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_tokid (lexer)) == NULL)
385 && lex_token (lexer) != T_ALL)
387 lex_match (lexer, '=');
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, '=');
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, '('))
494 if (!lex_force_int (lexer))
496 min = lex_integer (lexer);
499 lex_match (lexer, ',');
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, ')'))
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) == '/')
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 beginning at PB and continuing until PE,
912 exclusive. For efficiency, *MATP is a pointer to a matrix that can
913 hold *MAXROWS entries. */
915 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
917 struct tab_table *table = NULL; /* Crosstabulation table. */
918 struct tab_table *chisq = NULL; /* Chi-square table. */
919 bool showed_fisher = false;
920 struct tab_table *sym = NULL; /* Symmetric measures table. */
921 struct tab_table *risk = NULL; /* Risk estimate table. */
922 struct tab_table *direct = NULL; /* Directional measures table. */
925 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols, proc->descending);
928 table = create_crosstab_table (proc, pt);
929 if (proc->statistics & (1u << CRS_ST_CHISQ))
930 chisq = create_chisq_table (pt);
931 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
932 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
933 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
934 | (1u << CRS_ST_KAPPA)))
935 sym = create_sym_table (pt);
936 if (proc->statistics & (1u << CRS_ST_RISK))
937 risk = create_risk_table (pt);
938 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
939 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
940 direct = create_direct_table (pt);
943 while (find_crosstab (pt, &row0, &row1))
945 struct pivot_table x;
946 int first_difference;
948 make_pivot_table_subset (pt, row0, row1, &x);
950 /* Find all the row variable values. */
951 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows, proc->descending);
953 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
956 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
957 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
958 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
960 /* Allocate table space for the matrix. */
962 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
963 tab_realloc (table, -1,
964 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
965 tab_nr (table) * pt->n_entries / x.n_entries));
969 /* Find the first variable that differs from the last subtable. */
970 first_difference = find_first_difference (pt, row0);
973 display_dimensions (proc, &x, table, first_difference);
974 display_crosstabulation (proc, &x, table);
977 if (proc->exclude == MV_NEVER)
982 display_dimensions (proc, &x, chisq, first_difference);
983 display_chisq (&x, chisq, &showed_fisher);
987 display_dimensions (proc, &x, sym, first_difference);
988 display_symmetric (proc, &x, sym);
992 display_dimensions (proc, &x, risk, first_difference);
993 display_risk (&x, risk);
997 display_dimensions (proc, &x, direct, first_difference);
998 display_directional (proc, &x, direct);
1001 /* Free the parts of x that are not owned by pt. In
1002 particular we must not free x.cols, which is the same as
1003 pt->cols, which is freed at the end of this function. */
1011 submit (NULL, table);
1016 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1022 submit (pt, direct);
1028 build_matrix (struct pivot_table *x)
1030 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1031 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1034 struct table_entry **p;
1038 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1040 const struct table_entry *te = *p;
1042 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1044 for (; col < x->n_cols; col++)
1050 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1057 if (++col >= x->n_cols)
1063 while (mp < &x->mat[x->n_cols * x->n_rows])
1065 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1067 /* Column totals, row totals, ns_rows. */
1069 for (col = 0; col < x->n_cols; col++)
1070 x->col_tot[col] = 0.0;
1071 for (row = 0; row < x->n_rows; row++)
1072 x->row_tot[row] = 0.0;
1074 for (row = 0; row < x->n_rows; row++)
1076 bool row_is_empty = true;
1077 for (col = 0; col < x->n_cols; col++)
1081 row_is_empty = false;
1082 x->col_tot[col] += *mp;
1083 x->row_tot[row] += *mp;
1090 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1094 for (col = 0; col < x->n_cols; col++)
1095 for (row = 0; row < x->n_rows; row++)
1096 if (x->mat[col + row * x->n_cols] != 0.0)
1104 for (col = 0; col < x->n_cols; col++)
1105 x->total += x->col_tot[col];
1108 static struct tab_table *
1109 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1116 static const struct tuple names[] =
1118 {CRS_CL_COUNT, N_("count")},
1119 {CRS_CL_ROW, N_("row %")},
1120 {CRS_CL_COLUMN, N_("column %")},
1121 {CRS_CL_TOTAL, N_("total %")},
1122 {CRS_CL_EXPECTED, N_("expected")},
1123 {CRS_CL_RESIDUAL, N_("residual")},
1124 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1125 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1127 const int n_names = sizeof names / sizeof *names;
1128 const struct tuple *t;
1130 struct tab_table *table;
1131 struct string title;
1132 struct pivot_table x;
1136 make_pivot_table_subset (pt, 0, 0, &x);
1138 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1139 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1140 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1142 /* First header line. */
1143 tab_joint_text (table, x.n_consts + 1, 0,
1144 (x.n_consts + 1) + (x.n_cols - 1), 0,
1145 TAB_CENTER | TAT_TITLE, var_get_name (x.vars[COL_VAR]));
1147 tab_hline (table, TAL_1, x.n_consts + 1,
1148 x.n_consts + 2 + x.n_cols - 2, 1);
1150 /* Second header line. */
1151 for (i = 2; i < x.n_consts + 2; i++)
1152 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1153 x.n_consts + 2 - i - 1, 1,
1154 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1155 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1156 var_get_name (x.vars[ROW_VAR]));
1157 for (i = 0; i < x.n_cols; i++)
1158 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1159 &x.cols[i], x.vars[COL_VAR]);
1160 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1162 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1163 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1166 ds_init_empty (&title);
