pt->col_tot[c] / pt->total)));
1659 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1665 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1669 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1670 for (r = 0; r < pt->n_rows; r++)
1672 bool mark_missing = false;
1674 if (proc->exclude == MV_NEVER
1675 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1676 mark_missing = true;
1678 for (i = 0; i < proc->n_cells; i++)
1683 switch (proc->a_cells[i])
1693 v = pt->row_tot[r] / pt->total * 100.;
1697 v = pt->row_tot[r] / pt->total * 100.;
1700 case CRS_CL_EXPECTED:
1701 case CRS_CL_RESIDUAL:
1702 case CRS_CL_SRESIDUAL:
1703 case CRS_CL_ASRESIDUAL:
1710 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1711 tab_next_row (table);
1715 /* Column totals, grand total. */
1717 if (proc->n_cells > 1)
1718 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1719 for (c = 0; c <= pt->n_cols; c++)
1721 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1722 bool mark_missing = false;
1725 if (proc->exclude == MV_NEVER && c < pt->n_cols
1726 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1727 mark_missing = true;
1729 for (i = 0; i < proc->n_cells; i++)
1734 switch (proc->a_cells[i])
1740 v = ct / pt->total * 100.;
1748 v = ct / pt->total * 100.;
1751 case CRS_CL_EXPECTED:
1752 case CRS_CL_RESIDUAL:
1753 case CRS_CL_SRESIDUAL:
1754 case CRS_CL_ASRESIDUAL:
1760 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1765 tab_offset (table, -1, tab_row (table) + last_row);
1766 tab_offset (table, 0, -1);
1769 static void calc_r (struct pivot_table *,
1770 double *PT, double *Y, double *, double *, double *);
1771 static void calc_chisq (struct pivot_table *,
1772 double[N_CHISQ], int[N_CHISQ], double *, double *);
1774 /* Display chi-square statistics. */
1776 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1777 bool *showed_fisher)
1779 static const char *chisq_stats[N_CHISQ] =
1781 N_("Pearson Chi-Square"),
1782 N_("Likelihood Ratio"),
1783 N_("Fisher's Exact Test"),
1784 N_("Continuity Correction"),
1785 N_("Linear-by-Linear Association"),
1787 double chisq_v[N_CHISQ];
1788 double fisher1, fisher2;
1793 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1795 tab_offset (chisq, pt->n_consts + pt->n_vars - 2, -1);
1797 for (i = 0; i < N_CHISQ; i++)
1799 if ((i != 2 && chisq_v[i] == SYSMIS)
1800 || (i == 2 && fisher1 == SYSMIS))
1803 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1806 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL, RC_OTHER);
1807 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], NULL, RC_WEIGHT);
1808 tab_double (chisq, 3, 0, TAB_RIGHT,
1809 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL, RC_PVALUE);
1813 *showed_fisher = true;
1814 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL, RC_PVALUE);
1815 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL, RC_PVALUE);
1817 tab_next_row (chisq);
1820 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1821 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1822 tab_next_row (chisq);
1824 tab_offset (chisq, 0, -1);
1827 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1828 double[N_SYMMETRIC], double[N_SYMMETRIC],
1829 double[N_SYMMETRIC],
1830 double[3], double[3], double[3]);
1832 /* Display symmetric measures. */
1834 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1835 struct tab_table *sym)
1837 static const char *categories[] =
1839 N_("Nominal by Nominal"),
1840 N_("Ordinal by Ordinal"),
1841 N_("Interval by Interval"),
1842 N_("Measure of Agreement"),
1845 static const char *stats[N_SYMMETRIC] =
1849 N_("Contingency Coefficient"),
