1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 - Pearson's R (but not Spearman!) is off a little.
20 - T values for Spearman's R and Pearson's R are wrong.
21 - How to calculate significance of symmetric and directional measures?
22 - Asymmetric ASEs and T values for lambda are wrong.
23 - ASE of Goodman and Kruskal's tau is not calculated.
24 - ASE of symmetric somers' d is wrong.
25 - Approx. T of uncertainty coefficient is wrong.
32 #include <gsl/gsl_cdf.h>
36 #include <data/case.h>
37 #include <data/casegrouper.h>
38 #include <data/casereader.h>
39 #include <data/data-out.h>
40 #include <data/dictionary.h>
41 #include <data/format.h>
42 #include <data/procedure.h>
43 #include <data/value-labels.h>
44 #include <data/variable.h>
45 #include <language/command.h>
46 #include <language/dictionary/split-file.h>
47 #include <language/lexer/lexer.h>
48 #include <language/lexer/variable-parser.h>
49 #include <libpspp/array.h>
50 #include <libpspp/assertion.h>
51 #include <libpspp/compiler.h>
52 #include <libpspp/hash.h>
53 #include <libpspp/hmap.h>
54 #include <libpspp/hmapx.h>
55 #include <libpspp/message.h>
56 #include <libpspp/misc.h>
57 #include <libpspp/pool.h>
58 #include <libpspp/str.h>
59 #include <output/tab.h>
66 #define _(msgid) gettext (msgid)
67 #define N_(msgid) msgid
75 missing=miss:!table/include/report;
76 +write[wr_]=none,cells,all;
77 +format=fmt:!labels/nolabels/novallabs,
80 tabl:!tables/notables,
83 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
85 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
91 /* Number of chi-square statistics. */
94 /* Number of symmetric statistics. */
97 /* Number of directional statistics. */
98 #define N_DIRECTIONAL 13
100 /* A single table entry for general mode. */
103 struct hmap_node node; /* Entry in hash table. */
104 double freq; /* Frequency count. */
105 union value values[1]; /* Values. */
109 table_entry_size (size_t n_values)
111 return (offsetof (struct table_entry, values)
112 + n_values * sizeof (union value));
115 /* Indexes into the 'vars' member of struct pivot_table and
116 struct crosstab member. */
119 ROW_VAR = 0, /* Row variable. */
120 COL_VAR = 1 /* Column variable. */
121 /* Higher indexes cause multiple tables to be output. */
124 /* A crosstabulation of 2 or more variables. */
127 struct fmt_spec weight_format; /* Format for weight variable. */
128 double missing; /* Weight of missing cases. */
130 /* Variables (2 or more). */
132 const struct variable **vars;
134 /* Constants (0 or more). */
136 const struct variable **const_vars;
137 union value *const_values;
141 struct table_entry **entries;
144 /* Column values, number of columns. */
148 /* Row values, number of rows. */
152 /* Number of statistically interesting columns/rows
153 (columns/rows with data in them). */
154 int ns_cols, ns_rows;
156 /* Matrix contents. */
157 double *mat; /* Matrix proper. */
158 double *row_tot; /* Row totals. */
159 double *col_tot; /* Column totals. */
160 double total; /* Grand total. */
163 /* Integer mode variable info. */
166 int min; /* Minimum value. */
167 int max; /* Maximum value + 1. */
168 int count; /* max - min. */
171 static inline struct var_range *
172 get_var_range (const struct variable *v)
174 return var_get_aux (v);
177 struct crosstabs_proc
179 const struct dictionary *dict;
180 enum { INTEGER, GENERAL } mode;
181 enum mv_class exclude;
184 struct fmt_spec weight_format;
186 /* Variables specifies on VARIABLES. */
187 const struct variable **variables;
191 struct pivot_table *pivots;
195 int n_cells; /* Number of cells requested. */
196 unsigned int cells; /* Bit k is 1 if cell k is requested. */
197 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
200 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
203 static bool should_tabulate_case (const struct pivot_table *,
204 const struct ccase *, enum mv_class exclude);
205 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
207 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
209 static void postcalc (struct crosstabs_proc *);
210 static void submit (struct pivot_table *, struct tab_table *);
212 /* Parses and executes the CROSSTABS procedure. */
214 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
216 const struct variable *wv = dict_get_weight (dataset_dict (ds));
217 struct crosstabs_proc proc;
218 struct casegrouper *grouper;
219 struct casereader *input, *group;
220 struct cmd_crosstabs cmd;
221 struct pivot_table *pt;
226 proc.dict = dataset_dict (ds);
227 proc.bad_warn = true;
228 proc.variables = NULL;
229 proc.n_variables = 0;
232 proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
234 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
236 result = CMD_FAILURE;
240 proc.mode = proc.n_variables ? INTEGER : GENERAL;
244 proc.cells = 1u << CRS_CL_COUNT;
245 else if (cmd.a_cells[CRS_CL_ALL])
246 proc.cells = UINT_MAX;
250 for (i = 0; i < CRS_CL_count; i++)
252 proc.cells |= 1u << i;
254 proc.cells = ((1u << CRS_CL_COUNT)
256 | (1u << CRS_CL_COLUMN)
257 | (1u << CRS_CL_TOTAL));
259 proc.cells &= ((1u << CRS_CL_count) - 1);
260 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
262 for (i = 0; i < CRS_CL_count; i++)
263 if (proc.cells & (1u << i))
264 proc.a_cells[proc.n_cells++] = i;
267 if (cmd.a_statistics[CRS_ST_ALL])
268 proc.statistics = UINT_MAX;
269 else if (cmd.sbc_statistics)
274 for (i = 0; i < CRS_ST_count; i++)
275 if (cmd.a_statistics[i])
276 proc.statistics |= 1u << i;
277 if (proc.statistics == 0)
278 proc.statistics |= 1u << CRS_ST_CHISQ;
284 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
285 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
287 if (proc.mode == GENERAL && proc.mode == MV_NEVER)
289 msg (SE, _("Missing mode REPORT not allowed in general mode. "
290 "Assuming MISSING=TABLE."));
295 proc.pivot = cmd.pivot == CRS_PIVOT;
297 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
299 grouper = casegrouper_create_splits (input, dataset_dict (ds));
300 while (casegrouper_get_next_group (grouper, &group))
304 /* Output SPLIT FILE variables. */
305 c = casereader_peek (group, 0);
308 output_split_file_values (ds, c);
312 /* Initialize hash tables. */
313 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
314 hmap_init (&pt->data);
317 for (; (c = casereader_read (group)) != NULL; case_unref (c))
318 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
320 double weight = dict_get_case_weight (dataset_dict (ds), c,
322 if (should_tabulate_case (pt, c, proc.exclude))
324 if (proc.mode == GENERAL)
325 tabulate_general_case (pt, c, weight);
327 tabulate_integer_case (pt, c, weight);
330 pt->missing += weight;
332 casereader_destroy (group);
337 ok = casegrouper_destroy (grouper);
338 ok = proc_commit (ds) && ok;
340 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
343 free (proc.variables);
344 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
347 free (pt->const_vars);
348 /* We must not call value_destroy on const_values because
349 it is a wild pointer; it never pointed to anything owned
352 The rest of the data was allocated and destroyed at a
353 lower level already. */
360 /* Parses the TABLES subcommand. */
362 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
363 struct cmd_crosstabs *cmd UNUSED, void *proc_)
365 struct crosstabs_proc *proc = proc_;
366 struct const_var_set *var_set;
368 const struct variable ***by = NULL;
370 size_t *by_nvar = NULL;
375 /* Ensure that this is a TABLES subcommand. */
376 if (!lex_match_id (lexer, "TABLES")
377 && (lex_token (lexer) != T_ID ||