1167 for (i = 0; i < x.n_consts + 2; i++)
1170 ds_put_cstr (&title, " * ");
1171 ds_put_cstr (&title, var_get_name (x.vars[i]));
1173 for (i = 0; i < pt->n_consts; i++)
1175 const struct variable *var = pt->const_vars[i];
1179 ds_put_format (&title, ", %s=", var_get_name (var));
1181 /* Insert the formatted value of the variable, then trim
1182 leading spaces in what was just inserted. */
1183 ofs = ds_length (&title);
1184 s = data_out (&pt->const_values[i], var_get_encoding (var),
1185 var_get_print_format (var));
1186 ds_put_cstr (&title, s);
1188 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1192 ds_put_cstr (&title, " [");
1194 for (t = names; t < &names[n_names]; t++)
1195 if (proc->cells & (1u << t->value))
1198 ds_put_cstr (&title, ", ");
1199 ds_put_cstr (&title, gettext (t->name));
1201 ds_put_cstr (&title, "].");
1203 tab_title (table, "%s", ds_cstr (&title));
1204 ds_destroy (&title);
1206 tab_offset (table, 0, 2);
1210 static struct tab_table *
1211 create_chisq_table (struct pivot_table *pt)
1213 struct tab_table *chisq;
1215 chisq = tab_create (6 + (pt->n_vars - 2),
1216 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1217 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1219 tab_title (chisq, _("Chi-square tests."));
1221 tab_offset (chisq, pt->n_vars - 2, 0);
1222 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1223 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1224 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1225 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1226 _("Asymp. Sig. (2-tailed)"));
1227 tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1228 _("Exact Sig. (%d-tailed)"), 2);
1229 tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1230 _("Exact Sig. (%d-tailed)"), 1);
1231 tab_offset (chisq, 0, 1);
1236 /* Symmetric measures. */
1237 static struct tab_table *
1238 create_sym_table (struct pivot_table *pt)
1240 struct tab_table *sym;
1242 sym = tab_create (6 + (pt->n_vars - 2),
1243 pt->n_entries / pt->n_cols * 7 + 10);
1244 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1245 tab_title (sym, _("Symmetric measures."));
1247 tab_offset (sym, pt->n_vars - 2, 0);
1248 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1249 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1250 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1251 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1252 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1253 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1254 tab_offset (sym, 0, 1);
1259 /* Risk estimate. */
1260 static struct tab_table *
1261 create_risk_table (struct pivot_table *pt)
1263 struct tab_table *risk;
1265 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1266 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1267 tab_title (risk, _("Risk estimate."));
1269 tab_offset (risk, pt->n_vars - 2, 0);
1270 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1271 _("95%% Confidence Interval"));
1272 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1273 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1274 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1275 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1276 tab_hline (risk, TAL_1, 2, 3, 1);
1277 tab_vline (risk, TAL_1, 2, 0, 1);
1278 tab_offset (risk, 0, 2);
1283 /* Directional measures. */
1284 static struct tab_table *
1285 create_direct_table (struct pivot_table *pt)
1287 struct tab_table *direct;
1289 direct = tab_create (7 + (pt->n_vars - 2),
1290 pt->n_entries / pt->n_cols * 7 + 10);
1291 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1292 tab_title (direct, _("Directional measures."));
1294 tab_offset (direct, pt->n_vars - 2, 0);
1295 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1296 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1297 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1298 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1299 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1300 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1301 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1302 tab_offset (direct, 0, 1);
1308 /* Delete missing rows and columns for statistical analysis when
1311 delete_missing (struct pivot_table *pt)
1315 for (r = 0; r < pt->n_rows; r++)
1316 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1318 for (c = 0; c < pt->n_cols; c++)
1319 pt->mat[c + r * pt->n_cols] = 0.;
1324 for (c = 0; c < pt->n_cols; c++)
1325 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1327 for (r = 0; r < pt->n_rows; r++)
1328 pt->mat[c + r * pt->n_cols] = 0.;
1333 /* Prepare table T for submission, and submit it. */
1335 submit (struct pivot_table *pt, struct tab_table *t)
1342 tab_resize (t, -1, 0);
1343 if (tab_nr (t) == tab_t (t))
1345 table_unref (&t->table);
1348 tab_offset (t, 0, 0);
1350 for (i = 2; i < pt->n_vars; i++)
1351 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1352 var_to_string (pt->vars[i]));
1353 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1354 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1356 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1358 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1364 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1366 size_t row0 = *row1p;
1369 if (row0 >= pt->n_entries)
1372 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1374 struct table_entry *a = pt->entries[row0];
1375 struct table_entry *b = pt->entries[row1];
1376 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1384 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1385 result. WIDTH_ points to an int which is either 0 for a
1386 numeric value or a string width for a string value. */
1388 compare_value_3way (const void *a_, const void *b_, const void *width_)
1390 const union value *a = a_;
1391 const union value *b = b_;
1392 const int *width = width_;
1394 return value_compare_3way (a, b, *width);
1397 /* Inverted version of the above */
1399 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1401 return -compare_value_3way (a_, b_, width_);
1405 /* Given an array of ENTRY_CNT table_entry structures starting at
1406 ENTRIES, creates a sorted list of the values that the variable
1407 with index VAR_IDX takes on. The values are returned as a
1408 malloc()'d array stored in *VALUES, with the number of values
1409 stored in *VALUE_CNT.