1850 N_("Kendall's tau-b"),
1851 N_("Kendall's tau-c"),
1853 N_("Spearman Correlation"),
1858 static const int stats_categories[N_SYMMETRIC] =
1860 0, 0, 0, 1, 1, 1, 1, 2, 3,
1864 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1865 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1868 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1869 somers_d_v, somers_d_ase, somers_d_t))
1872 tab_offset (sym, pt->n_consts + pt->n_vars - 2, -1);
1874 for (i = 0; i < N_SYMMETRIC; i++)
1876 if (sym_v[i] == SYSMIS)
1879 if (stats_categories[i] != last_cat)
1881 last_cat = stats_categories[i];
1882 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1885 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1886 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL, RC_OTHER);
1887 if (sym_ase[i] != SYSMIS)
1888 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL, RC_OTHER);
1889 if (sym_t[i] != SYSMIS)
1890 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL, RC_OTHER);
1891 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL, RC_PVALUE);*/
1895 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1896 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1899 tab_offset (sym, 0, -1);
1902 static int calc_risk (struct pivot_table *,
1903 double[], double[], double[], union value *);
1905 /* Display risk estimate. */
1907 display_risk (struct pivot_table *pt, struct tab_table *risk)
1910 double risk_v[3], lower[3], upper[3];
1914 if (!calc_risk (pt, risk_v, upper, lower, c))
1917 tab_offset (risk, pt->n_consts + pt->n_vars - 2, -1);
1919 for (i = 0; i < 3; i++)
1921 const struct variable *cv = pt->vars[COL_VAR];
1922 const struct variable *rv = pt->vars[ROW_VAR];
1923 int cvw = var_get_width (cv);
1924 int rvw = var_get_width (rv);
1926 if (risk_v[i] == SYSMIS)
1932 if (var_is_numeric (cv))
1933 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1934 var_to_string (cv), c[0].f, c[1].f);
1936 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1938 cvw, value_str (&c[0], cvw),
1939 cvw, value_str (&c[1], cvw));
1943 if (var_is_numeric (rv))
1944 sprintf (buf, _("For cohort %s = %.*g"),
1945 var_to_string (rv), DBL_DIG + 1, pt->rows[i - 1].f);
1947 sprintf (buf, _("For cohort %s = %.*s"),
1949 rvw, value_str (&pt->rows[i - 1], rvw));
1953 tab_text (risk, 0, 0, TAB_LEFT, buf);
1954 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL, RC_OTHER);
1955 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL, RC_OTHER);
1956 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL, RC_OTHER);
1957 tab_next_row (risk);
1960 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1961 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1962 tab_next_row (risk);
1964 tab_offset (risk, 0, -1);
1967 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1968 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1969 double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
1971 /* Display directional measures. */
1973 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1974 struct tab_table *direct)
1976 static const char *categories[] =
1978 N_("Nominal by Nominal"),
1979 N_("Ordinal by Ordinal"),
1980 N_("Nominal by Interval"),
1983 static const char *stats[] =
1986 N_("Goodman and Kruskal tau"),
1987 N_("Uncertainty Coefficient"),
1992 static const char *types[] =
1999 static const int stats_categories[N_DIRECTIONAL] =
2001 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
2004 static const int stats_stats[N_DIRECTIONAL] =
2006 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2009 static const int stats_types[N_DIRECTIONAL] =
