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;
91 levene(struct variable *v_indep, int n_dep, struct variable **v_dep)
99 procedure(levene_precalc, levene_calc, levene_postcalc, &l);
100 procedure(levene2_precalc,levene2_calc,levene2_postcalc,&l);
104 static struct hsh_table **hash;
106 /* Return -1 if the id of a is less than b; +1 if greater than and
109 compare_group(const struct group_statistics *a,
110 const struct group_statistics *b,
113 int id_cmp = compare_values(&a->id, &b->id, width);
118 c= memcmp(&a->criterion,&b->criterion,sizeof(enum comparison));
127 hash_group(const struct group_statistics *g, int width)
132 id_hash = hsh_hash_double (g->id.f);
134 id_hash = hsh_hash_bytes (g->id.s, width);
139 /* Internal variables used in calculating the Levene statistic */
141 /* Per variable statistics */
144 /* Total of all lz */
150 /* The total number of cases */
153 /* Number of groups */
157 /* An array of lz_stats for each variable */
158 static struct lz_stats *lz;
160 /* Set to 1 if the groups require inequality comparisions */
161 static int inequality_compare;
165 levene_precalc (void *_l)
168 struct levene_info *l = (struct levene_info *) _l;
170 lz = xmalloc (sizeof (struct lz_stats ) * l->n_dep ) ;
172 hash = xmalloc (sizeof ( struct hsh_table *) * l->n_dep );
174 for(i=0; i < l->n_dep ; ++i )
176 struct variable *v = l->v_dep[i];
178 int number_of_groups = v->p.t_t.n_groups ;
180 hash[i] = hsh_create (l->n_dep * number_of_groups,
181 (hsh_compare_func *) compare_group,
182 (hsh_hash_func *) hash_group,
183 0,(void *) l->v_indep->width);
185 lz[i].grand_total = 0;
187 lz[i].n_groups = number_of_groups;
189 for (g = 0 ; g < v->p.t_t.n_groups ; ++g )
191 struct group_statistics *gs = &v->p.t_t.gs[g];
193 hsh_insert(hash[i], gs);
194 if ( gs->criterion != CMP_EQ )
196 inequality_compare = 1;
204 levene_calc (struct ccase *c, void *_l)
207 struct levene_info *l = (struct levene_info *) _l;
208 union value *gv = &c->data[l->v_indep->fv];
209 struct group_statistics key;
210 double weight = dict_get_case_weight(default_dict,c);
213 key.criterion = CMP_EQ;
215 for (var = 0; var < l->n_dep; ++var)
218 union value *v = &c->data[l->v_dep[var]->fv];
219 struct group_statistics *gs;
220 gs = get_group(var,&key);
224 /* FIXME: handle SYSMIS properly */
226 levene_z= fabs(v->f - gs->mean);
227 lz[var].grand_total += levene_z * weight;
228 lz[var].total_n += weight;
230 gs->lz_total += levene_z * weight;
238 levene_postcalc (void *_l)
242 struct levene_info *l = (struct levene_info *) _l;
244 for (v = 0; v < l->n_dep; ++v)
246 lz[v].grand_mean = lz[v].grand_total / lz[v].total_n ;
253 /* The denominator for the expression for the Levene */
254 static double *lz_denominator;
257 levene2_precalc (void *_l)
261 struct levene_info *l = (struct levene_info *) _l;
263 lz_denominator = (double *) xmalloc(sizeof(double) * l->n_dep);
265 /* This stuff could go in the first post calc . . . */
266 for (v = 0; v < l->n_dep; ++v)
268 struct hsh_iterator hi;
269 struct group_statistics *g;
270 for(g = (struct group_statistics *) hsh_first(hash[v],&hi);
272 g = (struct group_statistics *) hsh_next(hash[v],&hi) )
274 g->lz_mean = g->lz_total/g->n ;
276 lz_denominator[v] = 0;
281 levene2_calc (struct ccase *c, void *_l)
285 struct levene_info *l = (struct levene_info *) _l;
287 double weight = dict_get_case_weight(default_dict,c);
289 union value *gv = &c->data[l->v_indep->fv];
290 struct group_statistics key;
293 key.criterion = CMP_EQ;
295 for (var = 0; var < l->n_dep; ++var)
298 union value *v = &c->data[l->v_dep[var]->fv];
299 struct group_statistics *gs;
300 gs = get_group(var,&key);
304 /* FIXME: handle SYSMIS properly */
306 levene_z = fabs(v->f - gs->mean);
308 lz_denominator[var] += weight * sqr(levene_z - gs->lz_mean);
316 levene2_postcalc (void *_l)
320 struct levene_info *l = (struct levene_info *) _l;
322 for (v = 0; v < l->n_dep; ++v)
324 double lz_numerator = 0;
325 struct hsh_iterator hi;
326 struct group_statistics *g;
327 for(g = (struct group_statistics *) hsh_first(hash[v],&hi);
329 g = (struct group_statistics *) hsh_next(hash[v],&hi) )
332 lz_numerator += g->n * sqr(g->lz_mean - lz[v].grand_mean );
336 lz_numerator *= ( l->v_dep[v]->p.t_t.ugs.n -
337 l->v_dep[v]->p.t_t.n_groups );
339 lz_denominator[v] /= (l->v_dep[v]->p.t_t.n_groups - 1);
341 l->v_dep[v]->p.t_t.levene = lz_numerator/lz_denominator[v] ;
344 /* Now clear up after ourselves */
345 free(lz_denominator);
346 for (v = 0; v < l->n_dep; ++v)
348 hsh_destroy(hash[v]);
356 /* Return the group belonging to the v_th dependent variable
357 which matches the key */
358 static struct group_statistics *
359 get_group(int v, struct group_statistics *key)
361 struct group_statistics *gs;
362 gs = hsh_find(hash[v],key);
365 if ( ( !gs ) && inequality_compare)
367 /* Here we degrade to a linear search.
368 This would seem inefficient. However, it should only ever happen
369 with the T-TEST, for which there are exactly two groups */
371 struct hsh_iterator hi;
373 assert( hsh_count(hash[v]) == 2 ) ;
374 for(gs = (struct group_statistics *) hsh_first(hash[v],&hi);
376 gs = (struct group_statistics *) hsh_next(hash[v],&hi) )
380 cmp = compare_values(&gs->id, &key->id, 0);
382 assert( cmp != 0 ); /* or else the hash would have found something */
385 ( gs->criterion == CMP_GT || gs->criterion == CMP_GE )
390 ( gs->criterion == CMP_LT || gs->criterion == CMP_LE )