378 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
379 && lex_token (lexer) != T_ALL)
381 lex_match (lexer, '=');
383 if (proc->variables != NULL)
384 var_set = const_var_set_create_from_array (proc->variables,
387 var_set = const_var_set_create_from_dict (dataset_dict (ds));
388 assert (var_set != NULL);
392 by = xnrealloc (by, n_by + 1, sizeof *by);
393 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
394 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
395 PV_NO_DUPLICATE | PV_NO_SCRATCH))
397 if (xalloc_oversized (nx, by_nvar[n_by]))
399 msg (SE, _("Too many cross-tabulation variables or dimensions."));
405 if (!lex_match (lexer, T_BY))
409 lex_error (lexer, _("expecting 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++];
425 pt->weight_format = proc->weight_format;
428 pt->vars = xmalloc (n_by * sizeof *pt->vars);
430 pt->const_vars = NULL;
431 pt->const_values = NULL;
433 for (j = 0; j < n_by; j++)
434 pt->vars[j] = by[j][by_iter[j]];
436 for (j = n_by - 1; j >= 0; j--)
438 if (++by_iter[j] < by_nvar[j])
447 /* All return paths lead here. */
448 for (i = 0; i < n_by; i++)
453 const_var_set_destroy (var_set);
458 /* Parses the VARIABLES subcommand. */
460 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
461 struct cmd_crosstabs *cmd UNUSED, void *proc_)
463 struct crosstabs_proc *proc = proc_;
466 msg (SE, _("VARIABLES must be specified before TABLES."));
470 lex_match (lexer, '=');
474 size_t orig_nv = proc->n_variables;
479 if (!parse_variables_const (lexer, dataset_dict (ds),
480 &proc->variables, &proc->n_variables,
481 (PV_APPEND | PV_NUMERIC
482 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
485 if (lex_token (lexer) != '(')
487 lex_error (lexer, "expecting `('");
492 if (!lex_force_int (lexer))
494 min = lex_integer (lexer);
497 lex_match (lexer, ',');
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_token (lexer) != ')')
512 lex_error (lexer, "expecting `)'");
517 for (i = orig_nv; i < proc->n_variables; i++)
519 struct var_range *vr = xmalloc (sizeof *vr);
522 vr->count = max - min + 1;
523 var_attach_aux (proc->variables[i], vr, var_dtor_free);
526 if (lex_token (lexer) == '/')
533 free (proc->variables);
534 proc->variables = NULL;
535 proc->n_variables = 0;
539 /* Data file processing. */
542 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
543 enum mv_class exclude)
546 for (j = 0; j < pt->n_vars; j++)
548 const struct variable *var = pt->vars[j];
549 struct var_range *range = get_var_range (var);
551 if (var_is_value_missing (var, case_data (c, var), exclude))
556 double num = case_num (c, var);
557 if (num < range->min || num > range->max)
565 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
568 struct table_entry *te;
573 for (j = 0; j < pt->n_vars; j++)
575 /* Throw away fractional parts of values. */
576 hash = hash_int (case_num (c, pt->vars[j]), hash);
579 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
581 for (j = 0; j < pt->n_vars; j++)
582 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
585 /* Found an existing entry. */
592 /* No existing entry. Create a new one. */
593 te = xmalloc (table_entry_size (pt->n_vars));
595 for (j = 0; j < pt->n_vars; j++)
596 te->values[j].f = (int) case_num (c, pt->vars[j]);
597 hmap_insert (&pt->data, &te->node, hash);
601 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
604 struct table_entry *te;
609 for (j = 0; j < pt->n_vars; j++)
611 const struct variable *var = pt->vars[j];
612 hash = value_hash (case_data (c, var), var_get_width (var), hash);
615 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
617 for (j = 0; j < pt->n_vars; j++)
619 const struct variable *var = pt->vars[j];
620 if (!value_equal (case_data (c, var), &te->values[j],
621 var_get_width (var)))
625 /* Found an existing entry. */
632 /* No existing entry. Create a new one. */
633 te = xmalloc (table_entry_size (pt->n_vars));
635 for (j = 0; j < pt->n_vars; j++)
637 const struct variable *var = pt->vars[j];
638 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
640 hmap_insert (&pt->data, &te->node, hash);
643 /* Post-data reading calculations. */
645 static int compare_table_entry_vars_3way (const struct table_entry *a,
646 const struct table_entry *b,
647 const struct pivot_table *pt,
649 static int compare_table_entry_3way (const void *ap_, const void *bp_,
651 static void enum_var_values (const struct pivot_table *, int var_idx,
652 union value **valuesp, int *n_values);
653 static void output_pivot_table (struct crosstabs_proc *,
654 struct pivot_table *);
655 static void make_pivot_table_subset (struct pivot_table *pt,
656 size_t row0, size_t row1,
657 struct pivot_table *subset);
658 static void make_summary_table (struct crosstabs_proc *);
659 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
662 postcalc (struct crosstabs_proc *proc)
664 struct pivot_table *pt;
666 /* Convert hash tables into sorted arrays of entries. */
667 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
669 struct table_entry *e;
672 pt->n_entries = hmap_count (&pt->data);
673 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
675 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
676 pt->entries[i++] = e;
677 hmap_destroy (&pt->data);
679 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
680 compare_table_entry_3way, pt);
683 make_summary_table (proc);
685 /* Output each pivot table. */
686 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
688 if (proc->pivot || pt->n_vars == 2)
689 output_pivot_table (proc, pt);
692 size_t row0 = 0, row1 = 0;
693 while (find_crosstab (pt, &row0, &row1))
695 struct pivot_table subset;
696 make_pivot_table_subset (pt, row0, row1, &subset);
697 output_pivot_table (proc, &subset);
702 /* Free output and prepare for next split file. */
703 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
709 /* Free only the members that were allocated in this
710 function. The other pointer members are either both
711 allocated and destroyed at a lower level (in
712 output_pivot_table), or both allocated and destroyed at
713 a higher level (in crs_custom_tables and free_proc,
715 for (i = 0; i < pt->n_entries; i++)
716 free (pt->entries[i]);
722 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
723 struct pivot_table *subset)
728 assert (pt->n_consts == 0);
729 subset->missing = pt->missing;
731 subset->vars = pt->vars;
732 subset->n_consts = pt->n_vars - 2;
733 subset->const_vars = pt->vars + 2;
734 subset->const_values = &pt->entries[row0]->values[2];
736 subset->entries = &pt->entries[row0];
737 subset->n_entries = row1 - row0;
741 compare_table_entry_var_3way (const struct table_entry *a,
742 const struct table_entry *b,
743 const struct pivot_table *pt,
746 return value_compare_3way (&a->values[idx], &b->values[idx],
747 var_get_width (pt->vars[idx]));
751 compare_table_entry_vars_3way (const struct table_entry *a,
752 const struct table_entry *b,
753 const struct pivot_table *pt,
758 for (i = idx1 - 1; i >= idx0; i--)
760 int cmp = compare_table_entry_var_3way (a, b, pt, i);
767 /* Compare the struct table_entry at *AP to the one at *BP and
768 return a strcmp()-type result. */
770 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
772 const struct table_entry *const *ap = ap_;
773 const struct table_entry *const *bp = bp_;
774 const struct table_entry *a = *ap;
775 const struct table_entry *b = *bp;
776 const struct pivot_table *pt = pt_;
779 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
783 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
787 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