2011 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2014 static const int *stats_lookup[] =
2021 static const char **stats_names[] =
2033 double direct_v[N_DIRECTIONAL];
2034 double direct_ase[N_DIRECTIONAL];
2035 double direct_t[N_DIRECTIONAL];
2036 double sig[N_DIRECTIONAL];
2040 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t, sig))
2043 tab_offset (direct, pt->n_consts + pt->n_vars - 2, -1);
2045 for (i = 0; i < N_DIRECTIONAL; i++)
2047 if (direct_v[i] == SYSMIS)
2053 for (j = 0; j < 3; j++)
2054 if (last[j] != stats_lookup[j][i])
2057 tab_hline (direct, TAL_1, j, 6, 0);
2062 int k = last[j] = stats_lookup[j][i];
2067 string = var_to_string (pt->vars[0]);
2069 string = var_to_string (pt->vars[1]);
2071 tab_text_format (direct, j, 0, TAB_LEFT,
2072 gettext (stats_names[j][k]), string);
2077 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL, RC_OTHER);
2078 if (direct_ase[i] != SYSMIS)
2079 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL, RC_OTHER);
2080 if (direct_t[i] != SYSMIS)
2081 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL, RC_OTHER);
2082 tab_double (direct, 6, 0, TAB_RIGHT, sig[i], NULL, RC_PVALUE);
2083 tab_next_row (direct);
2086 tab_offset (direct, 0, -1);
2089 /* Statistical calculations. */
2091 /* Returns the value of the logarithm of gamma (factorial) function for an integer
2094 log_gamma_int (double pt)
2099 for (i = 2; i < pt; i++)
2105 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2107 static inline double
2108 Pr (int a, int b, int c, int d)
2110 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
2111 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
2112 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
2113 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
2114 - log_gamma_int (a + b + c + d + 1.));
2117 /* Swap the contents of A and B. */
2119 swap (int *a, int *b)
2126 /* Calculate significance for Fisher's exact test as specified in
2127 _SPSS Statistical Algorithms_, Appendix 5. */
2129 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2134 if (MIN (c, d) < MIN (a, b))
2135 swap (&a, &c), swap (&b, &d);
2136 if (MIN (b, d) < MIN (a, c))
2137 swap (&a, &b), swap (&c, &d);
2141 swap (&a, &b), swap (&c, &d);
2143 swap (&a, &c), swap (&b, &d);
2146 pn1 = Pr (a, b, c, d);
2148 for (pt = 1; pt <= a; pt++)
2150 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2153 *fisher2 = *fisher1;
2155 for (pt = 1; pt <= b; pt++)
2157 double p = Pr (a + pt, b - pt, c - pt, d + pt);
2163 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2164 columns with values COLS and N_ROWS rows with values ROWS. Values
2165 in the matrix sum to pt->total. */
2167 calc_chisq (struct pivot_table *pt,
2168 double chisq[N_CHISQ], int df[N_CHISQ],
2169 double *fisher1, double *fisher2)
2173 chisq[0] = chisq[1] = 0.;
2174 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2175 *fisher1 = *fisher2 = SYSMIS;
2177 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2179 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2181 chisq[0] = chisq[1] = SYSMIS;
2185 for (r = 0; r < pt->n_rows; r++)
2186 for (c = 0; c < pt->n_cols; c++)
2188 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2189 const double freq = pt->mat[pt->n_cols * r + c];
2190 const double residual = freq - expected;
2192 chisq[0] += residual * residual / expected;
2194 chisq[1] += freq * log (expected / freq);
2205 /* Calculate Yates and Fisher exact test. */
2206 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2208 double f11, f12, f21, f22;
2214 for (i = j = 0; i < pt->n_cols; i++)
2215 if (pt->col_tot[i] != 0.)