1412 enum_var_values (const struct pivot_table *pt, int var_idx,
1413 union value **valuesp, int *n_values, bool descending)
1415 const struct variable *var = pt->vars[var_idx];
1416 struct var_range *range = get_var_range (var);
1417 union value *values;
1422 values = *valuesp = xnmalloc (range->count, sizeof *values);
1423 *n_values = range->count;
1424 for (i = 0; i < range->count; i++)
1425 values[i].f = range->min + i;
1429 int width = var_get_width (var);
1430 struct hmapx_node *node;
1431 const union value *iter;
1435 for (i = 0; i < pt->n_entries; i++)
1437 const struct table_entry *te = pt->entries[i];
1438 const union value *value = &te->values[var_idx];
1439 size_t hash = value_hash (value, width, 0);
1441 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1442 if (value_equal (iter, value, width))
1445 hmapx_insert (&set, (union value *) value, hash);
1450 *n_values = hmapx_count (&set);
1451 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1453 HMAPX_FOR_EACH (iter, node, &set)
1454 values[i++] = *iter;
1455 hmapx_destroy (&set);
1457 sort (values, *n_values, sizeof *values,
1458 descending ? compare_value_3way_inv : compare_value_3way,
1463 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1464 from V, displayed with print format spec from variable VAR. When
1465 in REPORT missing-value mode, missing values have an M appended. */
1467 table_value_missing (struct crosstabs_proc *proc,
1468 struct tab_table *table, int c, int r, unsigned char opt,
1469 const union value *v, const struct variable *var)
1471 const char *label = var_lookup_value_label (var, v);
1473 tab_text (table, c, r, TAB_LEFT, label);
1476 const struct fmt_spec *print = var_get_print_format (var);
1477 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1479 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1480 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1484 tab_value (table, c, r, opt, v, proc->dict, print);
1488 /* Draws a line across TABLE at the current row to indicate the most
1489 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1490 that changed, and puts the values that changed into the table. TB
1491 and PT must be the corresponding table_entry and crosstab,
1494 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1495 struct tab_table *table, int first_difference)
1497 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1499 for (; first_difference >= 2; first_difference--)
1500 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1501 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1502 pt->vars[first_difference]);
1505 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1506 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1507 additionally suffixed with a letter `M'. */
1509 format_cell_entry (struct tab_table *table, int c, int r, double value,
1510 char suffix, bool mark_missing, const struct dictionary *dict)
1512 const struct fmt_spec f = {FMT_F, 10, 1};
1519 s = data_out (&v, dict_get_encoding (dict), &f);
1523 suffixes[suffix_len++] = suffix;
1525 suffixes[suffix_len++] = 'M';
1526 suffixes[suffix_len] = '\0';
1528 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1529 s + strspn (s, " "), suffixes);
1534 /* Displays the crosstabulation table. */
1536 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1537 struct tab_table *table)
1543 for (r = 0; r < pt->n_rows; r++)
1544 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1545 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1548 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1549 TAB_LEFT, _("Total"));
1551 /* Put in the actual cells. */
1553 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1554 for (r = 0; r < pt->n_rows; r++)
1556 if (proc->n_cells > 1)
1557 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1558 for (c = 0; c < pt->n_cols; c++)
1560 bool mark_missing = false;
1561 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1562 if (proc->exclude == MV_NEVER
1563 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1564 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1566 mark_missing = true;
1567 for (i = 0; i < proc->n_cells; i++)
1572 switch (proc->a_cells[i])
1578 v = *mp / pt->row_tot[r] * 100.;
1582 v = *mp / pt->col_tot[c] * 100.;
1586 v = *mp / pt->total * 100.;
1589 case CRS_CL_EXPECTED:
1592 case CRS_CL_RESIDUAL:
1593 v = *mp - expected_value;
1595 case CRS_CL_SRESIDUAL:
1596 v = (*mp - expected_value) / sqrt (expected_value);
1598 case CRS_CL_ASRESIDUAL:
1599 v = ((*mp - expected_value)
1600 / sqrt (expected_value
1601 * (1. - pt->row_tot[r] / pt->total)
1602 * (1. - pt->col_tot[c] / pt->total)));
1607 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1613 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1617 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1618 for (r = 0; r < pt->n_rows; r++)
1620 bool mark_missing = false;
1622 if (proc->exclude == MV_NEVER
1623 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1624 mark_missing = true;