791 find_first_difference (const struct pivot_table *pt, size_t row)
794 return pt->n_vars - 1;
797 const struct table_entry *a = pt->entries[row];
798 const struct table_entry *b = pt->entries[row - 1];
801 for (col = pt->n_vars - 1; col >= 0; col--)
802 if (compare_table_entry_var_3way (a, b, pt, col))
808 /* Output a table summarizing the cases processed. */
810 make_summary_table (struct crosstabs_proc *proc)
812 struct tab_table *summary;
813 struct pivot_table *pt;
817 summary = tab_create (7, 3 + proc->n_pivots);
818 tab_title (summary, _("Summary."));
819 tab_headers (summary, 1, 0, 3, 0);
820 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
821 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
822 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
823 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
824 tab_hline (summary, TAL_1, 1, 6, 1);
825 tab_hline (summary, TAL_1, 1, 6, 2);
826 tab_vline (summary, TAL_1, 3, 1, 1);
827 tab_vline (summary, TAL_1, 5, 1, 1);
828 for (i = 0; i < 3; i++)
830 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
831 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
833 tab_offset (summary, 0, 3);
835 ds_init_empty (&name);
836 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
842 tab_hline (summary, TAL_1, 0, 6, 0);
845 for (i = 0; i < pt->n_vars; i++)
848 ds_put_cstr (&name, " * ");
849 ds_put_cstr (&name, var_to_string (pt->vars[i]));
851 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
854 for (i = 0; i < pt->n_entries; i++)
855 valid += pt->entries[i]->freq;
860 for (i = 0; i < 3; i++)
862 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
863 &proc->weight_format);
864 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
868 tab_next_row (summary);
872 submit (NULL, summary);
877 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
878 struct pivot_table *);
879 static struct tab_table *create_chisq_table (struct pivot_table *);
880 static struct tab_table *create_sym_table (struct pivot_table *);
881 static struct tab_table *create_risk_table (struct pivot_table *);
882 static struct tab_table *create_direct_table (struct pivot_table *);
883 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
884 struct tab_table *, int first_difference);
885 static void display_crosstabulation (struct crosstabs_proc *,
886 struct pivot_table *,
888 static void display_chisq (struct pivot_table *, struct tab_table *,
889 bool *showed_fisher);
890 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
892 static void display_risk (struct pivot_table *, struct tab_table *);
893 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
895 static void table_value_missing (struct crosstabs_proc *proc,
896 struct tab_table *table, int c, int r,
897 unsigned char opt, const union value *v,
898 const struct variable *var);
899 static void delete_missing (struct pivot_table *);
900 static void build_matrix (struct pivot_table *);
902 /* Output pivot table beginning at PB and continuing until PE,
903 exclusive. For efficiency, *MATP is a pointer to a matrix that can
904 hold *MAXROWS entries. */
906 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
908 struct tab_table *table = NULL; /* Crosstabulation table. */
909 struct tab_table *chisq = NULL; /* Chi-square table. */
910 bool showed_fisher = false;
911 struct tab_table *sym = NULL; /* Symmetric measures table. */
912 struct tab_table *risk = NULL; /* Risk estimate table. */
913 struct tab_table *direct = NULL; /* Directional measures table. */
916 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
919 table = create_crosstab_table (proc, pt);
920 if (proc->statistics & (1u << CRS_ST_CHISQ))
921 chisq = create_chisq_table (pt);
922 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
923 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
924 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
925 | (1u << CRS_ST_KAPPA)))
926 sym = create_sym_table (pt);
927 if (proc->statistics & (1u << CRS_ST_RISK))
928 risk = create_risk_table (pt);
929 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
930 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
931 direct = create_direct_table (pt);
934 while (find_crosstab (pt, &row0, &row1))
936 struct pivot_table x;
937 int first_difference;
939 make_pivot_table_subset (pt, row0, row1, &x);
941 /* Find all the row variable values. */
942 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
944 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
947 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
948 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
949 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
951 /* Allocate table space for the matrix. */
953 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
954 tab_realloc (table, -1,
955 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
956 tab_nr (table) * pt->n_entries / x.n_entries));
960 /* Find the first variable that differs from the last subtable. */
961 first_difference = find_first_difference (pt, row0);
964 display_dimensions (proc, &x, table, first_difference);
965 display_crosstabulation (proc, &x, table);
968 if (proc->exclude == MV_NEVER)
973 display_dimensions (proc, &x, chisq, first_difference);
974 display_chisq (&x, chisq, &showed_fisher);
978 display_dimensions (proc, &x, sym, first_difference);
979 display_symmetric (proc, &x, sym);
983 display_dimensions (proc, &x, risk, first_difference);
984 display_risk (&x, risk);
988 display_dimensions (proc, &x, direct, first_difference);
989 display_directional (proc, &x, direct);
992 /* Free the parts of x that are not owned by pt. In
993 particular we must not free x.cols, which is the same as
994 pt->cols, which is freed at the end of this function. */
1002 submit (NULL, table);
1007 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1013 submit (pt, direct);
1019 build_matrix (struct pivot_table *x)
1021 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1022 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1025 struct table_entry **p;
1029 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1031 const struct table_entry *te = *p;
1033 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1035 for (; col < x->n_cols; col++)
1041 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1048 if (++col >= x->n_cols)
1054 while (mp < &x->mat[x->n_cols * x->n_rows])
1056 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1058 /* Column totals, row totals, ns_rows. */
1060 for (col = 0; col < x->n_cols; col++)
1061 x->col_tot[col] = 0.0;
1062 for (row = 0; row < x->n_rows; row++)
1063 x->row_tot[row] = 0.0;
1065 for (row = 0; row < x->n_rows; row++)
1067 bool row_is_empty = true;
1068 for (col = 0; col < x->n_cols; col++)
1072 row_is_empty = false;
1073 x->col_tot[col] += *mp;
1074 x->row_tot[row] += *mp;
1081 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1085 for (col = 0; col < x->n_cols; col++)
1086 for (row = 0; row < x->n_rows; row++)
1087 if (x->mat[col + row * x->n_cols] != 0.0)
1095 for (col = 0; col < x->n_cols; col++)
1096 x->total += x->col_tot[col];
1099 static struct tab_table *
1100 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1107 static const struct tuple names[] =
1109 {CRS_CL_COUNT, N_("count")},
1110 {CRS_CL_ROW, N_("row %")},
1111 {CRS_CL_COLUMN, N_("column %")},
1112 {CRS_CL_TOTAL, N_("total %")},
1113 {CRS_CL_EXPECTED, N_("expected")},
1114 {CRS_CL_RESIDUAL, N_("residual")},
1115 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1116 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1118 const int n_names = sizeof names / sizeof *names;
