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-functions.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. */
202 bool descending; /* True if descending sort order is requested. */
205 static bool should_tabulate_case (const struct pivot_table *,
206 const struct ccase *, enum mv_class exclude);
207 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
209 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
211 static void postcalc (struct crosstabs_proc *);
212 static void submit (struct pivot_table *, struct tab_table *);
214 /* Parses and executes the CROSSTABS procedure. */
216 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
218 const struct variable *wv = dict_get_weight (dataset_dict (ds));
219 struct crosstabs_proc proc;
220 struct casegrouper *grouper;
221 struct casereader *input, *group;
222 struct cmd_crosstabs cmd;
223 struct pivot_table *pt;
228 proc.dict = dataset_dict (ds);
229 proc.bad_warn = true;
230 proc.variables = NULL;
231 proc.n_variables = 0;
234 proc.descending = false;
235 proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
237 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
239 result = CMD_FAILURE;
243 proc.mode = proc.n_variables ? INTEGER : GENERAL;
246 proc.descending = cmd.val == CRS_DVALUE;
250 proc.cells = 1u << CRS_CL_COUNT;
251 else if (cmd.a_cells[CRS_CL_ALL])
252 proc.cells = UINT_MAX;
256 for (i = 0; i < CRS_CL_count; i++)
258 proc.cells |= 1u << i;
260 proc.cells = ((1u << CRS_CL_COUNT)
262 | (1u << CRS_CL_COLUMN)
263 | (1u << CRS_CL_TOTAL));
265 proc.cells &= ((1u << CRS_CL_count) - 1);
266 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
268 for (i = 0; i < CRS_CL_count; i++)
269 if (proc.cells & (1u << i))
270 proc.a_cells[proc.n_cells++] = i;
273 if (cmd.a_statistics[CRS_ST_ALL])
274 proc.statistics = UINT_MAX;
275 else if (cmd.sbc_statistics)
280 for (i = 0; i < CRS_ST_count; i++)
281 if (cmd.a_statistics[i])
282 proc.statistics |= 1u << i;
283 if (proc.statistics == 0)
284 proc.statistics |= 1u << CRS_ST_CHISQ;
290 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
291 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
293 if (proc.mode == GENERAL && proc.mode == MV_NEVER)
295 msg (SE, _("Missing mode REPORT not allowed in general mode. "
296 "Assuming MISSING=TABLE."));
301 proc.pivot = cmd.pivot == CRS_PIVOT;
303 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
305 grouper = casegrouper_create_splits (input, dataset_dict (ds));
306 while (casegrouper_get_next_group (grouper, &group))
310 /* Output SPLIT FILE variables. */
311 c = casereader_peek (group, 0);
314 output_split_file_values (ds, c);
318 /* Initialize hash tables. */
319 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
320 hmap_init (&pt->data);
323 for (; (c = casereader_read (group)) != NULL; case_unref (c))
324 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
326 double weight = dict_get_case_weight (dataset_dict (ds), c,
328 if (should_tabulate_case (pt, c, proc.exclude))
330 if (proc.mode == GENERAL)
331 tabulate_general_case (pt, c, weight);
333 tabulate_integer_case (pt, c, weight);
336 pt->missing += weight;
338 casereader_destroy (group);
343 ok = casegrouper_destroy (grouper);
344 ok = proc_commit (ds) && ok;
346 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
349 free (proc.variables);
350 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
353 free (pt->const_vars);
354 /* We must not call value_destroy on const_values because
355 it is a wild pointer; it never pointed to anything owned
358 The rest of the data was allocated and destroyed at a
359 lower level already. */
366 /* Parses the TABLES subcommand. */
368 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
369 struct cmd_crosstabs *cmd UNUSED, void *proc_)
371 struct crosstabs_proc *proc = proc_;
372 struct const_var_set *var_set;
374 const struct variable ***by = NULL;
376 size_t *by_nvar = NULL;
381 /* Ensure that this is a TABLES subcommand. */
382 if (!lex_match_id (lexer, "TABLES")
383 && (lex_token (lexer) != T_ID ||
384 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
385 && lex_token (lexer) != T_ALL)
387 lex_match (lexer, T_EQUALS);
389 if (proc->variables != NULL)
390 var_set = const_var_set_create_from_array (proc->variables,
393 var_set = const_var_set_create_from_dict (dataset_dict (ds));
394 assert (var_set != NULL);
398 by = xnrealloc (by, n_by + 1, sizeof *by);
399 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
400 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
401 PV_NO_DUPLICATE | PV_NO_SCRATCH))
403 if (xalloc_oversized (nx, by_nvar[n_by]))
405 msg (SE, _("Too many cross-tabulation variables or dimensions."));
411 if (!lex_match (lexer, T_BY))
415 lex_force_match (lexer, T_BY);
423 by_iter = xcalloc (n_by, sizeof *by_iter);
424 proc->pivots = xnrealloc (proc->pivots,
425 proc->n_pivots + nx, sizeof *proc->pivots);
426 for (i = 0; i < nx; i++)
428 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
431 pt->weight_format = proc->weight_format;
434 pt->vars = xmalloc (n_by * sizeof *pt->vars);
436 pt->const_vars = NULL;
437 pt->const_values = NULL;
439 for (j = 0; j < n_by; j++)
440 pt->vars[j] = by[j][by_iter[j]];
442 for (j = n_by - 1; j >= 0; j--)
444 if (++by_iter[j] < by_nvar[j])
453 /* All return paths lead here. */
454 for (i = 0; i < n_by; i++)
459 const_var_set_destroy (var_set);
464 /* Parses the VARIABLES subcommand. */
466 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
467 struct cmd_crosstabs *cmd UNUSED, void *proc_)
469 struct crosstabs_proc *proc = proc_;
472 msg (SE, _("VARIABLES must be specified before TABLES."));
476 lex_match (lexer, T_EQUALS);
480 size_t orig_nv = proc->n_variables;
485 if (!parse_variables_const (lexer, dataset_dict (ds),
486 &proc->variables, &proc->n_variables,
487 (PV_APPEND | PV_NUMERIC
488 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
491 if (!lex_force_match (lexer, T_LPAREN))
494 if (!lex_force_int (lexer))
496 min = lex_integer (lexer);
499 lex_match (lexer, T_COMMA);
501 if (!lex_force_int (lexer))
503 max = lex_integer (lexer);
506 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
512 if (!lex_force_match (lexer, T_RPAREN))
515 for (i = orig_nv; i < proc->n_variables; i++)
517 struct var_range *vr = xmalloc (sizeof *vr);
520 vr->count = max - min + 1;
521 var_attach_aux (proc->variables[i], vr, var_dtor_free);
524 if (lex_token (lexer) == T_SLASH)
531 free (proc->variables);
532 proc->variables = NULL;
533 proc->n_variables = 0;
537 /* Data file processing. */
540 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
541 enum mv_class exclude)
544 for (j = 0; j < pt->n_vars; j++)
546 const struct variable *var = pt->vars[j];
547 struct var_range *range = get_var_range (var);
549 if (var_is_value_missing (var, case_data (c, var), exclude))
554 double num = case_num (c, var);
555 if (num < range->min || num > range->max)
563 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
566 struct table_entry *te;
571 for (j = 0; j < pt->n_vars; j++)
573 /* Throw away fractional parts of values. */
574 hash = hash_int (case_num (c, pt->vars[j]), hash);
577 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
579 for (j = 0; j < pt->n_vars; j++)
580 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
583 /* Found an existing entry. */
590 /* No existing entry. Create a new one. */
591 te = xmalloc (table_entry_size (pt->n_vars));
593 for (j = 0; j < pt->n_vars; j++)
594 te->values[j].f = (int) case_num (c, pt->vars[j]);