2224 f11 = pt->mat[nz_cols[0]];
2225 f12 = pt->mat[nz_cols[1]];
2226 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2227 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2232 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2235 chisq[3] = (pt->total * pow2 (pt_)
2236 / (f11 + f12) / (f21 + f22)
2237 / (f11 + f21) / (f12 + f22));
2245 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2248 /* Calculate Mantel-Haenszel. */
2249 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2251 double r, ase_0, ase_1;
2252 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2254 chisq[4] = (pt->total - 1.) * r * r;
2259 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2260 T, and standard error into ERROR. The row and column values must be
2261 passed in PT and Y. */
2263 calc_r (struct pivot_table *pt,
2264 double *PT, double *Y, double *r, double *t, double *error)
2266 double SX, SY, S, T;
2268 double sum_XYf, sum_X2Y2f;
2269 double sum_Xr, sum_X2r;
2270 double sum_Yc, sum_Y2c;
2273 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2274 for (j = 0; j < pt->n_cols; j++)
2276 double fij = pt->mat[j + i * pt->n_cols];
2277 double product = PT[i] * Y[j];
2278 double temp = fij * product;
2280 sum_X2Y2f += temp * product;
2283 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2285 sum_Xr += PT[i] * pt->row_tot[i];
2286 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2288 Xbar = sum_Xr / pt->total;
2290 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2292 sum_Yc += Y[i] * pt->col_tot[i];
2293 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2295 Ybar = sum_Yc / pt->total;
2297 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2298 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2299 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2302 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (pt->total - 2);
2307 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2308 for (j = 0; j < pt->n_cols; j++)
2310 double Xresid, Yresid;
2313 Xresid = PT[i] - Xbar;
2314 Yresid = Y[j] - Ybar;
2315 temp = (T * Xresid * Yresid
2317 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2318 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2323 *error = sqrt (s) / (T * T);
2327 /* Calculate symmetric statistics and their asymptotic standard
2328 errors. Returns 0 if none could be calculated. */
2330 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2331 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2332 double t[N_SYMMETRIC],
2333 double somers_d_v[3], double somers_d_ase[3],
2334 double somers_d_t[3])
2338 q = MIN (pt->ns_rows, pt->ns_cols);
2342 for (i = 0; i < N_SYMMETRIC; i++)
2343 v[i] = ase[i] = t[i] = SYSMIS;
2345 /* Phi, Cramer's V, contingency coefficient. */
2346 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2348 double Xp = 0.; /* Pearson chi-square. */
2351 for (r = 0; r < pt->n_rows; r++)
2352 for (c = 0; c < pt->n_cols; c++)
2354 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2355 const double freq = pt->mat[pt->n_cols * r + c];
2356 const double residual = freq - expected;
2358 Xp += residual * residual / expected;
2361 if (proc->statistics & (1u << CRS_ST_PHI))
2363 v[0] = sqrt (Xp / pt->total);
2364 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2366 if (proc->statistics & (1u << CRS_ST_CC))
2367 v[2] = sqrt (Xp / (Xp + pt->total));
2370 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2371 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2376 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2380 Dr = Dc = pow2 (pt->total);
2381 for (r = 0; r < pt->n_rows; r++)
2382 Dr -= pow2 (pt->row_tot[r]);
2383 for (c = 0; c < pt->n_cols; c++)
2384 Dc -= pow2 (pt->col_tot[c]);
2386 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2387 for (c = 0; c < pt->n_cols; c++)
2391 for (r = 0; r < pt->n_rows; r++)
2392 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2401 for (i = 0; i < pt->n_rows; i++)
2405 for (j = 1; j < pt->n_cols; j++)
2406 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2409 for (j = 1; j < pt->n_cols; j++)
2410 Dij += cum[j + (i - 1) * pt->n_cols];
2414 double fij = pt->mat[j + i * pt->n_cols];
2418 if (++j == pt->n_cols)
2420 assert (j < pt->n_cols);
2422 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2423 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2427 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2428 Dij -= cum[j + (i - 1) * pt->n_cols];
2434 if (proc->statistics & (1u << CRS_ST_BTAU))
2435 v[3] = (P - Q) / sqrt (Dr * Dc);
2436 if (proc->statistics & (1u << CRS_ST_CTAU))