1119 const struct tuple *t;
1121 struct tab_table *table;
1122 struct string title;
1123 struct pivot_table x;
1127 make_pivot_table_subset (pt, 0, 0, &x);
1129 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1130 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1131 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1133 /* First header line. */
1134 tab_joint_text (table, x.n_consts + 1, 0,
1135 (x.n_consts + 1) + (x.n_cols - 1), 0,
1136 TAB_CENTER | TAT_TITLE, var_get_name (x.vars[COL_VAR]));
1138 tab_hline (table, TAL_1, x.n_consts + 1,
1139 x.n_consts + 2 + x.n_cols - 2, 1);
1141 /* Second header line. */
1142 for (i = 2; i < x.n_consts + 2; i++)
1143 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1144 x.n_consts + 2 - i - 1, 1,
1145 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1146 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1147 var_get_name (x.vars[ROW_VAR]));
1148 for (i = 0; i < x.n_cols; i++)
1149 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1150 &x.cols[i], x.vars[COL_VAR]);
1151 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1153 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1154 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1157 ds_init_empty (&title);
1158 for (i = 0; i < x.n_consts + 2; i++)
1161 ds_put_cstr (&title, " * ");
1162 ds_put_cstr (&title, var_get_name (x.vars[i]));
1164 for (i = 0; i < pt->n_consts; i++)
1166 const struct variable *var = pt->const_vars[i];
1170 ds_put_format (&title, ", %s=", var_get_name (var));
1172 /* Insert the formatted value of the variable, then trim
1173 leading spaces in what was just inserted. */
1174 ofs = ds_length (&title);
1175 s = data_out (&pt->const_values[i], var_get_encoding (var),
1176 var_get_print_format (var));
1177 ds_put_cstr (&title, s);
1179 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1183 ds_put_cstr (&title, " [");
1185 for (t = names; t < &names[n_names]; t++)
1186 if (proc->cells & (1u << t->value))
1189 ds_put_cstr (&title, ", ");
1190 ds_put_cstr (&title, gettext (t->name));
1192 ds_put_cstr (&title, "].");
1194 tab_title (table, "%s", ds_cstr (&title));
1195 ds_destroy (&title);
1197 tab_offset (table, 0, 2);
1201 static struct tab_table *
1202 create_chisq_table (struct pivot_table *pt)
1204 struct tab_table *chisq;
1206 chisq = tab_create (6 + (pt->n_vars - 2),
1207 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1208 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1210 tab_title (chisq, _("Chi-square tests."));
1212 tab_offset (chisq, pt->n_vars - 2, 0);
1213 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1214 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1215 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1216 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1217 _("Asymp. Sig. (2-sided)"));
1218 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1219 _("Exact Sig. (2-sided)"));
1220 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1221 _("Exact Sig. (1-sided)"));
1222 tab_offset (chisq, 0, 1);
1227 /* Symmetric measures. */
1228 static struct tab_table *
1229 create_sym_table (struct pivot_table *pt)
1231 struct tab_table *sym;
1233 sym = tab_create (6 + (pt->n_vars - 2),
1234 pt->n_entries / pt->n_cols * 7 + 10);
1235 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1236 tab_title (sym, _("Symmetric measures."));
1238 tab_offset (sym, pt->n_vars - 2, 0);
1239 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1240 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1241 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1242 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1243 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1244 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1245 tab_offset (sym, 0, 1);
1250 /* Risk estimate. */
1251 static struct tab_table *
1252 create_risk_table (struct pivot_table *pt)
1254 struct tab_table *risk;
1256 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1257 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1258 tab_title (risk, _("Risk estimate."));
1260 tab_offset (risk, pt->n_vars - 2, 0);
1261 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1262 _("95%% Confidence Interval"));
1263 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1264 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1265 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1266 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1267 tab_hline (risk, TAL_1, 2, 3, 1);
1268 tab_vline (risk, TAL_1, 2, 0, 1);
1269 tab_offset (risk, 0, 2);
1274 /* Directional measures. */
1275 static struct tab_table *
1276 create_direct_table (struct pivot_table *pt)
1278 struct tab_table *direct;
1280 direct = tab_create (7 + (pt->n_vars - 2),
1281 pt->n_entries / pt->n_cols * 7 + 10);
1282 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1283 tab_title (direct, _("Directional measures."));
1285 tab_offset (direct, pt->n_vars - 2, 0);
1286 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1287 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1288 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1289 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1290 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1291 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1292 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1293 tab_offset (direct, 0, 1);
1299 /* Delete missing rows and columns for statistical analysis when
1302 delete_missing (struct pivot_table *pt)
1306 for (r = 0; r < pt->n_rows; r++)
1307 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1309 for (c = 0; c < pt->n_cols; c++)
1310 pt->mat[c + r * pt->n_cols] = 0.;
1315 for (c = 0; c < pt->n_cols; c++)
1316 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1318 for (r = 0; r < pt->n_rows; r++)
1319 pt->mat[c + r * pt->n_cols] = 0.;
1324 /* Prepare table T for submission, and submit it. */
1326 submit (struct pivot_table *pt, struct tab_table *t)
1333 tab_resize (t, -1, 0);
1334 if (tab_nr (t) == tab_t (t))
1336 table_unref (&t->table);
1339 tab_offset (t, 0, 0);
1341 for (i = 2; i < pt->n_vars; i++)
1342 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1343 var_to_string (pt->vars[i]));
1344 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1345 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1347 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1349 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1355 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1357 size_t row0 = *row1p;
1360 if (row0 >= pt->n_entries)
1363 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1365 struct table_entry *a = pt->entries[row0];
1366 struct table_entry *b = pt->entries[row1];
1367 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1375 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1376 result. WIDTH_ points to an int which is either 0 for a
1377 numeric value or a string width for a string value. */
1379 compare_value_3way (const void *a_, const void *b_, const void *width_)
1381 const union value *a = a_;
1382 const union value *b = b_;
1383 const int *width = width_;
1385 return value_compare_3way (a, b, *width);
1388 /* Given an array of ENTRY_CNT table_entry structures starting at
1389 ENTRIES, creates a sorted list of the values that the variable
1390 with index VAR_IDX takes on. The values are returned as a
1391 malloc()'d array stored in *VALUES, with the number of values
1392 stored in *VALUE_CNT.