595 hmap_insert (&pt->data, &te->node, hash);
599 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
602 struct table_entry *te;
607 for (j = 0; j < pt->n_vars; j++)
609 const struct variable *var = pt->vars[j];
610 hash = value_hash (case_data (c, var), var_get_width (var), hash);
613 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
615 for (j = 0; j < pt->n_vars; j++)
617 const struct variable *var = pt->vars[j];
618 if (!value_equal (case_data (c, var), &te->values[j],
619 var_get_width (var)))
623 /* Found an existing entry. */
630 /* No existing entry. Create a new one. */
631 te = xmalloc (table_entry_size (pt->n_vars));
633 for (j = 0; j < pt->n_vars; j++)
635 const struct variable *var = pt->vars[j];
636 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
638 hmap_insert (&pt->data, &te->node, hash);
641 /* Post-data reading calculations. */
643 static int compare_table_entry_vars_3way (const struct table_entry *a,
644 const struct table_entry *b,
645 const struct pivot_table *pt,
647 static int compare_table_entry_3way (const void *ap_, const void *bp_,
649 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
652 static void enum_var_values (const struct pivot_table *, int var_idx,
653 union value **valuesp, int *n_values, bool descending);
654 static void output_pivot_table (struct crosstabs_proc *,
655 struct pivot_table *);
656 static void make_pivot_table_subset (struct pivot_table *pt,
657 size_t row0, size_t row1,
658 struct pivot_table *subset);
659 static void make_summary_table (struct crosstabs_proc *);
660 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
663 postcalc (struct crosstabs_proc *proc)
665 struct pivot_table *pt;
667 /* Convert hash tables into sorted arrays of entries. */
668 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
670 struct table_entry *e;
673 pt->n_entries = hmap_count (&pt->data);
674 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
676 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
677 pt->entries[i++] = e;
678 hmap_destroy (&pt->data);
680 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
681 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
685 make_summary_table (proc);
687 /* Output each pivot table. */
688 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
690 if (proc->pivot || pt->n_vars == 2)
691 output_pivot_table (proc, pt);
694 size_t row0 = 0, row1 = 0;
695 while (find_crosstab (pt, &row0, &row1))
697 struct pivot_table subset;
698 make_pivot_table_subset (pt, row0, row1, &subset);
699 output_pivot_table (proc, &subset);
704 /* Free output and prepare for next split file. */
705 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
711 /* Free only the members that were allocated in this
712 function. The other pointer members are either both
713 allocated and destroyed at a lower level (in
714 output_pivot_table), or both allocated and destroyed at
715 a higher level (in crs_custom_tables and free_proc,
717 for (i = 0; i < pt->n_entries; i++)
718 free (pt->entries[i]);
724 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
725 struct pivot_table *subset)
730 assert (pt->n_consts == 0);
731 subset->missing = pt->missing;
733 subset->vars = pt->vars;
734 subset->n_consts = pt->n_vars - 2;
735 subset->const_vars = pt->vars + 2;
736 subset->const_values = &pt->entries[row0]->values[2];
738 subset->entries = &pt->entries[row0];
739 subset->n_entries = row1 - row0;
743 compare_table_entry_var_3way (const struct table_entry *a,
744 const struct table_entry *b,
745 const struct pivot_table *pt,
748 return value_compare_3way (&a->values[idx], &b->values[idx],
749 var_get_width (pt->vars[idx]));
753 compare_table_entry_vars_3way (const struct table_entry *a,
754 const struct table_entry *b,
755 const struct pivot_table *pt,
760 for (i = idx1 - 1; i >= idx0; i--)
762 int cmp = compare_table_entry_var_3way (a, b, pt, i);
769 /* Compare the struct table_entry at *AP to the one at *BP and
770 return a strcmp()-type result. */
772 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
774 const struct table_entry *const *ap = ap_;
775 const struct table_entry *const *bp = bp_;
776 const struct table_entry *a = *ap;
777 const struct table_entry *b = *bp;
778 const struct pivot_table *pt = pt_;
781 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
785 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
789 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
792 /* Inverted version of compare_table_entry_3way */
794 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *pt_)
796 return -compare_table_entry_3way (ap_, bp_, pt_);
800 find_first_difference (const struct pivot_table *pt, size_t row)
803 return pt->n_vars - 1;
806 const struct table_entry *a = pt->entries[row];
807 const struct table_entry *b = pt->entries[row - 1];
810 for (col = pt->n_vars - 1; col >= 0; col--)
811 if (compare_table_entry_var_3way (a, b, pt, col))
817 /* Output a table summarizing the cases processed. */
819 make_summary_table (struct crosstabs_proc *proc)
821 struct tab_table *summary;
822 struct pivot_table *pt;
826 summary = tab_create (7, 3 + proc->n_pivots);
827 tab_title (summary, _("Summary."));
828 tab_headers (summary, 1, 0, 3, 0);
829 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
830 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
831 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
832 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
833 tab_hline (summary, TAL_1, 1, 6, 1);
834 tab_hline (summary, TAL_1, 1, 6, 2);
835 tab_vline (summary, TAL_1, 3, 1, 1);
836 tab_vline (summary, TAL_1, 5, 1, 1);
837 for (i = 0; i < 3; i++)
839 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
840 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
842 tab_offset (summary, 0, 3);
844 ds_init_empty (&name);
845 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
851 tab_hline (summary, TAL_1, 0, 6, 0);
854 for (i = 0; i < pt->n_vars; i++)
857 ds_put_cstr (&name, " * ");
858 ds_put_cstr (&name, var_to_string (pt->vars[i]));
860 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
863 for (i = 0; i < pt->n_entries; i++)
864 valid += pt->entries[i]->freq;
869 for (i = 0; i < 3; i++)
871 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
872 &proc->weight_format);
873 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
877 tab_next_row (summary);
881 submit (NULL, summary);
886 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
887 struct pivot_table *);
888 static struct tab_table *create_chisq_table (struct pivot_table *);
889 static struct tab_table *create_sym_table (struct pivot_table *);
890 static struct tab_table *create_risk_table (struct pivot_table *);
891 static struct tab_table *create_direct_table (struct pivot_table *);
892 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
893 struct tab_table *, int first_difference);
894 static void display_crosstabulation (struct crosstabs_proc *,
895 struct pivot_table *,
897 static void display_chisq (struct pivot_table *, struct tab_table *,
898 bool *showed_fisher);
899 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
901 static void display_risk (struct pivot_table *, struct tab_table *);
902 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
904 static void table_value_missing (struct crosstabs_proc *proc,
905 struct tab_table *table, int c, int r,
906 unsigned char opt, const union value *v,
907 const struct variable *var);