1626 for (i = 0; i < proc->n_cells; i++)
1631 switch (proc->a_cells[i])
1641 v = pt->row_tot[r] / pt->total * 100.;
1645 v = pt->row_tot[r] / pt->total * 100.;
1648 case CRS_CL_EXPECTED:
1649 case CRS_CL_RESIDUAL:
1650 case CRS_CL_SRESIDUAL:
1651 case CRS_CL_ASRESIDUAL:
1658 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1659 tab_next_row (table);
1663 /* Column totals, grand total. */
1665 if (proc->n_cells > 1)
1666 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1667 for (c = 0; c <= pt->n_cols; c++)
1669 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1670 bool mark_missing = false;
1673 if (proc->exclude == MV_NEVER && c < pt->n_cols
1674 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1675 mark_missing = true;
1677 for (i = 0; i < proc->n_cells; i++)
1682 switch (proc->a_cells[i])
1688 v = ct / pt->total * 100.;
1696 v = ct / pt->total * 100.;
1699 case CRS_CL_EXPECTED:
1700 case CRS_CL_RESIDUAL:
1701 case CRS_CL_SRESIDUAL:
1702 case CRS_CL_ASRESIDUAL:
1708 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1713 tab_offset (table, -1, tab_row (table) + last_row);
1714 tab_offset (table, 0, -1);
1717 static void calc_r (struct pivot_table *,
1718 double *PT, double *Y, double *, double *, double *);
1719 static void calc_chisq (struct pivot_table *,
1720 double[N_CHISQ], int[N_CHISQ], double *, double *);
1722 /* Display chi-square statistics. */
1724 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1725 bool *showed_fisher)
1727 static const char *chisq_stats[N_CHISQ] =
1729 N_("Pearson Chi-Square"),
1730 N_("Likelihood Ratio"),
1731 N_("Fisher's Exact Test"),
1732 N_("Continuity Correction"),
1733 N_("Linear-by-Linear Association"),
1735 double chisq_v[N_CHISQ];
1736 double fisher1, fisher2;
1741 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1743 tab_offset (chisq, pt->n_vars - 2, -1);
1745 for (i = 0; i < N_CHISQ; i++)
1747 if ((i != 2 && chisq_v[i] == SYSMIS)
1748 || (i == 2 && fisher1 == SYSMIS))
1751 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1754 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1755 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1756 tab_double (chisq, 3, 0, TAB_RIGHT,
1757 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1761 *showed_fisher = true;
1762 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1763 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1765 tab_next_row (chisq);
1768 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1769 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1770 tab_next_row (chisq);
1772 tab_offset (chisq, 0, -1);
1775 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1776 double[N_SYMMETRIC], double[N_SYMMETRIC],
1777 double[N_SYMMETRIC],
1778 double[3], double[3], double[3]);
1780 /* Display symmetric measures. */
1782 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1783 struct tab_table *sym)
1785 static const char *categories[] =
1787 N_("Nominal by Nominal"),
1788 N_("Ordinal by Ordinal"),
1789 N_("Interval by Interval"),
1790 N_("Measure of Agreement"),
1793 static const char *stats[N_SYMMETRIC] =
1797 N_("Contingency Coefficient"),
1798 N_("Kendall's tau-b"),
1799 N_("Kendall's tau-c"),
1801 N_("Spearman Correlation"),
1806 static const int stats_categories[N_SYMMETRIC] =
1808 0, 0, 0, 1, 1, 1, 1, 2, 3,
1812 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1813 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1816 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1817 somers_d_v, somers_d_ase, somers_d_t))
1820 tab_offset (sym, pt->n_vars - 2, -1);
1822 for (i = 0; i < N_SYMMETRIC; i++)
1824 if (sym_v[i] == SYSMIS)
1827 if (stats_categories[i] != last_cat)
1829 last_cat = stats_categories[i];
1830 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1833 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1834 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1835 if (sym_ase[i] != SYSMIS)
1836 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1837 if (sym_t[i] != SYSMIS)
1838 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1839 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1843 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1844 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1847 tab_offset (sym, 0, -1);
1850 static int calc_risk (struct pivot_table *,
1851 double[], double[], double[], union value *);
1853 /* Display risk estimate. */
1855 display_risk (struct pivot_table *pt, struct tab_table *risk)
1858 double risk_v[3], lower[3], upper[3];
1862 if (!calc_risk (pt, risk_v, upper, lower, c))
1865 tab_offset (risk, pt->n_vars - 2, -1);
1867 for (i = 0; i < 3; i++)
1869 const struct variable *cv = pt->vars[COL_VAR];
1870 const struct variable *rv = pt->vars[ROW_VAR];
1871 int cvw = var_get_width (cv);
1872 int rvw = var_get_width (rv);
1874 if (risk_v[i] == SYSMIS)
1880 if (var_is_numeric (cv))
1881 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1882 var_get_name (cv), c[0].f, c[1].f);
