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
38 /* This module calculates the Levene statistic for variables.
40 Just for reference, the Levene Statistic is a defines as follows:
42 W = \frac{ (n-k)\sum_{i=1}^k n_i(Z_{iL} - Z_{LL})^2}
43 { (k-1)\sum_{i=1}^k \sum_{j=1}^{n_i} (Z_{ij} - Z_{iL})^2}
46 k is the number of groups
47 n is the total number of samples
48 n_i is the number of samples in the ith group
49 Z_{ij} is | Y_{ij} - Y_{iL} | where Y_{iL} is the mean of the ith group
50 Z_{iL} is the mean of Z_{ij} over the ith group
51 Z_{LL} is the grand mean of Z_{ij}
53 Imagine calculating that with pencil and paper!
57 static struct group_statistics *get_group(int v, struct group_statistics *key);
63 /* Per group statistics */
64 struct t_test_proc **group_stats;
66 /* The independent variable */
67 struct variable *v_indep;
69 /* Number of dependent variables */
72 /* The dependent variables */
73 struct variable **v_dep;
75 /* How to treat missing values */
76 enum lev_missing missing;
78 /* Function to test for missing values */
79 is_missing_func is_missing;
84 static void levene_precalc (const struct levene_info *l);
85 static int levene_calc (const struct ccase *, void *);
86 static void levene_postcalc (void *);
90 static void levene2_precalc (void *);
91 static int levene2_calc (const struct ccase *, void *);
92 static void levene2_postcalc (void *);
96 levene(const struct casefile *cf,
97 struct variable *v_indep, int n_dep, struct variable **v_dep,
98 enum lev_missing missing, is_missing_func value_is_missing)
100 struct casereader *r;
101 const struct ccase *c;
102 struct levene_info l;
108 l.is_missing = value_is_missing;
113 for(r = casefile_get_reader (cf);
114 casereader_read (r, &c) ; )
118 casereader_destroy (r);
122 for(r = casefile_get_reader (cf);
123 casereader_read (r, &c) ; )
127 casereader_destroy (r);
128 levene2_postcalc(&l);
132 static struct hsh_table **hash;
135 /* Return -1 if the id of a is less than b; +1 if greater than and
138 compare_group(const struct group_statistics *a,
139 const struct group_statistics *b,
142 int id_cmp = compare_values(&a->id, &b->id, width);
147 c= memcmp(&a->criterion,&b->criterion,sizeof(enum comparison));
156 hash_group(const struct group_statistics *g, int width)
161 id_hash = hsh_hash_double (g->id.f);
163 id_hash = hsh_hash_bytes (g->id.s, width);
168 /* Internal variables used in calculating the Levene statistic */
170 /* Per variable statistics */
173 /* Total of all lz */
179 /* The total number of cases */
182 /* Number of groups */
186 /* An array of lz_stats for each variable */
187 static struct lz_stats *lz;
189 /* Set to 1 if the groups require inequality comparisions */
190 static int inequality_compare;
194 levene_precalc (const struct levene_info *l)
198 lz = xmalloc (sizeof (struct lz_stats ) * l->n_dep ) ;
200 hash = xmalloc (sizeof ( struct hsh_table *) * l->n_dep );
202 for(i=0; i < l->n_dep ; ++i )
204 struct variable *v = l->v_dep[i];
206 int number_of_groups = v->p.t_t.n_groups ;
208 hash[i] = hsh_create (l->n_dep * number_of_groups,
209 (hsh_compare_func *) compare_group,
210 (hsh_hash_func *) hash_group,
211 0,(void *) l->v_indep->width);
213 lz[i].grand_total = 0;
215 lz[i].n_groups = number_of_groups;
217 for (g = 0 ; g < v->p.t_t.n_groups ; ++g )
219 struct group_statistics *gs = &v->p.t_t.gs[g];
221 hsh_insert(hash[i], gs);
222 if ( gs->criterion != CMP_EQ )
224 inequality_compare = 1;
232 levene_calc (const struct ccase *c, void *_l)
235 struct levene_info *l = (struct levene_info *) _l;
236 const union value *gv = &c->data[l->v_indep->fv];