908 static void delete_missing (struct pivot_table *);
909 static void build_matrix (struct pivot_table *);
911 /* Output pivot table PT in the context of PROC. */
913 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
915 struct tab_table *table = NULL; /* Crosstabulation table. */
916 struct tab_table *chisq = NULL; /* Chi-square table. */
917 bool showed_fisher = false;
918 struct tab_table *sym = NULL; /* Symmetric measures table. */
919 struct tab_table *risk = NULL; /* Risk estimate table. */
920 struct tab_table *direct = NULL; /* Directional measures table. */
923 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols, proc->descending);
930 ds_init_cstr (&vars, var_get_name (pt->vars[0]));
931 for (i = 1; i < pt->n_vars; i++)
932 ds_put_format (&vars, " * %s", var_get_name (pt->vars[i]));
934 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
935 form "var1 * var2 * var3 * ...". */
936 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
944 table = create_crosstab_table (proc, pt);
945 if (proc->statistics & (1u << CRS_ST_CHISQ))
946 chisq = create_chisq_table (pt);
947 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
948 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
949 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
950 | (1u << CRS_ST_KAPPA)))
951 sym = create_sym_table (pt);
952 if (proc->statistics & (1u << CRS_ST_RISK))
953 risk = create_risk_table (pt);
954 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
955 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
956 direct = create_direct_table (pt);
959 while (find_crosstab (pt, &row0, &row1))
961 struct pivot_table x;
962 int first_difference;
964 make_pivot_table_subset (pt, row0, row1, &x);
966 /* Find all the row variable values. */
967 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows, proc->descending);
969 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
972 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
973 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
974 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
976 /* Allocate table space for the matrix. */
978 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
979 tab_realloc (table, -1,
980 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
981 tab_nr (table) * pt->n_entries / x.n_entries));
985 /* Find the first variable that differs from the last subtable. */
986 first_difference = find_first_difference (pt, row0);
989 display_dimensions (proc, &x, table, first_difference);
990 display_crosstabulation (proc, &x, table);
993 if (proc->exclude == MV_NEVER)
998 display_dimensions (proc, &x, chisq, first_difference);
999 display_chisq (&x, chisq, &showed_fisher);
1003 display_dimensions (proc, &x, sym, first_difference);
1004 display_symmetric (proc, &x, sym);
1008 display_dimensions (proc, &x, risk, first_difference);
1009 display_risk (&x, risk);
1013 display_dimensions (proc, &x, direct, first_difference);
1014 display_directional (proc, &x, direct);
1017 /* Free the parts of x that are not owned by pt. In
1018 particular we must not free x.cols, which is the same as
1019 pt->cols, which is freed at the end of this function. */
1027 submit (NULL, table);
1032 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1038 submit (pt, direct);
1044 build_matrix (struct pivot_table *x)
1046 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1047 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1050 struct table_entry **p;
1054 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1056 const struct table_entry *te = *p;
1058 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1060 for (; col < x->n_cols; col++)
1066 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1073 if (++col >= x->n_cols)
1079 while (mp < &x->mat[x->n_cols * x->n_rows])
1081 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1083 /* Column totals, row totals, ns_rows. */
1085 for (col = 0; col < x->n_cols; col++)
1086 x->col_tot[col] = 0.0;
1087 for (row = 0; row < x->n_rows; row++)
1088 x->row_tot[row] = 0.0;
1090 for (row = 0; row < x->n_rows; row++)
1092 bool row_is_empty = true;
1093 for (col = 0; col < x->n_cols; col++)
1097 row_is_empty = false;
1098 x->col_tot[col] += *mp;
1099 x->row_tot[row] += *mp;
1106 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1110 for (col = 0; col < x->n_cols; col++)
1111 for (row = 0; row < x->n_rows; row++)
1112 if (x->mat[col + row * x->n_cols] != 0.0)
1120 for (col = 0; col < x->n_cols; col++)
1121 x->total += x->col_tot[col];
1124 static struct tab_table *
1125 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1132 static const struct tuple names[] =
1134 {CRS_CL_COUNT, N_("count")},
1135 {CRS_CL_ROW, N_("row %")},
1136 {CRS_CL_COLUMN, N_("column %")},
1137 {CRS_CL_TOTAL, N_("total %")},
1138 {CRS_CL_EXPECTED, N_("expected")},
1139 {CRS_CL_RESIDUAL, N_("residual")},
1140 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1141 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1143 const int n_names = sizeof names / sizeof *names;
1144 const struct tuple *t;
1146 struct tab_table *table;
1147 struct string title;
1148 struct pivot_table x;
1152 make_pivot_table_subset (pt, 0, 0, &x);
1154 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1155 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1156 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1158 /* First header line. */
1159 tab_joint_text (table, x.n_consts + 1, 0,
1160 (x.n_consts + 1) + (x.n_cols - 1), 0,
1161 TAB_CENTER | TAT_TITLE, var_get_name (x.vars[COL_VAR]));
1163 tab_hline (table, TAL_1, x.n_consts + 1,
1164 x.n_consts + 2 + x.n_cols - 2, 1);
1166 /* Second header line. */
1167 for (i = 2; i < x.n_consts + 2; i++)
1168 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1169 x.n_consts + 2 - i - 1, 1,
1170 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1171 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1172 var_get_name (x.vars[ROW_VAR]));
1173 for (i = 0; i < x.n_cols; i++)
1174 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1175 &x.cols[i], x.vars[COL_VAR]);
1176 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1178 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1179 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1182 ds_init_empty (&title);
1183 for (i = 0; i < x.n_consts + 2; i++)
1186 ds_put_cstr (&title, " * ");
1187 ds_put_cstr (&title, var_get_name (x.vars[i]));
1189 for (i = 0; i < pt->n_consts; i++)
1191 const struct variable *var = pt->const_vars[i];
1195 ds_put_format (&title, ", %s=", var_get_name (var));
1197 /* Insert the formatted value of the variable, then trim
1198 leading spaces in what was just inserted. */
1199 ofs = ds_length (&title);
1200 s = data_out (&pt->const_values[i], var_get_encoding (var),
1201 var_get_print_format (var));
1202 ds_put_cstr (&title, s);
1204 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1208 ds_put_cstr (&title, " [");
1210 for (t = names; t < &names[n_names]; t++)
1211 if (proc->cells & (1u << t->value))
1214 ds_put_cstr (&title, ", ");
1215 ds_put_cstr (&title, gettext (t->name));
1217 ds_put_cstr (&title, "].");
1219 tab_title (table, "%s", ds_cstr (&title));
1220 ds_destroy (&title);
1222 tab_offset (table, 0, 2);
1226 static struct tab_table *
1227 create_chisq_table (struct pivot_table *pt)
1229 struct tab_table *chisq;
1231 chisq = tab_create (6 + (pt->n_vars - 2),
1232 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1233 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1235 tab_title (chisq, _("Chi-square tests."));