1884 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1886 cvw, value_str (&c[0], cvw),
1887 cvw, value_str (&c[1], cvw));
1891 if (var_is_numeric (rv))
1892 sprintf (buf, _("For cohort %s = %g"),
1893 var_get_name (rv), pt->rows[i - 1].f);
1895 sprintf (buf, _("For cohort %s = %.*s"),
1897 rvw, value_str (&pt->rows[i - 1], rvw));
1901 tab_text (risk, 0, 0, TAB_LEFT, buf);
1902 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1903 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1904 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1905 tab_next_row (risk);
1908 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1909 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1910 tab_next_row (risk);
1912 tab_offset (risk, 0, -1);
1915 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1916 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1917 double[N_DIRECTIONAL]);
1919 /* Display directional measures. */
1921 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1922 struct tab_table *direct)
1924 static const char *categories[] =
1926 N_("Nominal by Nominal"),
1927 N_("Ordinal by Ordinal"),
1928 N_("Nominal by Interval"),
1931 static const char *stats[] =
1934 N_("Goodman and Kruskal tau"),
1935 N_("Uncertainty Coefficient"),
1940 static const char *types[] =
1947 static const int stats_categories[N_DIRECTIONAL] =
1949 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1952 static const int stats_stats[N_DIRECTIONAL] =
1954 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1957 static const int stats_types[N_DIRECTIONAL] =
1959 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
1962 static const int *stats_lookup[] =
1969 static const char **stats_names[] =
1981 double direct_v[N_DIRECTIONAL];
1982 double direct_ase[N_DIRECTIONAL];
1983 double direct_t[N_DIRECTIONAL];
1987 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
1990 tab_offset (direct, pt->n_vars - 2, -1);
1992 for (i = 0; i < N_DIRECTIONAL; i++)
1994 if (direct_v[i] == SYSMIS)
2000 for (j = 0; j < 3; j++)
2001 if (last[j] != stats_lookup[j][i])
2004 tab_hline (direct, TAL_1, j, 6, 0);
2009 int k = last[j] = stats_lookup[j][i];
2014 string = var_get_name (pt->vars[0]);
2016 string = var_get_name (pt->vars[1]);
2018 tab_text_format (direct, j, 0, TAB_LEFT,
2019 gettext (stats_names[j][k]), string);
2024 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2025 if (direct_ase[i] != SYSMIS)
2026 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2027 if (direct_t[i] != SYSMIS)
2028 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2029 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2030 tab_next_row (direct);
2033 tab_offset (direct, 0, -1);
2036 /* Statistical calculations. */
2038 /* Returns the value of the gamma (factorial) function for an integer
2041 gamma_int (double pt)
2046 for (i = 2; i < pt; i++)
2051 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2053 static inline double
2054 Pr (int a, int b, int c, int d)
2056 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2057 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2058 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2059 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2060 / gamma_int (a + b + c + d + 1.));
2063 /* Swap the contents of A and B. */
2065 swap (int *a, int *b)
2072 /* Calculate significance for Fisher's exact test as specified in
2073 _SPSS Statistical Algorithms_, Appendix 5. */
2075 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2079 if (MIN (c, d) < MIN (a, b))
2080 swap (&a, &c), swap (&b, &d);
2081 if (MIN (b, d) < MIN (a, c))
2082 swap (&a, &b), swap (&c, &d);
2086 swap (&a, &b), swap (&c, &d);
2088 swap (&a, &c), swap (&b, &d);
2092 for (pt = 0; pt <= a; pt++)
2093 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2095 *fisher2 = *fisher1;
2096 for (pt = 1; pt <= b; pt++)
2097 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2100 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2101 columns with values COLS and N_ROWS rows with values ROWS. Values
2102 in the matrix sum to pt->total. */
2104 calc_chisq (struct pivot_table *pt,
2105 double chisq[N_CHISQ], int df[N_CHISQ],
2106 double *fisher1, double *fisher2)
2110 chisq[0] = chisq[1] = 0.;
2111 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2112 *fisher1 = *fisher2 = SYSMIS;
2114 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2116 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2118 chisq[0] = chisq[1] = SYSMIS;
2122 for (r = 0; r < pt->n_rows; r++)
2123 for (c = 0; c < pt->n_cols; c++)
2125 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2126 const double freq = pt->mat[pt->n_cols * r + c];
2127 const double residual = freq - expected;
2129 chisq[0] += residual * residual / expected;
2131 chisq[1] += freq * log (expected / freq);
2142 /* Calculate Yates and Fisher exact test. */
2143 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2145 double f11, f12, f21, f22;
2151 for (i = j = 0; i < pt->n_cols; i++)
2152 if (pt->col_tot[i] != 0.)