2437 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2438 if (proc->statistics & (1u << CRS_ST_GAMMA))
2439 v[5] = (P - Q) / (P + Q);
2441 /* ASE for tau-b, tau-c, gamma. Calculations could be
2442 eliminated here, at expense of memory. */
2447 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2448 for (i = 0; i < pt->n_rows; i++)
2452 for (j = 1; j < pt->n_cols; j++)
2453 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2456 for (j = 1; j < pt->n_cols; j++)
2457 Dij += cum[j + (i - 1) * pt->n_cols];
2461 double fij = pt->mat[j + i * pt->n_cols];
2463 if (proc->statistics & (1u << CRS_ST_BTAU))
2465 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2466 + v[3] * (pt->row_tot[i] * Dc
2467 + pt->col_tot[j] * Dr));
2468 btau_cum += fij * temp * temp;
2472 const double temp = Cij - Dij;
2473 ctau_cum += fij * temp * temp;
2476 if (proc->statistics & (1u << CRS_ST_GAMMA))
2478 const double temp = Q * Cij - P * Dij;
2479 gamma_cum += fij * temp * temp;
2482 if (proc->statistics & (1u << CRS_ST_D))
2484 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2485 - (P - Q) * (pt->total - pt->row_tot[i]));
2486 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2487 - (Q - P) * (pt->total - pt->col_tot[j]));
2490 if (++j == pt->n_cols)
2492 assert (j < pt->n_cols);
2494 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2495 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2499 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2500 Dij -= cum[j + (i - 1) * pt->n_cols];
2506 btau_var = ((btau_cum
2507 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2509 if (proc->statistics & (1u << CRS_ST_BTAU))
2511 ase[3] = sqrt (btau_var);
2512 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2515 if (proc->statistics & (1u << CRS_ST_CTAU))
2517 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2518 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2519 t[4] = v[4] / ase[4];
2521 if (proc->statistics & (1u << CRS_ST_GAMMA))
2523 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2524 t[5] = v[5] / (2. / (P + Q)
2525 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2527 if (proc->statistics & (1u << CRS_ST_D))
2529 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2530 somers_d_ase[0] = SYSMIS;
2531 somers_d_t[0] = (somers_d_v[0]
2533 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2534 somers_d_v[1] = (P - Q) / Dc;
2535 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2536 somers_d_t[1] = (somers_d_v[1]
2538 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2539 somers_d_v[2] = (P - Q) / Dr;
2540 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2541 somers_d_t[2] = (somers_d_v[2]
2543 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2549 /* Spearman correlation, Pearson's r. */
2550 if (proc->statistics & (1u << CRS_ST_CORR))
2552 double *R = xmalloc (sizeof *R * pt->n_rows);
2553 double *C = xmalloc (sizeof *C * pt->n_cols);
2556 double y, t, c = 0., s = 0.;
2561 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2562 y = pt->row_tot[i] - c;
2566 if (++i == pt->n_rows)
2568 assert (i < pt->n_rows);
2573 double y, t, c = 0., s = 0.;
2578 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2579 y = pt->col_tot[j] - c;
2583 if (++j == pt->n_cols)
2585 assert (j < pt->n_cols);
2589 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2594 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2597 /* Cohen's kappa. */
2598 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2600 double ase_under_h0;
2601 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2604 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2605 i < pt->ns_rows; i++, j++)
2609 while (pt->col_tot[j] == 0.)
2612 prod = pt->row_tot[i] * pt->col_tot[j];
2613 sum = pt->row_tot[i] + pt->col_tot[j];
2615 sum_fii += pt->mat[j + i * pt->n_cols];
2617 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2618 sum_riciri_ci += prod * sum;
2620 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2621 for (j = 0; j < pt->ns_cols; j++)
2623 double sum = pt->row_tot[i] + pt->col_tot[j];
2624 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2627 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2629 ase_under_h0 = sqrt ((pow2 (pt->total) * sum_rici
2630 + sum_rici * sum_rici
2631 - pt->total * sum_riciri_ci)
2632 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2634 ase[8] = sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2635 / pow2 (pow2 (pt->total) - sum_rici))
2636 + ((2. * (pt->total - sum_fii)
2637 * (2. * sum_fii * sum_rici
2638 - pt->total * sum_fiiri_ci))
2639 / pow3 (pow2 (pt->total) - sum_rici))
2640 + (pow2 (pt->total - sum_fii)
2641 * (pt->total * sum_fijri_ci2 - 4.