1237 tab_offset (chisq, pt->n_vars - 2, 0);
1238 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1239 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1240 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1241 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1242 _("Asymp. Sig. (2-tailed)"));
1243 tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1244 _("Exact Sig. (%d-tailed)"), 2);
1245 tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1246 _("Exact Sig. (%d-tailed)"), 1);
1247 tab_offset (chisq, 0, 1);
1252 /* Symmetric measures. */
1253 static struct tab_table *
1254 create_sym_table (struct pivot_table *pt)
1256 struct tab_table *sym;
1258 sym = tab_create (6 + (pt->n_vars - 2),
1259 pt->n_entries / pt->n_cols * 7 + 10);
1260 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1261 tab_title (sym, _("Symmetric measures."));
1263 tab_offset (sym, pt->n_vars - 2, 0);
1264 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1265 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1266 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1267 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1268 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1269 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1270 tab_offset (sym, 0, 1);
1275 /* Risk estimate. */
1276 static struct tab_table *
1277 create_risk_table (struct pivot_table *pt)
1279 struct tab_table *risk;
1281 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1282 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1283 tab_title (risk, _("Risk estimate."));
1285 tab_offset (risk, pt->n_vars - 2, 0);
1286 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1287 _("95%% Confidence Interval"));
1288 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1289 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1290 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1291 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1292 tab_hline (risk, TAL_1, 2, 3, 1);
1293 tab_vline (risk, TAL_1, 2, 0, 1);
1294 tab_offset (risk, 0, 2);
1299 /* Directional measures. */
1300 static struct tab_table *
1301 create_direct_table (struct pivot_table *pt)
1303 struct tab_table *direct;
1305 direct = tab_create (7 + (pt->n_vars - 2),
1306 pt->n_entries / pt->n_cols * 7 + 10);
1307 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1308 tab_title (direct, _("Directional measures."));
1310 tab_offset (direct, pt->n_vars - 2, 0);
1311 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1312 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1313 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1314 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1315 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1316 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1317 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1318 tab_offset (direct, 0, 1);
1324 /* Delete missing rows and columns for statistical analysis when
1327 delete_missing (struct pivot_table *pt)
1331 for (r = 0; r < pt->n_rows; r++)
1332 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1334 for (c = 0; c < pt->n_cols; c++)
1335 pt->mat[c + r * pt->n_cols] = 0.;
1340 for (c = 0; c < pt->n_cols; c++)
1341 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1343 for (r = 0; r < pt->n_rows; r++)
1344 pt->mat[c + r * pt->n_cols] = 0.;
1349 /* Prepare table T for submission, and submit it. */
1351 submit (struct pivot_table *pt, struct tab_table *t)
1358 tab_resize (t, -1, 0);
1359 if (tab_nr (t) == tab_t (t))
1361 table_unref (&t->table);
1364 tab_offset (t, 0, 0);
1366 for (i = 2; i < pt->n_vars; i++)
1367 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1368 var_to_string (pt->vars[i]));
1369 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1370 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1372 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1374 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1380 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1382 size_t row0 = *row1p;
1385 if (row0 >= pt->n_entries)
1388 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1390 struct table_entry *a = pt->entries[row0];
1391 struct table_entry *b = pt->entries[row1];
1392 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1400 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1401 result. WIDTH_ points to an int which is either 0 for a
1402 numeric value or a string width for a string value. */
1404 compare_value_3way (const void *a_, const void *b_, const void *width_)
1406 const union value *a = a_;
1407 const union value *b = b_;
1408 const int *width = width_;
1410 return value_compare_3way (a, b, *width);
1413 /* Inverted version of the above */
1415 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1417 return -compare_value_3way (a_, b_, width_);
1421 /* Given an array of ENTRY_CNT table_entry structures starting at
1422 ENTRIES, creates a sorted list of the values that the variable
1423 with index VAR_IDX takes on. The values are returned as a
1424 malloc()'d array stored in *VALUES, with the number of values
1425 stored in *VALUE_CNT.
1428 enum_var_values (const struct pivot_table *pt, int var_idx,
1429 union value **valuesp, int *n_values, bool descending)
1431 const struct variable *var = pt->vars[var_idx];
1432 struct var_range *range = get_var_range (var);
1433 union value *values;
1438 values = *valuesp = xnmalloc (range->count, sizeof *values);
1439 *n_values = range->count;
1440 for (i = 0; i < range->count; i++)
1441 values[i].f = range->min + i;
1445 int width = var_get_width (var);
1446 struct hmapx_node *node;
1447 const union value *iter;
1451 for (i = 0; i < pt->n_entries; i++)
1453 const struct table_entry *te = pt->entries[i];
1454 const union value *value = &te->values[var_idx];
1455 size_t hash = value_hash (value, width, 0);
1457 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1458 if (value_equal (iter, value, width))
1461 hmapx_insert (&set, (union value *) value, hash);
1466 *n_values = hmapx_count (&set);
1467 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1469 HMAPX_FOR_EACH (iter, node, &set)
1470 values[i++] = *iter;
1471 hmapx_destroy (&set);
1473 sort (values, *n_values, sizeof *values,
1474 descending ? compare_value_3way_inv : compare_value_3way,
1479 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1480 from V, displayed with print format spec from variable VAR. When
1481 in REPORT missing-value mode, missing values have an M appended. */
1483 table_value_missing (struct crosstabs_proc *proc,
1484 struct tab_table *table, int c, int r, unsigned char opt,
1485 const union value *v, const struct variable *var)
1487 const char *label = var_lookup_value_label (var, v);
1489 tab_text (table, c, r, TAB_LEFT, label);
1492 const struct fmt_spec *print = var_get_print_format (var);
1493 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1495 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1496 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1500 tab_value (table, c, r, opt, v, proc->dict, print);
1504 /* Draws a line across TABLE at the current row to indicate the most
1505 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1506 that changed, and puts the values that changed into the table. TB
1507 and PT must be the corresponding table_entry and crosstab,
1510 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1511 struct tab_table *table, int first_difference)
