1 /* This file is part of GNU PSPP
2 Computes Levene test statistic.
4 Copyright (C) 2004 Free Software Foundation, Inc.
5 Written by John Darrington <john@darrington.wattle.id.au>
7 This program is free software; you can redistribute it and/or
8 modify it under the terms of the GNU General Public License as
9 published by the Free Software Foundation; either version 2 of the
10 License, or (at your option) any later version.
12 This program is distributed in the hope that it will be useful, but
13 WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 General Public License for more details.
17 You should have received a copy of the GNU General Public License
18 along with this program; if not, write to the Free Software
19 Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
35 /* This module calculates the Levene statistic for variables.
37 Just for reference, the Levene Statistic is a defines as follows:
39 W = \frac{ (n-k)\sum_{i=1}^k n_i(Z_{iL} - Z_{LL})^2}
40 { (k-1)\sum_{i=1}^k \sum_{j=1}^{n_i} (Z_{ij} - Z_{iL})^2}
43 k is the number of groups
44 n is the total number of samples
45 n_i is the number of samples in the ith group
46 Z_{ij} is | Y_{ij} - Y_{iL} | where Y_{iL} is the mean of the ith group
47 Z_{iL} is the mean of Z_{ij} over the ith group
48 Z_{LL} is the grand mean of Z_{ij}
50 Imagine calculating that with pencil and paper!
54 static struct group_statistics *get_group(int v, struct group_statistics *key);
57 static void levene_precalc (void *);
58 static int levene_calc (struct ccase *, void *);
59 static void levene_postcalc (void *);
63 static void levene2_precalc (void *);
64 static int levene2_calc (struct ccase *, void *);
65 static void levene2_postcalc (void *);
71 /* The number of groups */
74 /* Per group statistics */
75 struct t_test_proc **group_stats;
77 /* The independent variable */
78 struct variable *v_indep;
80 /* Number of dependent variables */
83 /* The dependent variables */
84 struct variable **v_dep;
86 /* How to treat missing values */
87 enum lev_missing missing;
89 /* Function to test for missing values */
90 is_missing_func is_missing;
97 levene(struct variable *v_indep, int n_dep, struct variable **v_dep,
98 enum lev_missing missing, is_missing_func value_is_missing)
100 struct levene_info l;
106 l.is_missing = value_is_missing;
108 procedure(levene_precalc, levene_calc, levene_postcalc, &l);
109 procedure(levene2_precalc,levene2_calc,levene2_postcalc,&l);
113 static struct hsh_table **hash;
115 /* Return -1 if the id of a is less than b; +1 if greater than and
118 compare_group(const struct group_statistics *a,
119 const struct group_statistics *b,
122 int id_cmp = compare_values(&a->id, &b->id, width);
127 c= memcmp(&a->criterion,&b->criterion,sizeof(enum comparison));
136 hash_group(const struct group_statistics *g, int width)
141 id_hash = hsh_hash_double (g->id.f);
143 id_hash = hsh_hash_bytes (g->id.s, width);
148 /* Internal variables used in calculating the Levene statistic */
150 /* Per variable statistics */
153 /* Total of all lz */
159 /* The total number of cases */
162 /* Number of groups */
166 /* An array of lz_stats for each variable */
167 static struct lz_stats *lz;
169 /* Set to 1 if the groups require inequality comparisions */
170 static int inequality_compare;
174 levene_precalc (void *_l)
177 struct levene_info *l = (struct levene_info *) _l;
179 lz = xmalloc (sizeof (struct lz_stats ) * l->n_dep ) ;
181 hash = xmalloc (sizeof ( struct hsh_table *) * l->n_dep );
183 for(i=0; i < l->n_dep ; ++i )
185 struct variable *v = l->v_dep[i];
187 int number_of_groups = v->p.t_t.n_groups ;
189 hash[i] = hsh_create (l->n_dep * number_of_groups,
190 (hsh_compare_func *) compare_group,
191 (hsh_hash_func *) hash_group,
192 0,(void *) l->v_indep->width);
194 lz[i].grand_total = 0;
196 lz[i].n_groups = number_of_groups;
198 for (g = 0 ; g < v->p.t_t.n_groups ; ++g )
200 struct group_statistics *gs = &v->p.t_t.gs[g];
202 hsh_insert(hash[i], gs);
203 if ( gs->criterion != CMP_EQ )
205 inequality_compare = 1;