2161 f11 = pt->mat[nz_cols[0]];
2162 f12 = pt->mat[nz_cols[1]];
2163 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2164 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2169 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2172 chisq[3] = (pt->total * pow2 (pt_)
2173 / (f11 + f12) / (f21 + f22)
2174 / (f11 + f21) / (f12 + f22));
2182 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2183 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2186 /* Calculate Mantel-Haenszel. */
2187 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2189 double r, ase_0, ase_1;
2190 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2192 chisq[4] = (pt->total - 1.) * r * r;
2197 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2198 ASE_1, and ase_0 into ASE_0. The row and column values must be
2199 passed in PT and Y. */
2201 calc_r (struct pivot_table *pt,
2202 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2204 double SX, SY, S, T;
2206 double sum_XYf, sum_X2Y2f;
2207 double sum_Xr, sum_X2r;
2208 double sum_Yc, sum_Y2c;
2211 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2212 for (j = 0; j < pt->n_cols; j++)
2214 double fij = pt->mat[j + i * pt->n_cols];
2215 double product = PT[i] * Y[j];
2216 double temp = fij * product;
2218 sum_X2Y2f += temp * product;
2221 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2223 sum_Xr += PT[i] * pt->row_tot[i];
2224 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2226 Xbar = sum_Xr / pt->total;
2228 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2230 sum_Yc += Y[i] * pt->col_tot[i];
2231 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2233 Ybar = sum_Yc / pt->total;
2235 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2236 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2237 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2240 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2245 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2246 for (j = 0; j < pt->n_cols; j++)
2248 double Xresid, Yresid;
2251 Xresid = PT[i] - Xbar;
2252 Yresid = Y[j] - Ybar;
2253 temp = (T * Xresid * Yresid
2255 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2256 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2261 *ase_1 = sqrt (s) / (T * T);
2265 /* Calculate symmetric statistics and their asymptotic standard
2266 errors. Returns 0 if none could be calculated. */
2268 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2269 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2270 double t[N_SYMMETRIC],
2271 double somers_d_v[3], double somers_d_ase[3],
2272 double somers_d_t[3])
2276 q = MIN (pt->ns_rows, pt->ns_cols);
2280 for (i = 0; i < N_SYMMETRIC; i++)
2281 v[i] = ase[i] = t[i] = SYSMIS;
2283 /* Phi, Cramer's V, contingency coefficient. */
2284 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2286 double Xp = 0.; /* Pearson chi-square. */
2289 for (r = 0; r < pt->n_rows; r++)
2290 for (c = 0; c < pt->n_cols; c++)
2292 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2293 const double freq = pt->mat[pt->n_cols * r + c];
2294 const double residual = freq - expected;
2296 Xp += residual * residual / expected;
2299 if (proc->statistics & (1u << CRS_ST_PHI))
2301 v[0] = sqrt (Xp / pt->total);
2302 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2304 if (proc->statistics & (1u << CRS_ST_CC))
2305 v[2] = sqrt (Xp / (Xp + pt->total));
2308 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2309 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2314 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2318 Dr = Dc = pow2 (pt->total);
2319 for (r = 0; r < pt->n_rows; r++)
2320 Dr -= pow2 (pt->row_tot[r]);
2321 for (c = 0; c < pt->n_cols; c++)
2322 Dc -= pow2 (pt->col_tot[c]);
2324 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2325 for (c = 0; c < pt->n_cols; c++)
2329 for (r = 0; r < pt->n_rows; r++)
2330 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2339 for (i = 0; i < pt->n_rows; i++)
2343 for (j = 1; j < pt->n_cols; j++)
2344 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2347 for (j = 1; j < pt->n_cols; j++)
2348 Dij += cum[j + (i - 1) * pt->n_cols];
2352 double fij = pt->mat[j + i * pt->n_cols];
2356 if (++j == pt->n_cols)
2358 assert (j < pt->n_cols);
2360 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2361 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2365 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2366 Dij -= cum[j + (i - 1) * pt->n_cols];
2372 if (proc->statistics & (1u << CRS_ST_BTAU))
2373 v[3] = (P - Q) / sqrt (Dr * Dc);
2374 if (proc->statistics & (1u << CRS_ST_CTAU))
2375 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2376 if (proc->statistics & (1u << CRS_ST_GAMMA))
2377 v[5] = (P - Q) / (P + Q);
2379 /* ASE for tau-b, tau-c, gamma. Calculations could be
2380 eliminated here, at expense of memory. */
2385 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2386 for (i = 0; i < pt->n_rows; i++)
2390 for (j = 1; j < pt->n_cols; j++)
2391 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2394 for (j = 1; j < pt->n_cols; j++)
2395 Dij += cum[j + (i - 1) * pt->n_cols];
2399 double fij = pt->mat[j + i * pt->n_cols];
2401 if (proc->statistics & (1u << CRS_ST_BTAU))
2403 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2404 + v[3] * (pt->row_tot[i] * Dc
2405 + pt->col_tot[j] * Dr));
2406 btau_cum += fij * temp * temp;
2410 const double temp = Cij - Dij;
2411 ctau_cum += fij * temp * temp;
2414 if (proc->statistics & (1u << CRS_ST_GAMMA))
2416 const double temp = Q * Cij - P * Dij;
2417 gamma_cum += fij * temp * temp;
2420 if (proc->statistics & (1u << CRS_ST_D))
2422 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2423 - (P - Q) * (pt->total - pt->row_tot[i]));
2424 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2425 - (Q - P) * (pt->total - pt->col_tot[j]));
2428 if (++j == pt->n_cols)
2430 assert (j < pt->n_cols);
2432 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2433 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2437 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2438 Dij -= cum[j + (i - 1) * pt->n_cols];
2444 btau_var = ((btau_cum
2445 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2447 if (proc->statistics & (1u << CRS_ST_BTAU))
2449 ase[3] = sqrt (btau_var);
2450 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2453 if (proc->statistics & (1u << CRS_ST_CTAU))
2455 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2456 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2457 t[4] = v[4] / ase[4];
2459 if (proc->statistics & (1u << CRS_ST_GAMMA))
2461 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2462 t[5] = v[5] / (2. / (P + Q)
2463 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2465 if (proc->statistics & (1u << CRS_ST_D))
2467 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2468 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2469 somers_d_t[0] = (somers_d_v[0]
2471 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2472 somers_d_v[1] = (P - Q) / Dc;
2473 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2474 somers_d_t[1] = (somers_d_v[1]
2476 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2477 somers_d_v[2] = (P - Q) / Dr;
2478 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2479 somers_d_t[2] = (somers_d_v[2]
2481 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2487 /* Spearman correlation, Pearson's r. */
2488 if (proc->statistics & (1u << CRS_ST_CORR))
2490 double *R = xmalloc (sizeof *R * pt->n_rows);
2491 double *C = xmalloc (sizeof *C * pt->n_cols);
2494 double y, t, c = 0., s = 0.;
2499 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2500 y = pt->row_tot[i] - c;
2504 if (++i == pt->n_rows)
2506 assert (i < pt->n_rows);
2511 double y, t, c = 0., s = 0.;
2516 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2517 y = pt->col_tot[j] - c;
2521 if (++j == pt->n_cols)
2523 assert (j < pt->n_cols);
2527 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2533 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2537 /* Cohen's kappa. */
2538 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2540 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2543 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2544 i < pt->ns_rows; i++, j++)
2548 while (pt->col_tot[j] == 0.)