1513 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1515 for (; first_difference >= 2; first_difference--)
1516 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1517 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1518 pt->vars[first_difference]);
1521 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1522 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1523 additionally suffixed with a letter `M'. */
1525 format_cell_entry (struct tab_table *table, int c, int r, double value,
1526 char suffix, bool mark_missing, const struct dictionary *dict)
1528 const struct fmt_spec f = {FMT_F, 10, 1};
1535 s = data_out (&v, dict_get_encoding (dict), &f);
1539 suffixes[suffix_len++] = suffix;
1541 suffixes[suffix_len++] = 'M';
1542 suffixes[suffix_len] = '\0';
1544 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1545 s + strspn (s, " "), suffixes);
1550 /* Displays the crosstabulation table. */
1552 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1553 struct tab_table *table)
1559 for (r = 0; r < pt->n_rows; r++)
1560 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1561 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1564 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1565 TAB_LEFT, _("Total"));
1567 /* Put in the actual cells. */
1569 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1570 for (r = 0; r < pt->n_rows; r++)
1572 if (proc->n_cells > 1)
1573 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1574 for (c = 0; c < pt->n_cols; c++)
1576 bool mark_missing = false;
1577 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1578 if (proc->exclude == MV_NEVER
1579 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1580 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1582 mark_missing = true;
1583 for (i = 0; i < proc->n_cells; i++)
1588 switch (proc->a_cells[i])
1594 v = *mp / pt->row_tot[r] * 100.;
1598 v = *mp / pt->col_tot[c] * 100.;
1602 v = *mp / pt->total * 100.;
1605 case CRS_CL_EXPECTED:
1608 case CRS_CL_RESIDUAL:
1609 v = *mp - expected_value;
1611 case CRS_CL_SRESIDUAL:
1612 v = (*mp - expected_value) / sqrt (expected_value);
1614 case CRS_CL_ASRESIDUAL:
1615 v = ((*mp - expected_value)
1616 / sqrt (expected_value
1617 * (1. - pt->row_tot[r] / pt->total)
1618 * (1. - pt->col_tot[c] / pt->total)));
1623 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1629 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1633 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1634 for (r = 0; r < pt->n_rows; r++)
1636 bool mark_missing = false;
1638 if (proc->exclude == MV_NEVER
1639 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1640 mark_missing = true;
1642 for (i = 0; i < proc->n_cells; i++)
1647 switch (proc->a_cells[i])
1657 v = pt->row_tot[r] / pt->total * 100.;
1661 v = pt->row_tot[r] / pt->total * 100.;
1664 case CRS_CL_EXPECTED:
1665 case CRS_CL_RESIDUAL:
1666 case CRS_CL_SRESIDUAL:
1667 case CRS_CL_ASRESIDUAL:
1674 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1675 tab_next_row (table);
1679 /* Column totals, grand total. */
1681 if (proc->n_cells > 1)
1682 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1683 for (c = 0; c <= pt->n_cols; c++)
1685 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1686 bool mark_missing = false;
1689 if (proc->exclude == MV_NEVER && c < pt->n_cols
1690 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1691 mark_missing = true;
1693 for (i = 0; i < proc->n_cells; i++)
1698 switch (proc->a_cells[i])
1704 v = ct / pt->total * 100.;
1712 v = ct / pt->total * 100.;
1715 case CRS_CL_EXPECTED:
1716 case CRS_CL_RESIDUAL:
1717 case CRS_CL_SRESIDUAL:
1718 case CRS_CL_ASRESIDUAL:
1724 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1729 tab_offset (table, -1, tab_row (table) + last_row);
1730 tab_offset (table, 0, -1);
1733 static void calc_r (struct pivot_table *,
1734 double *PT, double *Y, double *, double *, double *);
1735 static void calc_chisq (struct pivot_table *,
1736 double[N_CHISQ], int[N_CHISQ], double *, double *);
1738 /* Display chi-square statistics. */
1740 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1741 bool *showed_fisher)
1743 static const char *chisq_stats[N_CHISQ] =
1745 N_("Pearson Chi-Square"),
1746 N_("Likelihood Ratio"),
1747 N_("Fisher's Exact Test"),
1748 N_("Continuity Correction"),
1749 N_("Linear-by-Linear Association"),
1751 double chisq_v[N_CHISQ];
1752 double fisher1, fisher2;
1757 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1759 tab_offset (chisq, pt->n_vars - 2, -1);
1761 for (i = 0; i < N_CHISQ; i++)
1763 if ((i != 2 && chisq_v[i] == SYSMIS)
1764 || (i == 2 && fisher1 == SYSMIS))
1767 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1770 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1771 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1772 tab_double (chisq, 3, 0, TAB_RIGHT,
1773 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1777 *showed_fisher = true;
1778 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1779 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1781 tab_next_row (chisq);
1784 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1785 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1786 tab_next_row (chisq);
1788 tab_offset (chisq, 0, -1);
1791 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1792 double[N_SYMMETRIC], double[N_SYMMETRIC],
1793 double[N_SYMMETRIC],
1794 double[3], double[3], double[3]);
1796 /* Display symmetric measures. */
1798 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1799 struct tab_table *sym)
1801 static const char *categories[] =
1803 N_("Nominal by Nominal"),
1804 N_("Ordinal by Ordinal"),
1805 N_("Interval by Interval"),
1806 N_("Measure of Agreement"),
1809 static const char *stats[N_SYMMETRIC] =
1813 N_("Contingency Coefficient"),
1814 N_("Kendall's tau-b"),
1815 N_("Kendall's tau-c"),
1817 N_("Spearman Correlation"),
1822 static const int stats_categories[N_SYMMETRIC] =
1824 0, 0, 0, 1, 1, 1, 1, 2, 3,
1828 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1829 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1832 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1833 somers_d_v, somers_d_ase, somers_d_t))
1836 tab_offset (sym, pt->n_vars - 2, -1);
1838 for (i = 0; i < N_SYMMETRIC; i++)
1840 if (sym_v[i] == SYSMIS)
1843 if (stats_categories[i] != last_cat)
1845 last_cat = stats_categories[i];
1846 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1849 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1850 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1851 if (sym_ase[i] != SYSMIS)
1852 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1853 if (sym_t[i] != SYSMIS)
1854 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1855 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1859 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1860 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1863 tab_offset (sym, 0, -1);
1866 static int calc_risk (struct pivot_table *,
1867 double[], double[], double[], union value *);
1869 /* Display risk estimate. */
1871 display_risk (struct pivot_table *pt, struct tab_table *risk)
1874 double risk_v[3], lower[3], upper[3];
1878 if (!calc_risk (pt, risk_v, upper, lower, c))
1881 tab_offset (risk, pt->n_vars - 2, -1);
1883 for (i = 0; i < 3; i++)
1885 const struct variable *cv = pt->vars[COL_VAR];
1886 const struct variable *rv = pt->vars[ROW_VAR];
1887 int cvw = var_get_width (cv);
1888 int rvw = var_get_width (rv);