1395 enum_var_values (const struct pivot_table *pt, int var_idx,
1396 union value **valuesp, int *n_values)
1398 const struct variable *var = pt->vars[var_idx];
1399 struct var_range *range = get_var_range (var);
1400 union value *values;
1405 values = *valuesp = xnmalloc (range->count, sizeof *values);
1406 *n_values = range->count;
1407 for (i = 0; i < range->count; i++)
1408 values[i].f = range->min + i;
1412 int width = var_get_width (var);
1413 struct hmapx_node *node;
1414 const union value *iter;
1418 for (i = 0; i < pt->n_entries; i++)
1420 const struct table_entry *te = pt->entries[i];
1421 const union value *value = &te->values[var_idx];
1422 size_t hash = value_hash (value, width, 0);
1424 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1425 if (value_equal (iter, value, width))
1428 hmapx_insert (&set, (union value *) value, hash);
1433 *n_values = hmapx_count (&set);
1434 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1436 HMAPX_FOR_EACH (iter, node, &set)
1437 values[i++] = *iter;
1438 hmapx_destroy (&set);
1440 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1444 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1445 from V, displayed with print format spec from variable VAR. When
1446 in REPORT missing-value mode, missing values have an M appended. */
1448 table_value_missing (struct crosstabs_proc *proc,
1449 struct tab_table *table, int c, int r, unsigned char opt,
1450 const union value *v, const struct variable *var)
1452 const char *label = var_lookup_value_label (var, v);
1454 tab_text (table, c, r, TAB_LEFT, label);
1457 const struct fmt_spec *print = var_get_print_format (var);
1458 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1460 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1461 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1465 tab_value (table, c, r, opt, v, proc->dict, print);
1469 /* Draws a line across TABLE at the current row to indicate the most
1470 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1471 that changed, and puts the values that changed into the table. TB
1472 and PT must be the corresponding table_entry and crosstab,
1475 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1476 struct tab_table *table, int first_difference)
1478 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1480 for (; first_difference >= 2; first_difference--)
1481 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1482 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1483 pt->vars[first_difference]);
1486 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1487 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1488 additionally suffixed with a letter `M'. */
1490 format_cell_entry (struct tab_table *table, int c, int r, double value,
1491 char suffix, bool mark_missing, const struct dictionary *dict)
1493 const struct fmt_spec f = {FMT_F, 10, 1};
1500 s = data_out (&v, dict_get_encoding (dict), &f);
1504 suffixes[suffix_len++] = suffix;
1506 suffixes[suffix_len++] = 'M';
1507 suffixes[suffix_len] = '\0';
1509 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1510 s + strspn (s, " "), suffixes);
1513 /* Displays the crosstabulation table. */
1515 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1516 struct tab_table *table)
1522 for (r = 0; r < pt->n_rows; r++)
1523 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1524 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1527 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1528 TAB_LEFT, _("Total"));
1530 /* Put in the actual cells. */
1532 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1533 for (r = 0; r < pt->n_rows; r++)
1535 if (proc->n_cells > 1)
1536 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1537 for (c = 0; c < pt->n_cols; c++)
1539 bool mark_missing = false;
1540 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1541 if (proc->exclude == MV_NEVER
1542 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1543 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1545 mark_missing = true;
1546 for (i = 0; i < proc->n_cells; i++)
1551 switch (proc->a_cells[i])
1557 v = *mp / pt->row_tot[r] * 100.;
1561 v = *mp / pt->col_tot[c] * 100.;
1565 v = *mp / pt->total * 100.;
1568 case CRS_CL_EXPECTED:
1571 case CRS_CL_RESIDUAL:
1572 v = *mp - expected_value;
1574 case CRS_CL_SRESIDUAL:
1575 v = (*mp - expected_value) / sqrt (expected_value);
1577 case CRS_CL_ASRESIDUAL:
1578 v = ((*mp - expected_value)
1579 / sqrt (expected_value
1580 * (1. - pt->row_tot[r] / pt->total)
1581 * (1. - pt->col_tot[c] / pt->total)));
1586 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1592 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1596 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1597 for (r = 0; r < pt->n_rows; r++)
1599 bool mark_missing = false;
1601 if (proc->exclude == MV_NEVER
1602 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1603 mark_missing = true;
1605 for (i = 0; i < proc->n_cells; i++)
1610 switch (proc->a_cells[i])
1620 v = pt->row_tot[r] / pt->total * 100.;
1624 v = pt->row_tot[r] / pt->total * 100.;
1627 case CRS_CL_EXPECTED:
1628 case CRS_CL_RESIDUAL:
1629 case CRS_CL_SRESIDUAL:
1630 case CRS_CL_ASRESIDUAL:
1637 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1638 tab_next_row (table);
1642 /* Column totals, grand total. */
1644 if (proc->n_cells > 1)
1645 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1646 for (c = 0; c <= pt->n_cols; c++)
1648 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1649 bool mark_missing = false;
1652 if (proc->exclude == MV_NEVER && c < pt->n_cols
1653 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1654 mark_missing = true;
1656 for (i = 0; i < proc->n_cells; i++)
1661 switch (proc->a_cells[i])
1667 v = ct / pt->total * 100.;
1675 v = ct / pt->total * 100.;
1678 case CRS_CL_EXPECTED:
1679 case CRS_CL_RESIDUAL:
1680 case CRS_CL_SRESIDUAL:
1681 case CRS_CL_ASRESIDUAL:
1687 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1692 tab_offset (table, -1, tab_row (table) + last_row);
1693 tab_offset (table, 0, -1);
1696 static void calc_r (struct pivot_table *,
1697 double *PT, double *Y, double *, double *, double *);
1698 static void calc_chisq (struct pivot_table *,
1699 double[N_CHISQ], int[N_CHISQ], double *, double *);
1701 /* Display chi-square statistics. */
1703 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1704 bool *showed_fisher)
1706 static const char *chisq_stats[N_CHISQ] =
1708 N_("Pearson Chi-Square"),
1709 N_("Likelihood Ratio"),
1710 N_("Fisher's Exact Test"),
1711 N_("Continuity Correction"),
1712 N_("Linear-by-Linear Association"),
1714 double chisq_v[N_CHISQ];
1715 double fisher1, fisher2;
1720 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1722 tab_offset (chisq, pt->n_vars - 2, -1);
1724 for (i = 0; i < N_CHISQ; i++)
1726 if ((i != 2 && chisq_v[i] == SYSMIS)
1727 || (i == 2 && fisher1 == SYSMIS))
1730 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1733 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1734 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1735 tab_double (chisq, 3, 0, TAB_RIGHT,
1736 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1740 *showed_fisher = true;
1741 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1742 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1744 tab_next_row (chisq);
1747 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1748 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1749 tab_next_row (chisq);