2551 prod = pt->row_tot[i] * pt->col_tot[j];
2552 sum = pt->row_tot[i] + pt->col_tot[j];
2554 sum_fii += pt->mat[j + i * pt->n_cols];
2556 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2557 sum_riciri_ci += prod * sum;
2559 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2560 for (j = 0; j < pt->ns_cols; j++)
2562 double sum = pt->row_tot[i] + pt->col_tot[j];
2563 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2566 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2568 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2569 + sum_rici * sum_rici
2570 - pt->total * sum_riciri_ci)
2571 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2573 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2574 / pow2 (pow2 (pt->total) - sum_rici))
2575 + ((2. * (pt->total - sum_fii)
2576 * (2. * sum_fii * sum_rici
2577 - pt->total * sum_fiiri_ci))
2578 / cube (pow2 (pt->total) - sum_rici))
2579 + (pow2 (pt->total - sum_fii)
2580 * (pt->total * sum_fijri_ci2 - 4.
2581 * sum_rici * sum_rici)
2582 / pow4 (pow2 (pt->total) - sum_rici))));
2584 t[8] = v[8] / ase[8];
2591 /* Calculate risk estimate. */
2593 calc_risk (struct pivot_table *pt,
2594 double *value, double *upper, double *lower, union value *c)
2596 double f11, f12, f21, f22;
2602 for (i = 0; i < 3; i++)
2603 value[i] = upper[i] = lower[i] = SYSMIS;
2606 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2613 for (i = j = 0; i < pt->n_cols; i++)
2614 if (pt->col_tot[i] != 0.)
2623 f11 = pt->mat[nz_cols[0]];
2624 f12 = pt->mat[nz_cols[1]];
2625 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2626 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2628 c[0] = pt->cols[nz_cols[0]];
2629 c[1] = pt->cols[nz_cols[1]];
2632 value[0] = (f11 * f22) / (f12 * f21);
2633 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2634 lower[0] = value[0] * exp (-1.960 * v);
2635 upper[0] = value[0] * exp (1.960 * v);
2637 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2638 v = sqrt ((f12 / (f11 * (f11 + f12)))
2639 + (f22 / (f21 * (f21 + f22))));
2640 lower[1] = value[1] * exp (-1.960 * v);
2641 upper[1] = value[1] * exp (1.960 * v);
2643 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2644 v = sqrt ((f11 / (f12 * (f11 + f12)))
2645 + (f21 / (f22 * (f21 + f22))));
2646 lower[2] = value[2] * exp (-1.960 * v);
2647 upper[2] = value[2] * exp (1.960 * v);
2652 /* Calculate directional measures. */
2654 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2655 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2656 double t[N_DIRECTIONAL])
2661 for (i = 0; i < N_DIRECTIONAL; i++)
2662 v[i] = ase[i] = t[i] = SYSMIS;
2666 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2668 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2669 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2670 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2671 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2672 double sum_fim, sum_fmj;
2674 int rm_index, cm_index;
2677 /* Find maximum for each row and their sum. */
2678 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2680 double max = pt->mat[i * pt->n_cols];
2683 for (j = 1; j < pt->n_cols; j++)
2684 if (pt->mat[j + i * pt->n_cols] > max)
2686 max = pt->mat[j + i * pt->n_cols];
2690 sum_fim += fim[i] = max;
2691 fim_index[i] = index;
2694 /* Find maximum for each column. */
2695 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2697 double max = pt->mat[j];
2700 for (i = 1; i < pt->n_rows; i++)
2701 if (pt->mat[j + i * pt->n_cols] > max)
2703 max = pt->mat[j + i * pt->n_cols];
2707 sum_fmj += fmj[j] = max;
2708 fmj_index[j] = index;
2711 /* Find maximum row total. */
2712 rm = pt->row_tot[0];
2714 for (i = 1; i < pt->n_rows; i++)
2715 if (pt->row_tot[i] > rm)
2717 rm = pt->row_tot[i];
2721 /* Find maximum column total. */
2722 cm = pt->col_tot[0];
2724 for (j = 1; j < pt->n_cols; j++)
2725 if (pt->col_tot[j] > cm)
2727 cm = pt->col_tot[j];
2731 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2732 v[1] = (sum_fmj - rm) / (pt->total - rm);
2733 v[2] = (sum_fim - cm) / (pt->total - cm);
2735 /* ASE1 for Y given PT. */
2739 for (accum = 0., i = 0; i < pt->n_rows; i++)
2740 for (j = 0; j < pt->n_cols; j++)
2742 const int deltaj = j == cm_index;
2743 accum += (pt->mat[j + i * pt->n_cols]
2744 * pow2 ((j == fim_index[i])
2749 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2752 /* ASE0 for Y given PT. */
2756 for (accum = 0., i = 0; i < pt->n_rows; i++)
2757 if (cm_index != fim_index[i])
2758 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2759 + pt->mat[i * pt->n_cols + cm_index]);
2760 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2763 /* ASE1 for PT given Y. */
2767 for (accum = 0., i = 0; i < pt->n_rows; i++)
2768 for (j = 0; j < pt->n_cols; j++)
2770 const int deltaj = i == rm_index;
2771 accum += (pt->mat[j + i * pt->n_cols]