1890 if (risk_v[i] == SYSMIS)
1896 if (var_is_numeric (cv))
1897 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1898 var_get_name (cv), c[0].f, c[1].f);
1900 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1902 cvw, value_str (&c[0], cvw),
1903 cvw, value_str (&c[1], cvw));
1907 if (var_is_numeric (rv))
1908 sprintf (buf, _("For cohort %s = %g"),
1909 var_get_name (rv), pt->rows[i - 1].f);
1911 sprintf (buf, _("For cohort %s = %.*s"),
1913 rvw, value_str (&pt->rows[i - 1], rvw));
1917 tab_text (risk, 0, 0, TAB_LEFT, buf);
1918 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1919 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1920 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1921 tab_next_row (risk);
1924 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1925 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1926 tab_next_row (risk);
1928 tab_offset (risk, 0, -1);
1931 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1932 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1933 double[N_DIRECTIONAL]);
1935 /* Display directional measures. */
1937 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1938 struct tab_table *direct)
1940 static const char *categories[] =
1942 N_("Nominal by Nominal"),
1943 N_("Ordinal by Ordinal"),
1944 N_("Nominal by Interval"),
1947 static const char *stats[] =
1950 N_("Goodman and Kruskal tau"),
1951 N_("Uncertainty Coefficient"),
1956 static const char *types[] =
1963 static const int stats_categories[N_DIRECTIONAL] =
1965 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1968 static const int stats_stats[N_DIRECTIONAL] =
1970 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1973 static const int stats_types[N_DIRECTIONAL] =
1975 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
1978 static const int *stats_lookup[] =
1985 static const char **stats_names[] =
1997 double direct_v[N_DIRECTIONAL];
1998 double direct_ase[N_DIRECTIONAL];
1999 double direct_t[N_DIRECTIONAL];
2003 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2006 tab_offset (direct, pt->n_vars - 2, -1);
2008 for (i = 0; i < N_DIRECTIONAL; i++)
2010 if (direct_v[i] == SYSMIS)
2016 for (j = 0; j < 3; j++)
2017 if (last[j] != stats_lookup[j][i])
2020 tab_hline (direct, TAL_1, j, 6, 0);
2025 int k = last[j] = stats_lookup[j][i];
2030 string = var_get_name (pt->vars[0]);
2032 string = var_get_name (pt->vars[1]);
2034 tab_text_format (direct, j, 0, TAB_LEFT,
2035 gettext (stats_names[j][k]), string);
2040 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2041 if (direct_ase[i] != SYSMIS)
2042 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2043 if (direct_t[i] != SYSMIS)
2044 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2045 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2046 tab_next_row (direct);
2049 tab_offset (direct, 0, -1);
2052 /* Statistical calculations. */
2054 /* Returns the value of the gamma (factorial) function for an integer
2057 gamma_int (double pt)
2062 for (i = 2; i < pt; i++)
2067 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2069 static inline double
2070 Pr (int a, int b, int c, int d)
2072 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2073 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2074 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2075 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2076 / gamma_int (a + b + c + d + 1.));
2079 /* Swap the contents of A and B. */
2081 swap (int *a, int *b)
2088 /* Calculate significance for Fisher's exact test as specified in
2089 _SPSS Statistical Algorithms_, Appendix 5. */
2091 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2095 if (MIN (c, d) < MIN (a, b))
2096 swap (&a, &c), swap (&b, &d);
2097 if (MIN (b, d) < MIN (a, c))
2098 swap (&a, &b), swap (&c, &d);
2102 swap (&a, &b), swap (&c, &d);
2104 swap (&a, &c), swap (&b, &d);
2108 for (pt = 0; pt <= a; pt++)
2109 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2111 *fisher2 = *fisher1;
2112 for (pt = 1; pt <= b; pt++)
2113 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2116 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2117 columns with values COLS and N_ROWS rows with values ROWS. Values
2118 in the matrix sum to pt->total. */
2120 calc_chisq (struct pivot_table *pt,
2121 double chisq[N_CHISQ], int df[N_CHISQ],
2122 double *fisher1, double *fisher2)
2126 chisq[0] = chisq[1] = 0.;
2127 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2128 *fisher1 = *fisher2 = SYSMIS;
2130 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2132 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2134 chisq[0] = chisq[1] = SYSMIS;
2138 for (r = 0; r < pt->n_rows; r++)
2139 for (c = 0; c < pt->n_cols; c++)
2141 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2142 const double freq = pt->mat[pt->n_cols * r + c];
2143 const double residual = freq - expected;
2145 chisq[0] += residual * residual / expected;
2147 chisq[1] += freq * log (expected / freq);
2158 /* Calculate Yates and Fisher exact test. */
2159 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2161 double f11, f12, f21, f22;
2167 for (i = j = 0; i < pt->n_cols; i++)
2168 if (pt->col_tot[i] != 0.)
2177 f11 = pt->mat[nz_cols[0]];
2178 f12 = pt->mat[nz_cols[1]];
2179 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2180 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2185 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2188 chisq[3] = (pt->total * pow2 (pt_)
2189 / (f11 + f12) / (f21 + f22)
2190 / (f11 + f21) / (f12 + f22));
2198 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2199 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2202 /* Calculate Mantel-Haenszel. */
2203 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2205 double r, ase_0, ase_1;
2206 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2208 chisq[4] = (pt->total - 1.) * r * r;
2213 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2214 ASE_1, and ase_0 into ASE_0. The row and column values must be
2215 passed in PT and Y. */
2217 calc_r (struct pivot_table *pt,
2218 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2220 double SX, SY, S, T;
2222 double sum_XYf, sum_X2Y2f;
2223 double sum_Xr, sum_X2r;
2224 double sum_Yc, sum_Y2c;
2227 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2228 for (j = 0; j < pt->n_cols; j++)
2230 double fij = pt->mat[j + i * pt->n_cols];
2231 double product = PT[i] * Y[j];
2232 double temp = fij * product;
2234 sum_X2Y2f += temp * product;
2237 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2239 sum_Xr += PT[i] * pt->row_tot[i];
2240 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2242 Xbar = sum_Xr / pt->total;
2244 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2246 sum_Yc += Y[i] * pt->col_tot[i];
2247 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2249 Ybar = sum_Yc / pt->total;
2251 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2252 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2253 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2256 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2261 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2262 for (j = 0; j < pt->n_cols; j++)
2264 double Xresid, Yresid;
2267 Xresid = PT[i] - Xbar;
2268 Yresid = Y[j] - Ybar;
2269 temp = (T * Xresid * Yresid
2271 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2272 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2277 *ase_1 = sqrt (s) / (T * T);