1751 tab_offset (chisq, 0, -1);
1754 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1755 double[N_SYMMETRIC], double[N_SYMMETRIC],
1756 double[N_SYMMETRIC],
1757 double[3], double[3], double[3]);
1759 /* Display symmetric measures. */
1761 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1762 struct tab_table *sym)
1764 static const char *categories[] =
1766 N_("Nominal by Nominal"),
1767 N_("Ordinal by Ordinal"),
1768 N_("Interval by Interval"),
1769 N_("Measure of Agreement"),
1772 static const char *stats[N_SYMMETRIC] =
1776 N_("Contingency Coefficient"),
1777 N_("Kendall's tau-b"),
1778 N_("Kendall's tau-c"),
1780 N_("Spearman Correlation"),
1785 static const int stats_categories[N_SYMMETRIC] =
1787 0, 0, 0, 1, 1, 1, 1, 2, 3,
1791 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1792 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1795 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1796 somers_d_v, somers_d_ase, somers_d_t))
1799 tab_offset (sym, pt->n_vars - 2, -1);
1801 for (i = 0; i < N_SYMMETRIC; i++)
1803 if (sym_v[i] == SYSMIS)
1806 if (stats_categories[i] != last_cat)
1808 last_cat = stats_categories[i];
1809 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1812 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1813 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1814 if (sym_ase[i] != SYSMIS)
1815 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1816 if (sym_t[i] != SYSMIS)
1817 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1818 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1822 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1823 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1826 tab_offset (sym, 0, -1);
1829 static int calc_risk (struct pivot_table *,
1830 double[], double[], double[], union value *);
1832 /* Display risk estimate. */
1834 display_risk (struct pivot_table *pt, struct tab_table *risk)
1837 double risk_v[3], lower[3], upper[3];
1841 if (!calc_risk (pt, risk_v, upper, lower, c))
1844 tab_offset (risk, pt->n_vars - 2, -1);
1846 for (i = 0; i < 3; i++)
1848 const struct variable *cv = pt->vars[COL_VAR];
1849 const struct variable *rv = pt->vars[ROW_VAR];
1850 int cvw = var_get_width (cv);
1851 int rvw = var_get_width (rv);
1853 if (risk_v[i] == SYSMIS)
1859 if (var_is_numeric (cv))
1860 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1861 var_get_name (cv), c[0].f, c[1].f);
1863 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1865 cvw, value_str (&c[0], cvw),
1866 cvw, value_str (&c[1], cvw));
1870 if (var_is_numeric (rv))
1871 sprintf (buf, _("For cohort %s = %g"),
1872 var_get_name (rv), pt->rows[i - 1].f);
1874 sprintf (buf, _("For cohort %s = %.*s"),
1876 rvw, value_str (&pt->rows[i - 1], rvw));
1880 tab_text (risk, 0, 0, TAB_LEFT, buf);
1881 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1882 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1883 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1884 tab_next_row (risk);
1887 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1888 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1889 tab_next_row (risk);
1891 tab_offset (risk, 0, -1);
1894 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1895 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1896 double[N_DIRECTIONAL]);
1898 /* Display directional measures. */
1900 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1901 struct tab_table *direct)
1903 static const char *categories[] =
1905 N_("Nominal by Nominal"),
1906 N_("Ordinal by Ordinal"),
1907 N_("Nominal by Interval"),
1910 static const char *stats[] =
1913 N_("Goodman and Kruskal tau"),
1914 N_("Uncertainty Coefficient"),
1919 static const char *types[] =
1926 static const int stats_categories[N_DIRECTIONAL] =
1928 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1931 static const int stats_stats[N_DIRECTIONAL] =
1933 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1936 static const int stats_types[N_DIRECTIONAL] =
1938 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
1941 static const int *stats_lookup[] =
1948 static const char **stats_names[] =
1960 double direct_v[N_DIRECTIONAL];
1961 double direct_ase[N_DIRECTIONAL];
1962 double direct_t[N_DIRECTIONAL];
1966 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
1969 tab_offset (direct, pt->n_vars - 2, -1);
1971 for (i = 0; i < N_DIRECTIONAL; i++)
1973 if (direct_v[i] == SYSMIS)
1979 for (j = 0; j < 3; j++)
1980 if (last[j] != stats_lookup[j][i])
1983 tab_hline (direct, TAL_1, j, 6, 0);
1988 int k = last[j] = stats_lookup[j][i];
1993 string = var_get_name (pt->vars[0]);
1995 string = var_get_name (pt->vars[1]);
1997 tab_text_format (direct, j, 0, TAB_LEFT,
1998 gettext (stats_names[j][k]), string);
2003 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2004 if (direct_ase[i] != SYSMIS)
2005 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2006 if (direct_t[i] != SYSMIS)
2007 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2008 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2009 tab_next_row (direct);
2012 tab_offset (direct, 0, -1);
2015 /* Statistical calculations. */
2017 /* Returns the value of the gamma (factorial) function for an integer
2020 gamma_int (double pt)
2025 for (i = 2; i < pt; i++)
2030 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2032 static inline double
2033 Pr (int a, int b, int c, int d)
2035 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2036 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2037 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2038 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2039 / gamma_int (a + b + c + d + 1.));
2042 /* Swap the contents of A and B. */
2044 swap (int *a, int *b)
2051 /* Calculate significance for Fisher's exact test as specified in
2052 _SPSS Statistical Algorithms_, Appendix 5. */
2054 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2058 if (MIN (c, d) < MIN (a, b))
2059 swap (&a, &c), swap (&b, &d);
2060 if (MIN (b, d) < MIN (a, c))
2061 swap (&a, &b), swap (&c, &d);
2065 swap (&a, &b), swap (&c, &d);
2067 swap (&a, &c), swap (&b, &d);
2071 for (pt = 0; pt <= a; pt++)
2072 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2074 *fisher2 = *fisher1;
2075 for (pt = 1; pt <= b; pt++)
2076 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2079 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2080 columns with values COLS and N_ROWS rows with values ROWS. Values
2081 in the matrix sum to pt->total. */
2083 calc_chisq (struct pivot_table *pt,
2084 double chisq[N_CHISQ], int df[N_CHISQ],
2085 double *fisher1, double *fisher2)
2089 chisq[0] = chisq[1] = 0.;
2090 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2091 *fisher1 = *fisher2 = SYSMIS;
2093 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2095 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2097 chisq[0] = chisq[1] = SYSMIS;
2101 for (r = 0; r < pt->n_rows; r++)
2102 for (c = 0; c < pt->n_cols; c++)
2104 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2105 const double freq = pt->mat[pt->n_cols * r + c];
2106 const double residual = freq - expected;
2108 chisq[0] += residual * residual / expected;
2110 chisq[1] += freq * log (expected / freq);
2121 /* Calculate Yates and Fisher exact test. */
2122 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2124 double f11, f12, f21, f22;
2130 for (i = j = 0; i < pt->n_cols; i++)
2131 if (pt->col_tot[i] != 0.)