2642 * sum_rici * sum_rici)
2643 / pow4 (pow2 (pt->total) - sum_rici))));
2645 t[8] = v[8] / ase_under_h0;
2651 /* Calculate risk estimate. */
2653 calc_risk (struct pivot_table *pt,
2654 double *value, double *upper, double *lower, union value *c)
2656 double f11, f12, f21, f22;
2662 for (i = 0; i < 3; i++)
2663 value[i] = upper[i] = lower[i] = SYSMIS;
2666 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2673 for (i = j = 0; i < pt->n_cols; i++)
2674 if (pt->col_tot[i] != 0.)
2683 f11 = pt->mat[nz_cols[0]];
2684 f12 = pt->mat[nz_cols[1]];
2685 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2686 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2688 c[0] = pt->cols[nz_cols[0]];
2689 c[1] = pt->cols[nz_cols[1]];
2692 value[0] = (f11 * f22) / (f12 * f21);
2693 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2694 lower[0] = value[0] * exp (-1.960 * v);
2695 upper[0] = value[0] * exp (1.960 * v);
2697 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2698 v = sqrt ((f12 / (f11 * (f11 + f12)))
2699 + (f22 / (f21 * (f21 + f22))));
2700 lower[1] = value[1] * exp (-1.960 * v);
2701 upper[1] = value[1] * exp (1.960 * v);
2703 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2704 v = sqrt ((f11 / (f12 * (f11 + f12)))
2705 + (f21 / (f22 * (f21 + f22))));
2706 lower[2] = value[2] * exp (-1.960 * v);
2707 upper[2] = value[2] * exp (1.960 * v);
2712 /* Calculate directional measures. */
2714 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2715 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2716 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
2721 for (i = 0; i < N_DIRECTIONAL; i++)
2722 v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
2726 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2728 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2729 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2730 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2731 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2732 double sum_fim, sum_fmj;
2734 int rm_index, cm_index;
2737 /* Find maximum for each row and their sum. */
2738 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2740 double max = pt->mat[i * pt->n_cols];
2743 for (j = 1; j < pt->n_cols; j++)
2744 if (pt->mat[j + i * pt->n_cols] > max)
2746 max = pt->mat[j + i * pt->n_cols];
2750 sum_fim += fim[i] = max;
2751 fim_index[i] = index;
2754 /* Find maximum for each column. */
2755 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2757 double max = pt->mat[j];
2760 for (i = 1; i < pt->n_rows; i++)
2761 if (pt->mat[j + i * pt->n_cols] > max)
2763 max = pt->mat[j + i * pt->n_cols];
2767 sum_fmj += fmj[j] = max;
2768 fmj_index[j] = index;
2771 /* Find maximum row total. */
2772 rm = pt->row_tot[0];
2774 for (i = 1; i < pt->n_rows; i++)
2775 if (pt->row_tot[i] > rm)
2777 rm = pt->row_tot[i];
2781 /* Find maximum column total. */
2782 cm = pt->col_tot[0];
2784 for (j = 1; j < pt->n_cols; j++)
2785 if (pt->col_tot[j] > cm)
2787 cm = pt->col_tot[j];
2791 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2792 v[1] = (sum_fmj - rm) / (pt->total - rm);
2793 v[2] = (sum_fim - cm) / (pt->total - cm);
2795 /* ASE1 for Y given PT. */
2800 for (i = 0; i < pt->n_rows; i++)
2801 if (cm_index == fim_index[i])
2803 ase[2] = sqrt ((pt->total - sum_fim) * (sum_fim + cm - 2. * accum)
2804 / pow3 (pt->total - cm));
2807 /* ASE0 for Y given PT. */
2811 for (accum = 0., i = 0; i < pt->n_rows; i++)
2812 if (cm_index != fim_index[i])
2813 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2814 + pt->mat[i * pt->n_cols + cm_index]);
2815 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2818 /* ASE1 for PT given Y. */
2823 for (j = 0; j < pt->n_cols; j++)
2824 if (rm_index == fmj_index[j])
2826 ase[1] = sqrt ((pt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
2827 / pow3 (pt->total - rm));
2830 /* ASE0 for PT given Y. */
2834 for (accum = 0., j = 0; j < pt->n_cols; j++)
2835 if (rm_index != fmj_index[j])
2836 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2837 + pt->mat[j + pt->n_cols * rm_index]);
2838 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2841 /* Symmetric ASE0 and ASE1. */
2846 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2847 for (j = 0; j < pt->n_cols; j++)
2849 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2850 int temp1 = (i == rm_index) + (j == cm_index);