2281 /* Calculate symmetric statistics and their asymptotic standard
2282 errors. Returns 0 if none could be calculated. */
2284 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2285 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2286 double t[N_SYMMETRIC],
2287 double somers_d_v[3], double somers_d_ase[3],
2288 double somers_d_t[3])
2292 q = MIN (pt->ns_rows, pt->ns_cols);
2296 for (i = 0; i < N_SYMMETRIC; i++)
2297 v[i] = ase[i] = t[i] = SYSMIS;
2299 /* Phi, Cramer's V, contingency coefficient. */
2300 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2302 double Xp = 0.; /* Pearson chi-square. */
2305 for (r = 0; r < pt->n_rows; r++)
2306 for (c = 0; c < pt->n_cols; c++)
2308 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2309 const double freq = pt->mat[pt->n_cols * r + c];
2310 const double residual = freq - expected;
2312 Xp += residual * residual / expected;
2315 if (proc->statistics & (1u << CRS_ST_PHI))
2317 v[0] = sqrt (Xp / pt->total);
2318 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2320 if (proc->statistics & (1u << CRS_ST_CC))
2321 v[2] = sqrt (Xp / (Xp + pt->total));
2324 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2325 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2330 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2334 Dr = Dc = pow2 (pt->total);
2335 for (r = 0; r < pt->n_rows; r++)
2336 Dr -= pow2 (pt->row_tot[r]);
2337 for (c = 0; c < pt->n_cols; c++)
2338 Dc -= pow2 (pt->col_tot[c]);
2340 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2341 for (c = 0; c < pt->n_cols; c++)
2345 for (r = 0; r < pt->n_rows; r++)
2346 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2355 for (i = 0; i < pt->n_rows; i++)
2359 for (j = 1; j < pt->n_cols; j++)
2360 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2363 for (j = 1; j < pt->n_cols; j++)
2364 Dij += cum[j + (i - 1) * pt->n_cols];
2368 double fij = pt->mat[j + i * pt->n_cols];
2372 if (++j == pt->n_cols)
2374 assert (j < pt->n_cols);
2376 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2377 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2381 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2382 Dij -= cum[j + (i - 1) * pt->n_cols];
2388 if (proc->statistics & (1u << CRS_ST_BTAU))
2389 v[3] = (P - Q) / sqrt (Dr * Dc);
2390 if (proc->statistics & (1u << CRS_ST_CTAU))
2391 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2392 if (proc->statistics & (1u << CRS_ST_GAMMA))
2393 v[5] = (P - Q) / (P + Q);
2395 /* ASE for tau-b, tau-c, gamma. Calculations could be
2396 eliminated here, at expense of memory. */
2401 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2402 for (i = 0; i < pt->n_rows; i++)
2406 for (j = 1; j < pt->n_cols; j++)
2407 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2410 for (j = 1; j < pt->n_cols; j++)
2411 Dij += cum[j + (i - 1) * pt->n_cols];
2415 double fij = pt->mat[j + i * pt->n_cols];
2417 if (proc->statistics & (1u << CRS_ST_BTAU))
2419 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2420 + v[3] * (pt->row_tot[i] * Dc
2421 + pt->col_tot[j] * Dr));
2422 btau_cum += fij * temp * temp;
2426 const double temp = Cij - Dij;
2427 ctau_cum += fij * temp * temp;
2430 if (proc->statistics & (1u << CRS_ST_GAMMA))
2432 const double temp = Q * Cij - P * Dij;
2433 gamma_cum += fij * temp * temp;
2436 if (proc->statistics & (1u << CRS_ST_D))
2438 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2439 - (P - Q) * (pt->total - pt->row_tot[i]));
2440 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2441 - (Q - P) * (pt->total - pt->col_tot[j]));
2444 if (++j == pt->n_cols)
2446 assert (j < pt->n_cols);
2448 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2449 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2453 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2454 Dij -= cum[j + (i - 1) * pt->n_cols];
2460 btau_var = ((btau_cum
2461 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2463 if (proc->statistics & (1u << CRS_ST_BTAU))
2465 ase[3] = sqrt (btau_var);
2466 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2469 if (proc->statistics & (1u << CRS_ST_CTAU))
2471 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2472 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2473 t[4] = v[4] / ase[4];
2475 if (proc->statistics & (1u << CRS_ST_GAMMA))
2477 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2478 t[5] = v[5] / (2. / (P + Q)
2479 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2481 if (proc->statistics & (1u << CRS_ST_D))
2483 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2484 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2485 somers_d_t[0] = (somers_d_v[0]
2487 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2488 somers_d_v[1] = (P - Q) / Dc;
2489 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2490 somers_d_t[1] = (somers_d_v[1]
2492 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2493 somers_d_v[2] = (P - Q) / Dr;
2494 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2495 somers_d_t[2] = (somers_d_v[2]
2497 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2503 /* Spearman correlation, Pearson's r. */
2504 if (proc->statistics & (1u << CRS_ST_CORR))
2506 double *R = xmalloc (sizeof *R * pt->n_rows);
2507 double *C = xmalloc (sizeof *C * pt->n_cols);
2510 double y, t, c = 0., s = 0.;
2515 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2516 y = pt->row_tot[i] - c;
2520 if (++i == pt->n_rows)
2522 assert (i < pt->n_rows);
2527 double y, t, c = 0., s = 0.;
2532 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2533 y = pt->col_tot[j] - c;
2537 if (++j == pt->n_cols)
2539 assert (j < pt->n_cols);
2543 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2549 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2553 /* Cohen's kappa. */
2554 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2556 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2559 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2560 i < pt->ns_rows; i++, j++)
2564 while (pt->col_tot[j] == 0.)
2567 prod = pt->row_tot[i] * pt->col_tot[j];
2568 sum = pt->row_tot[i] + pt->col_tot[j];
2570 sum_fii += pt->mat[j + i * pt->n_cols];
2572 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2573 sum_riciri_ci += prod * sum;
2575 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2576 for (j = 0; j < pt->ns_cols; j++)
2578 double sum = pt->row_tot[i] + pt->col_tot[j];
2579 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2582 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2584 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2585 + sum_rici * sum_rici
2586 - pt->total * sum_riciri_ci)
2587 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2589 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2590 / pow2 (pow2 (pt->total) - sum_rici))
2591 + ((2. * (pt->total - sum_fii)
2592 * (2. * sum_fii * sum_rici
2593 - pt->total * sum_fiiri_ci))
2594 / cube (pow2 (pt->total) - sum_rici))
2595 + (pow2 (pt->total - sum_fii)
2596 * (pt->total * sum_fijri_ci2 - 4.
2597 * sum_rici * sum_rici)
2598 / pow4 (pow2 (pt->total) - sum_rici))));
2600 t[8] = v[8] / ase[8];
2607 /* Calculate risk estimate. */
2609 calc_risk (struct pivot_table *pt,
2610 double *value, double *upper, double *lower, union value *c)
2612 double f11, f12, f21, f22;
2618 for (i = 0; i < 3; i++)
2619 value[i] = upper[i] = lower[i] = SYSMIS;
2622 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2629 for (i = j = 0; i < pt->n_cols; i++)
2630 if (pt->col_tot[i] != 0.)