213 levene_calc (struct ccase *c, void *_l)
216 struct levene_info *l = (struct levene_info *) _l;
217 union value *gv = &c->data[l->v_indep->fv];
218 struct group_statistics key;
219 double weight = dict_get_case_weight(default_dict,c);
222 /* Skip the entire case if /MISSING=LISTWISE is set */
223 if ( l->missing == LEV_LISTWISE )
225 for (i = 0; i < l->n_dep; ++i)
227 struct variable *v = l->v_dep[i];
228 union value *val = &c->data[v->fv];
230 if (l->is_missing(val,v) )
239 key.criterion = CMP_EQ;
241 for (i = 0; i < l->n_dep; ++i)
243 struct variable *var = l->v_dep[i];
245 union value *v = &c->data[var->fv];
246 struct group_statistics *gs;
247 gs = get_group(i,&key);
251 if ( ! l->is_missing(v,var))
253 levene_z= fabs(v->f - gs->mean);
254 lz[i].grand_total += levene_z * weight;
255 lz[i].total_n += weight;
257 gs->lz_total += levene_z * weight;
265 levene_postcalc (void *_l)
269 struct levene_info *l = (struct levene_info *) _l;
271 for (v = 0; v < l->n_dep; ++v)
273 lz[v].grand_mean = lz[v].grand_total / lz[v].total_n ;
280 /* The denominator for the expression for the Levene */
281 static double *lz_denominator;
284 levene2_precalc (void *_l)
288 struct levene_info *l = (struct levene_info *) _l;
290 lz_denominator = (double *) xmalloc(sizeof(double) * l->n_dep);
292 /* This stuff could go in the first post calc . . . */
293 for (v = 0; v < l->n_dep; ++v)
295 struct hsh_iterator hi;
296 struct group_statistics *g;
297 for(g = (struct group_statistics *) hsh_first(hash[v],&hi);
299 g = (struct group_statistics *) hsh_next(hash[v],&hi) )
301 g->lz_mean = g->lz_total/g->n ;
303 lz_denominator[v] = 0;
308 levene2_calc (struct ccase *c, void *_l)
312 struct levene_info *l = (struct levene_info *) _l;
314 double weight = dict_get_case_weight(default_dict,c);
316 union value *gv = &c->data[l->v_indep->fv];
317 struct group_statistics key;
319 /* Skip the entire case if /MISSING=LISTWISE is set */
320 if ( l->missing == LEV_LISTWISE )
322 for (i = 0; i < l->n_dep; ++i)
324 struct variable *v = l->v_dep[i];
325 union value *val = &c->data[v->fv];
327 if (l->is_missing(val,v) )
335 key.criterion = CMP_EQ;
337 for (i = 0; i < l->n_dep; ++i)
340 struct variable *var = l->v_dep[i] ;
341 union value *v = &c->data[var->fv];
342 struct group_statistics *gs;
343 gs = get_group(i,&key);
347 if ( ! l->is_missing(v,var) )
349 levene_z = fabs(v->f - gs->mean);
350 lz_denominator[i] += weight * sqr(levene_z - gs->lz_mean);
359 levene2_postcalc (void *_l)
363 struct levene_info *l = (struct levene_info *) _l;
365 for (v = 0; v < l->n_dep; ++v)
367 double lz_numerator = 0;
368 struct hsh_iterator hi;
369 struct group_statistics *g;
370 for(g = (struct group_statistics *) hsh_first(hash[v],&hi);
372 g = (struct group_statistics *) hsh_next(hash[v],&hi) )
375 lz_numerator += g->n * sqr(g->lz_mean - lz[v].grand_mean );
379 lz_numerator *= ( l->v_dep[v]->p.t_t.ugs.n -
380 l->v_dep[v]->p.t_t.n_groups );
382 lz_denominator[v] /= (l->v_dep[v]->p.t_t.n_groups - 1);
384 l->v_dep[v]->p.t_t.levene = lz_numerator/lz_denominator[v] ;
387 /* Now clear up after ourselves */
388 free(lz_denominator);
389 for (v = 0; v < l->n_dep; ++v)
391 hsh_destroy(hash[v]);
399 /* Return the group belonging to the v_th dependent variable
400 which matches the key */
401 static struct group_statistics *
402 get_group(int v, struct group_statistics *key)
404 struct group_statistics *gs;
405 gs = hsh_find(hash[v],key);
408 if ( ( !gs ) && inequality_compare)
410 /* Here we degrade to a linear search.
411 This would seem inefficient. However, it should only ever happen
412 with the T-TEST, for which there are exactly two groups */
414 struct hsh_iterator hi;
416 assert( hsh_count(hash[v]) == 2 ) ;
417 for(gs = (struct group_statistics *) hsh_first(hash[v],&hi);
419 gs = (struct group_statistics *) hsh_next(hash[v],&hi) )
423 cmp = compare_values(&gs->id, &key->id, 0);
425 assert( cmp != 0 ); /* or else the hash would have found something */
428 ( gs->criterion == CMP_GT || gs->criterion == CMP_GE )
433 ( gs->criterion == CMP_LT || gs->criterion == CMP_LE )