2851 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2852 accum1 += (pt->mat[j + i * pt->n_cols]
2853 * pow2 (temp0 + (v[0] - 1.) * temp1));
2855 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2856 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / pt->total)
2857 / (2. * pt->total - rm - cm));
2860 for (i = 0; i < 3; i++)
2861 sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
2870 double sum_fij2_ri, sum_fij2_ci;
2871 double sum_ri2, sum_cj2;
2873 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2874 for (j = 0; j < pt->n_cols; j++)
2876 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2877 sum_fij2_ri += temp / pt->row_tot[i];
2878 sum_fij2_ci += temp / pt->col_tot[j];
2881 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2882 sum_ri2 += pow2 (pt->row_tot[i]);
2884 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2885 sum_cj2 += pow2 (pt->col_tot[j]);
2887 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2888 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2892 if (proc->statistics & (1u << CRS_ST_UC))
2894 double UX, UY, UXY, P;
2895 double ase1_yx, ase1_xy, ase1_sym;
2898 for (UX = 0., i = 0; i < pt->n_rows; i++)
2899 if (pt->row_tot[i] > 0.)
2900 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2902 for (UY = 0., j = 0; j < pt->n_cols; j++)
2903 if (pt->col_tot[j] > 0.)
2904 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2906 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2907 for (j = 0; j < pt->n_cols; j++)
2909 double entry = pt->mat[j + i * pt->n_cols];
2914 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2915 UXY -= entry / pt->total * log (entry / pt->total);
2918 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2919 for (j = 0; j < pt->n_cols; j++)
2921 double entry = pt->mat[j + i * pt->n_cols];
2926 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2927 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2928 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2929 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2930 ase1_sym += entry * pow2 ((UXY
2931 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2932 - (UX + UY) * log (entry / pt->total));
2935 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2936 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2939 v[6] = (UX + UY - UXY) / UX;
2940 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2941 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2943 v[7] = (UX + UY - UXY) / UY;
2944 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2945 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2949 if (proc->statistics & (1u << CRS_ST_D))
2951 double v_dummy[N_SYMMETRIC];
2952 double ase_dummy[N_SYMMETRIC];
2953 double t_dummy[N_SYMMETRIC];
2954 double somers_d_v[3];
2955 double somers_d_ase[3];
2956 double somers_d_t[3];
2958 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2959 somers_d_v, somers_d_ase, somers_d_t))
2962 for (i = 0; i < 3; i++)
2964 v[8 + i] = somers_d_v[i];
2965 ase[8 + i] = somers_d_ase[i];
2966 t[8 + i] = somers_d_t[i];
2967 sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
2973 if (proc->statistics & (1u << CRS_ST_ETA))
2976 double sum_Xr, sum_X2r;
2980 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2982 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2983 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2985 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2987 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2991 for (cum = 0., i = 0; i < pt->n_rows; i++)
2993 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2994 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2997 SXW -= cum * cum / pt->col_tot[j];
2999 v[11] = sqrt (1. - SXW / SX);
3003 double sum_Yc, sum_Y2c;
3007 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
3009 sum_Yc += pt->cols[i].f * pt->col_tot[i];
3010 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
3012 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3014 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3018 for (cum = 0., j = 0; j < pt->n_cols; j++)
3020 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3021 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3024 SYW -= cum * cum / pt->row_tot[i];
3026 v[12] = sqrt (1. - SYW / SY);