2639 f11 = pt->mat[nz_cols[0]];
2640 f12 = pt->mat[nz_cols[1]];
2641 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2642 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2644 c[0] = pt->cols[nz_cols[0]];
2645 c[1] = pt->cols[nz_cols[1]];
2648 value[0] = (f11 * f22) / (f12 * f21);
2649 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2650 lower[0] = value[0] * exp (-1.960 * v);
2651 upper[0] = value[0] * exp (1.960 * v);
2653 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2654 v = sqrt ((f12 / (f11 * (f11 + f12)))
2655 + (f22 / (f21 * (f21 + f22))));
2656 lower[1] = value[1] * exp (-1.960 * v);
2657 upper[1] = value[1] * exp (1.960 * v);
2659 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2660 v = sqrt ((f11 / (f12 * (f11 + f12)))
2661 + (f21 / (f22 * (f21 + f22))));
2662 lower[2] = value[2] * exp (-1.960 * v);
2663 upper[2] = value[2] * exp (1.960 * v);
2668 /* Calculate directional measures. */
2670 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2671 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2672 double t[N_DIRECTIONAL])
2677 for (i = 0; i < N_DIRECTIONAL; i++)
2678 v[i] = ase[i] = t[i] = SYSMIS;
2682 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2684 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2685 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2686 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2687 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2688 double sum_fim, sum_fmj;
2690 int rm_index, cm_index;
2693 /* Find maximum for each row and their sum. */
2694 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2696 double max = pt->mat[i * pt->n_cols];
2699 for (j = 1; j < pt->n_cols; j++)
2700 if (pt->mat[j + i * pt->n_cols] > max)
2702 max = pt->mat[j + i * pt->n_cols];
2706 sum_fim += fim[i] = max;
2707 fim_index[i] = index;
2710 /* Find maximum for each column. */
2711 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2713 double max = pt->mat[j];
2716 for (i = 1; i < pt->n_rows; i++)
2717 if (pt->mat[j + i * pt->n_cols] > max)
2719 max = pt->mat[j + i * pt->n_cols];
2723 sum_fmj += fmj[j] = max;
2724 fmj_index[j] = index;
2727 /* Find maximum row total. */
2728 rm = pt->row_tot[0];
2730 for (i = 1; i < pt->n_rows; i++)
2731 if (pt->row_tot[i] > rm)
2733 rm = pt->row_tot[i];
2737 /* Find maximum column total. */
2738 cm = pt->col_tot[0];
2740 for (j = 1; j < pt->n_cols; j++)
2741 if (pt->col_tot[j] > cm)
2743 cm = pt->col_tot[j];
2747 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2748 v[1] = (sum_fmj - rm) / (pt->total - rm);
2749 v[2] = (sum_fim - cm) / (pt->total - cm);
2751 /* ASE1 for Y given PT. */
2755 for (accum = 0., i = 0; i < pt->n_rows; i++)
2756 for (j = 0; j < pt->n_cols; j++)
2758 const int deltaj = j == cm_index;
2759 accum += (pt->mat[j + i * pt->n_cols]
2760 * pow2 ((j == fim_index[i])
2765 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2768 /* ASE0 for Y given PT. */
2772 for (accum = 0., i = 0; i < pt->n_rows; i++)
2773 if (cm_index != fim_index[i])
2774 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2775 + pt->mat[i * pt->n_cols + cm_index]);
2776 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2779 /* ASE1 for PT given Y. */
2783 for (accum = 0., i = 0; i < pt->n_rows; i++)
2784 for (j = 0; j < pt->n_cols; j++)
2786 const int deltaj = i == rm_index;
2787 accum += (pt->mat[j + i * pt->n_cols]
2788 * pow2 ((i == fmj_index[j])
2793 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2796 /* ASE0 for PT given Y. */
2800 for (accum = 0., j = 0; j < pt->n_cols; j++)
2801 if (rm_index != fmj_index[j])
2802 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2803 + pt->mat[j + pt->n_cols * rm_index]);
2804 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2807 /* Symmetric ASE0 and ASE1. */
2812 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2813 for (j = 0; j < pt->n_cols; j++)
2815 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2816 int temp1 = (i == rm_index) + (j == cm_index);
2817 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2818 accum1 += (pt->mat[j + i * pt->n_cols]
2819 * pow2 (temp0 + (v[0] - 1.) * temp1));
2821 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2822 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2823 / (2. * pt->total - rm - cm));
2832 double sum_fij2_ri, sum_fij2_ci;
2833 double sum_ri2, sum_cj2;
2835 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2836 for (j = 0; j < pt->n_cols; j++)
2838 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2839 sum_fij2_ri += temp / pt->row_tot[i];
2840 sum_fij2_ci += temp / pt->col_tot[j];
2843 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2844 sum_ri2 += pow2 (pt->row_tot[i]);
2846 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2847 sum_cj2 += pow2 (pt->col_tot[j]);
2849 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2850 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2854 if (proc->statistics & (1u << CRS_ST_UC))
2856 double UX, UY, UXY, P;
2857 double ase1_yx, ase1_xy, ase1_sym;
2860 for (UX = 0., i = 0; i < pt->n_rows; i++)
2861 if (pt->row_tot[i] > 0.)
2862 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2864 for (UY = 0., j = 0; j < pt->n_cols; j++)
2865 if (pt->col_tot[j] > 0.)
2866 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2868 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2869 for (j = 0; j < pt->n_cols; j++)
2871 double entry = pt->mat[j + i * pt->n_cols];
2876 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2877 UXY -= entry / pt->total * log (entry / pt->total);
2880 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2881 for (j = 0; j < pt->n_cols; j++)
2883 double entry = pt->mat[j + i * pt->n_cols];
2888 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2889 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2890 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2891 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2892 ase1_sym += entry * pow2 ((UXY
2893 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2894 - (UX + UY) * log (entry / pt->total));
2897 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2898 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2899 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2900 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2902 v[6] = (UX + UY - UXY) / UX;
2903 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2904 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2906 v[7] = (UX + UY - UXY) / UY;
2907 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2908 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2912 if (proc->statistics & (1u << CRS_ST_D))
2914 double v_dummy[N_SYMMETRIC];
2915 double ase_dummy[N_SYMMETRIC];
2916 double t_dummy[N_SYMMETRIC];
2917 double somers_d_v[3];
2918 double somers_d_ase[3];
2919 double somers_d_t[3];
2921 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2922 somers_d_v, somers_d_ase, somers_d_t))
2925 for (i = 0; i < 3; i++)
2927 v[8 + i] = somers_d_v[i];
2928 ase[8 + i] = somers_d_ase[i];
2929 t[8 + i] = somers_d_t[i];
2935 if (proc->statistics & (1u << CRS_ST_ETA))
2938 double sum_Xr, sum_X2r;
2942 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2944 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2945 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2947 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2949 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2953 for (cum = 0., i = 0; i < pt->n_rows; i++)
2955 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2956 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2959 SXW -= cum * cum / pt->col_tot[j];
2961 v[11] = sqrt (1. - SXW / SX);
2965 double sum_Yc, sum_Y2c;
2969 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2971 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2972 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2974 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
2976 for (SYW = 0., i = 0; i < pt->n_rows; i++)
2980 for (cum = 0., j = 0; j < pt->n_cols; j++)
2982 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
2983 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
2986 SYW -= cum * cum / pt->row_tot[i];
2988 v[12] = sqrt (1. - SYW / SY);