2140 f11 = pt->mat[nz_cols[0]];
2141 f12 = pt->mat[nz_cols[1]];
2142 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2143 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2148 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2151 chisq[3] = (pt->total * pow2 (pt_)
2152 / (f11 + f12) / (f21 + f22)
2153 / (f11 + f21) / (f12 + f22));
2161 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2162 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2165 /* Calculate Mantel-Haenszel. */
2166 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2168 double r, ase_0, ase_1;
2169 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2171 chisq[4] = (pt->total - 1.) * r * r;
2176 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2177 ASE_1, and ase_0 into ASE_0. The row and column values must be
2178 passed in PT and Y. */
2180 calc_r (struct pivot_table *pt,
2181 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2183 double SX, SY, S, T;
2185 double sum_XYf, sum_X2Y2f;
2186 double sum_Xr, sum_X2r;
2187 double sum_Yc, sum_Y2c;
2190 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2191 for (j = 0; j < pt->n_cols; j++)
2193 double fij = pt->mat[j + i * pt->n_cols];
2194 double product = PT[i] * Y[j];
2195 double temp = fij * product;
2197 sum_X2Y2f += temp * product;
2200 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2202 sum_Xr += PT[i] * pt->row_tot[i];
2203 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2205 Xbar = sum_Xr / pt->total;
2207 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2209 sum_Yc += Y[i] * pt->col_tot[i];
2210 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2212 Ybar = sum_Yc / pt->total;
2214 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2215 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2216 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2219 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2224 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2225 for (j = 0; j < pt->n_cols; j++)
2227 double Xresid, Yresid;
2230 Xresid = PT[i] - Xbar;
2231 Yresid = Y[j] - Ybar;
2232 temp = (T * Xresid * Yresid
2234 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2235 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2240 *ase_1 = sqrt (s) / (T * T);
2244 /* Calculate symmetric statistics and their asymptotic standard
2245 errors. Returns 0 if none could be calculated. */
2247 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2248 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2249 double t[N_SYMMETRIC],
2250 double somers_d_v[3], double somers_d_ase[3],
2251 double somers_d_t[3])
2255 q = MIN (pt->ns_rows, pt->ns_cols);
2259 for (i = 0; i < N_SYMMETRIC; i++)
2260 v[i] = ase[i] = t[i] = SYSMIS;
2262 /* Phi, Cramer's V, contingency coefficient. */
2263 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2265 double Xp = 0.; /* Pearson chi-square. */
2268 for (r = 0; r < pt->n_rows; r++)
2269 for (c = 0; c < pt->n_cols; c++)
2271 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2272 const double freq = pt->mat[pt->n_cols * r + c];
2273 const double residual = freq - expected;
2275 Xp += residual * residual / expected;
2278 if (proc->statistics & (1u << CRS_ST_PHI))
2280 v[0] = sqrt (Xp / pt->total);
2281 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2283 if (proc->statistics & (1u << CRS_ST_CC))
2284 v[2] = sqrt (Xp / (Xp + pt->total));
2287 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2288 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2293 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2297 Dr = Dc = pow2 (pt->total);
2298 for (r = 0; r < pt->n_rows; r++)
2299 Dr -= pow2 (pt->row_tot[r]);
2300 for (c = 0; c < pt->n_cols; c++)
2301 Dc -= pow2 (pt->col_tot[c]);
2303 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2304 for (c = 0; c < pt->n_cols; c++)
2308 for (r = 0; r < pt->n_rows; r++)
2309 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2318 for (i = 0; i < pt->n_rows; i++)
2322 for (j = 1; j < pt->n_cols; j++)
2323 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2326 for (j = 1; j < pt->n_cols; j++)
2327 Dij += cum[j + (i - 1) * pt->n_cols];
2331 double fij = pt->mat[j + i * pt->n_cols];
2335 if (++j == pt->n_cols)
2337 assert (j < pt->n_cols);
2339 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2340 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2344 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2345 Dij -= cum[j + (i - 1) * pt->n_cols];
2351 if (proc->statistics & (1u << CRS_ST_BTAU))
2352 v[3] = (P - Q) / sqrt (Dr * Dc);
2353 if (proc->statistics & (1u << CRS_ST_CTAU))
2354 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2355 if (proc->statistics & (1u << CRS_ST_GAMMA))
2356 v[5] = (P - Q) / (P + Q);
2358 /* ASE for tau-b, tau-c, gamma. Calculations could be
2359 eliminated here, at expense of memory. */
2364 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2365 for (i = 0; i < pt->n_rows; i++)
2369 for (j = 1; j < pt->n_cols; j++)
2370 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2373 for (j = 1; j < pt->n_cols; j++)
2374 Dij += cum[j + (i - 1) * pt->n_cols];
2378 double fij = pt->mat[j + i * pt->n_cols];
2380 if (proc->statistics & (1u << CRS_ST_BTAU))
2382 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2383 + v[3] * (pt->row_tot[i] * Dc
2384 + pt->col_tot[j] * Dr));
2385 btau_cum += fij * temp * temp;
2389 const double temp = Cij - Dij;
2390 ctau_cum += fij * temp * temp;
2393 if (proc->statistics & (1u << CRS_ST_GAMMA))
2395 const double temp = Q * Cij - P * Dij;
2396 gamma_cum += fij * temp * temp;
2399 if (proc->statistics & (1u << CRS_ST_D))
2401 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2402 - (P - Q) * (pt->total - pt->row_tot[i]));
2403 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2404 - (Q - P) * (pt->total - pt->col_tot[j]));
2407 if (++j == pt->n_cols)
2409 assert (j < pt->n_cols);
2411 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2412 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2416 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2417 Dij -= cum[j + (i - 1) * pt->n_cols];
2423 btau_var = ((btau_cum
2424 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2426 if (proc->statistics & (1u << CRS_ST_BTAU))
2428 ase[3] = sqrt (btau_var);
2429 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2432 if (proc->statistics & (1u << CRS_ST_CTAU))
2434 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2435 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2436 t[4] = v[4] / ase[4];
2438 if (proc->statistics & (1u << CRS_ST_GAMMA))
2440 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2441 t[5] = v[5] / (2. / (P + Q)
2442 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2444 if (proc->statistics & (1u << CRS_ST_D))
2446 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2447 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2448 somers_d_t[0] = (somers_d_v[0]
2450 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2451 somers_d_v[1] = (P - Q) / Dc;
2452 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2453 somers_d_t[1] = (somers_d_v[1]
2455 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2456 somers_d_v[2] = (P - Q) / Dr;
2457 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2458 somers_d_t[2] = (somers_d_v[2]
2460 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2466 /* Spearman correlation, Pearson's r. */
2467 if (proc->statistics & (1u << CRS_ST_CORR))
2469 double *R = xmalloc (sizeof *R * pt->n_rows);
2470 double *C = xmalloc (sizeof *C * pt->n_cols);
2473 double y, t, c = 0., s = 0.;
2478 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2479 y = pt->row_tot[i] - c;
2483 if (++i == pt->n_rows)
2485 assert (i < pt->n_rows);
2490 double y, t, c = 0., s = 0.;
2495 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2496 y = pt->col_tot[j] - c;
2500 if (++j == pt->n_cols)
2502 assert (j < pt->n_cols);
2506 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2512 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2516 /* Cohen's kappa. */
2517 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2519 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2522 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2523 i < pt->ns_rows; i++, j++)
2527 while (pt->col_tot[j] == 0.)
2530 prod = pt->row_tot[i] * pt->col_tot[j];
2531 sum = pt->row_tot[i] + pt->col_tot[j];
2533 sum_fii += pt->mat[j + i * pt->n_cols];
2535 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2536 sum_riciri_ci += prod * sum;
2538 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2539 for (j = 0; j < pt->ns_cols; j++)
2541 double sum = pt->row_tot[i] + pt->col_tot[j];
2542 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2545 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2547 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2548 + sum_rici * sum_rici
2549 - pt->total * sum_riciri_ci)
2550 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2552 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2553 / pow2 (pow2 (pt->total) - sum_rici))
2554 + ((2. * (pt->total - sum_fii)
2555 * (2. * sum_fii * sum_rici
2556 - pt->total * sum_fiiri_ci))
2557 / cube (pow2 (pt->total) - sum_rici))
2558 + (pow2 (pt->total - sum_fii)
2559 * (pt->total * sum_fijri_ci2 - 4.
2560 * sum_rici * sum_rici)
2561 / pow4 (pow2 (pt->total) - sum_rici))));
2563 t[8] = v[8] / ase[8];
2570 /* Calculate risk estimate. */
2572 calc_risk (struct pivot_table *pt,
2573 double *value, double *upper, double *lower, union value *c)
2575 double f11, f12, f21, f22;
2581 for (i = 0; i < 3; i++)
2582 value[i] = upper[i] = lower[i] = SYSMIS;
2585 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2592 for (i = j = 0; i < pt->n_cols; i++)
2593 if (pt->col_tot[i] != 0.)