2772 * pow2 ((i == fmj_index[j])
2777 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2780 /* ASE0 for PT given Y. */
2784 for (accum = 0., j = 0; j < pt->n_cols; j++)
2785 if (rm_index != fmj_index[j])
2786 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2787 + pt->mat[j + pt->n_cols * rm_index]);
2788 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2791 /* Symmetric ASE0 and ASE1. */
2796 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2797 for (j = 0; j < pt->n_cols; j++)
2799 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2800 int temp1 = (i == rm_index) + (j == cm_index);
2801 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2802 accum1 += (pt->mat[j + i * pt->n_cols]
2803 * pow2 (temp0 + (v[0] - 1.) * temp1));
2805 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2806 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2807 / (2. * pt->total - rm - cm));
2816 double sum_fij2_ri, sum_fij2_ci;
2817 double sum_ri2, sum_cj2;
2819 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2820 for (j = 0; j < pt->n_cols; j++)
2822 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2823 sum_fij2_ri += temp / pt->row_tot[i];
2824 sum_fij2_ci += temp / pt->col_tot[j];
2827 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2828 sum_ri2 += pow2 (pt->row_tot[i]);
2830 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2831 sum_cj2 += pow2 (pt->col_tot[j]);
2833 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2834 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2838 if (proc->statistics & (1u << CRS_ST_UC))
2840 double UX, UY, UXY, P;
2841 double ase1_yx, ase1_xy, ase1_sym;
2844 for (UX = 0., i = 0; i < pt->n_rows; i++)
2845 if (pt->row_tot[i] > 0.)
2846 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2848 for (UY = 0., j = 0; j < pt->n_cols; j++)
2849 if (pt->col_tot[j] > 0.)
2850 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2852 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2853 for (j = 0; j < pt->n_cols; j++)
2855 double entry = pt->mat[j + i * pt->n_cols];
2860 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2861 UXY -= entry / pt->total * log (entry / pt->total);
2864 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2865 for (j = 0; j < pt->n_cols; j++)
2867 double entry = pt->mat[j + i * pt->n_cols];
2872 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2873 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2874 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2875 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2876 ase1_sym += entry * pow2 ((UXY
2877 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2878 - (UX + UY) * log (entry / pt->total));
2881 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2882 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2883 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2884 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2886 v[6] = (UX + UY - UXY) / UX;
2887 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2888 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2890 v[7] = (UX + UY - UXY) / UY;
2891 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2892 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2896 if (proc->statistics & (1u << CRS_ST_D))
2898 double v_dummy[N_SYMMETRIC];
2899 double ase_dummy[N_SYMMETRIC];
2900 double t_dummy[N_SYMMETRIC];
2901 double somers_d_v[3];
2902 double somers_d_ase[3];
2903 double somers_d_t[3];
2905 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2906 somers_d_v, somers_d_ase, somers_d_t))
2909 for (i = 0; i < 3; i++)
2911 v[8 + i] = somers_d_v[i];
2912 ase[8 + i] = somers_d_ase[i];
2913 t[8 + i] = somers_d_t[i];
2919 if (proc->statistics & (1u << CRS_ST_ETA))
2922 double sum_Xr, sum_X2r;
2926 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2928 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2929 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2931 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2933 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2937 for (cum = 0., i = 0; i < pt->n_rows; i++)
2939 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2940 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2943 SXW -= cum * cum / pt->col_tot[j];
2945 v[11] = sqrt (1. - SXW / SX);
2949 double sum_Yc, sum_Y2c;
2953 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2955 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2956 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2958 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
2960 for (SYW = 0., i = 0; i < pt->n_rows; i++)
2964 for (cum = 0., j = 0; j < pt->n_cols; j++)
2966 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
2967 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
2970 SYW -= cum * cum / pt->row_tot[i];
2972 v[12] = sqrt (1. - SYW / SY);