2602 f11 = pt->mat[nz_cols[0]];
2603 f12 = pt->mat[nz_cols[1]];
2604 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2605 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2607 c[0] = pt->cols[nz_cols[0]];
2608 c[1] = pt->cols[nz_cols[1]];
2611 value[0] = (f11 * f22) / (f12 * f21);
2612 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2613 lower[0] = value[0] * exp (-1.960 * v);
2614 upper[0] = value[0] * exp (1.960 * v);
2616 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2617 v = sqrt ((f12 / (f11 * (f11 + f12)))
2618 + (f22 / (f21 * (f21 + f22))));
2619 lower[1] = value[1] * exp (-1.960 * v);
2620 upper[1] = value[1] * exp (1.960 * v);
2622 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2623 v = sqrt ((f11 / (f12 * (f11 + f12)))
2624 + (f21 / (f22 * (f21 + f22))));
2625 lower[2] = value[2] * exp (-1.960 * v);
2626 upper[2] = value[2] * exp (1.960 * v);
2631 /* Calculate directional measures. */
2633 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2634 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2635 double t[N_DIRECTIONAL])
2640 for (i = 0; i < N_DIRECTIONAL; i++)
2641 v[i] = ase[i] = t[i] = SYSMIS;
2645 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2647 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2648 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2649 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2650 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2651 double sum_fim, sum_fmj;
2653 int rm_index, cm_index;
2656 /* Find maximum for each row and their sum. */
2657 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2659 double max = pt->mat[i * pt->n_cols];
2662 for (j = 1; j < pt->n_cols; j++)
2663 if (pt->mat[j + i * pt->n_cols] > max)
2665 max = pt->mat[j + i * pt->n_cols];
2669 sum_fim += fim[i] = max;
2670 fim_index[i] = index;
2673 /* Find maximum for each column. */
2674 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2676 double max = pt->mat[j];
2679 for (i = 1; i < pt->n_rows; i++)
2680 if (pt->mat[j + i * pt->n_cols] > max)
2682 max = pt->mat[j + i * pt->n_cols];
2686 sum_fmj += fmj[j] = max;
2687 fmj_index[j] = index;
2690 /* Find maximum row total. */
2691 rm = pt->row_tot[0];
2693 for (i = 1; i < pt->n_rows; i++)
2694 if (pt->row_tot[i] > rm)
2696 rm = pt->row_tot[i];
2700 /* Find maximum column total. */
2701 cm = pt->col_tot[0];
2703 for (j = 1; j < pt->n_cols; j++)
2704 if (pt->col_tot[j] > cm)
2706 cm = pt->col_tot[j];
2710 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2711 v[1] = (sum_fmj - rm) / (pt->total - rm);
2712 v[2] = (sum_fim - cm) / (pt->total - cm);
2714 /* ASE1 for Y given PT. */
2718 for (accum = 0., i = 0; i < pt->n_rows; i++)
2719 for (j = 0; j < pt->n_cols; j++)
2721 const int deltaj = j == cm_index;
2722 accum += (pt->mat[j + i * pt->n_cols]
2723 * pow2 ((j == fim_index[i])
2728 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2731 /* ASE0 for Y given PT. */
2735 for (accum = 0., i = 0; i < pt->n_rows; i++)
2736 if (cm_index != fim_index[i])
2737 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2738 + pt->mat[i * pt->n_cols + cm_index]);
2739 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2742 /* ASE1 for PT given Y. */
2746 for (accum = 0., i = 0; i < pt->n_rows; i++)
2747 for (j = 0; j < pt->n_cols; j++)
2749 const int deltaj = i == rm_index;
2750 accum += (pt->mat[j + i * pt->n_cols]
2751 * pow2 ((i == fmj_index[j])
2756 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2759 /* ASE0 for PT given Y. */
2763 for (accum = 0., j = 0; j < pt->n_cols; j++)
2764 if (rm_index != fmj_index[j])
2765 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2766 + pt->mat[j + pt->n_cols * rm_index]);
2767 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2770 /* Symmetric ASE0 and ASE1. */
2775 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2776 for (j = 0; j < pt->n_cols; j++)
2778 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2779 int temp1 = (i == rm_index) + (j == cm_index);
2780 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2781 accum1 += (pt->mat[j + i * pt->n_cols]
2782 * pow2 (temp0 + (v[0] - 1.) * temp1));
2784 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2785 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2786 / (2. * pt->total - rm - cm));
2795 double sum_fij2_ri, sum_fij2_ci;
2796 double sum_ri2, sum_cj2;
2798 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2799 for (j = 0; j < pt->n_cols; j++)
2801 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2802 sum_fij2_ri += temp / pt->row_tot[i];
2803 sum_fij2_ci += temp / pt->col_tot[j];
2806 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2807 sum_ri2 += pow2 (pt->row_tot[i]);
2809 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2810 sum_cj2 += pow2 (pt->col_tot[j]);
2812 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2813 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2817 if (proc->statistics & (1u << CRS_ST_UC))
2819 double UX, UY, UXY, P;
2820 double ase1_yx, ase1_xy, ase1_sym;
2823 for (UX = 0., i = 0; i < pt->n_rows; i++)
2824 if (pt->row_tot[i] > 0.)
2825 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2827 for (UY = 0., j = 0; j < pt->n_cols; j++)
2828 if (pt->col_tot[j] > 0.)
2829 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2831 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2832 for (j = 0; j < pt->n_cols; j++)
2834 double entry = pt->mat[j + i * pt->n_cols];
2839 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2840 UXY -= entry / pt->total * log (entry / pt->total);
2843 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2844 for (j = 0; j < pt->n_cols; j++)
2846 double entry = pt->mat[j + i * pt->n_cols];
2851 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2852 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2853 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2854 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2855 ase1_sym += entry * pow2 ((UXY
2856 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2857 - (UX + UY) * log (entry / pt->total));
2860 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2861 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2862 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2863 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2865 v[6] = (UX + UY - UXY) / UX;
2866 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2867 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2869 v[7] = (UX + UY - UXY) / UY;
2870 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2871 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2875 if (proc->statistics & (1u << CRS_ST_D))
2877 double v_dummy[N_SYMMETRIC];
2878 double ase_dummy[N_SYMMETRIC];
2879 double t_dummy[N_SYMMETRIC];
2880 double somers_d_v[3];
2881 double somers_d_ase[3];
2882 double somers_d_t[3];
2884 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2885 somers_d_v, somers_d_ase, somers_d_t))
2888 for (i = 0; i < 3; i++)
2890 v[8 + i] = somers_d_v[i];
2891 ase[8 + i] = somers_d_ase[i];
2892 t[8 + i] = somers_d_t[i];
2898 if (proc->statistics & (1u << CRS_ST_ETA))
2901 double sum_Xr, sum_X2r;
2905 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2907 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2908 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2910 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2912 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2916 for (cum = 0., i = 0; i < pt->n_rows; i++)
2918 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2919 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2922 SXW -= cum * cum / pt->col_tot[j];
2924 v[11] = sqrt (1. - SXW / SX);
2928 double sum_Yc, sum_Y2c;
2932 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2934 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2935 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2937 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
2939 for (SYW = 0., i = 0; i < pt->n_rows; i++)
2943 for (cum = 0., j = 0; j < pt->n_cols; j++)
2945 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
2946 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
2949 SYW -= cum * cum / pt->row_tot[i];
2951 v[12] = sqrt (1. - SYW / SY);