237 struct group_statistics key;
238 double weight = dict_get_case_weight(default_dict,c);
241 /* Skip the entire case if /MISSING=LISTWISE is set */
242 if ( l->missing == LEV_LISTWISE )
244 for (i = 0; i < l->n_dep; ++i)
246 struct variable *v = l->v_dep[i];
247 const union value *val = &c->data[v->fv];
249 if (l->is_missing(val,v) )
258 key.criterion = CMP_EQ;
260 for (i = 0; i < l->n_dep; ++i)
262 struct variable *var = l->v_dep[i];
264 const union value *v = &c->data[var->fv];
265 struct group_statistics *gs;
266 gs = get_group(i,&key);
270 if ( ! l->is_missing(v,var))
272 levene_z= fabs(v->f - gs->mean);
273 lz[i].grand_total += levene_z * weight;
274 lz[i].total_n += weight;
276 gs->lz_total += levene_z * weight;
284 levene_postcalc (void *_l)
288 struct levene_info *l = (struct levene_info *) _l;
290 for (v = 0; v < l->n_dep; ++v)
292 lz[v].grand_mean = lz[v].grand_total / lz[v].total_n ;
299 /* The denominator for the expression for the Levene */
300 static double *lz_denominator;
303 levene2_precalc (void *_l)
307 struct levene_info *l = (struct levene_info *) _l;
309 lz_denominator = (double *) xmalloc(sizeof(double) * l->n_dep);
311 /* This stuff could go in the first post calc . . . */
312 for (v = 0; v < l->n_dep; ++v)
314 struct hsh_iterator hi;
315 struct group_statistics *g;
316 for(g = (struct group_statistics *) hsh_first(hash[v],&hi);
318 g = (struct group_statistics *) hsh_next(hash[v],&hi) )
320 g->lz_mean = g->lz_total/g->n ;
322 lz_denominator[v] = 0;
327 levene2_calc (const struct ccase *c, void *_l)
331 struct levene_info *l = (struct levene_info *) _l;
333 double weight = dict_get_case_weight(default_dict,c);
335 const union value *gv = &c->data[l->v_indep->fv];
336 struct group_statistics key;
338 /* Skip the entire case if /MISSING=LISTWISE is set */
339 if ( l->missing == LEV_LISTWISE )
341 for (i = 0; i < l->n_dep; ++i)
343 struct variable *v = l->v_dep[i];
344 const union value *val = &c->data[v->fv];
346 if (l->is_missing(val,v) )
354 key.criterion = CMP_EQ;
356 for (i = 0; i < l->n_dep; ++i)
359 struct variable *var = l->v_dep[i] ;
360 const union value *v = &c->data[var->fv];
361 struct group_statistics *gs;
362 gs = get_group(i,&key);
366 if ( ! l->is_missing(v,var) )
368 levene_z = fabs(v->f - gs->mean);
369 lz_denominator[i] += weight * pow2(levene_z - gs->lz_mean);
378 levene2_postcalc (void *_l)
382 struct levene_info *l = (struct levene_info *) _l;
384 for (v = 0; v < l->n_dep; ++v)
386 double lz_numerator = 0;
387 struct hsh_iterator hi;
388 struct group_statistics *g;
389 for(g = (struct group_statistics *) hsh_first(hash[v],&hi);
391 g = (struct group_statistics *) hsh_next(hash[v],&hi) )
394 lz_numerator += g->n * pow2(g->lz_mean - lz[v].grand_mean );
398 lz_numerator *= ( l->v_dep[v]->p.t_t.ugs.n -
399 l->v_dep[v]->p.t_t.n_groups );
401 lz_denominator[v] /= (l->v_dep[v]->p.t_t.n_groups - 1);
403 l->v_dep[v]->p.t_t.levene = lz_numerator/lz_denominator[v] ;
406 /* Now clear up after ourselves */
407 free(lz_denominator);
408 for (v = 0; v < l->n_dep; ++v)
410 hsh_destroy(hash[v]);
418 /* Return the group belonging to the v_th dependent variable
419 which matches the key */
420 static struct group_statistics *
421 get_group(int v, struct group_statistics *key)
423 struct group_statistics *gs;
424 gs = hsh_find(hash[v],key);
427 if ( ( !gs ) && inequality_compare)
429 /* Here we degrade to a linear search.
430 This would seem inefficient. However, it should only ever happen
431 with the T-TEST, for which there are exactly two groups */
433 struct hsh_iterator hi;
435 assert( hsh_count(hash[v]) == 2 ) ;
436 for(gs = (struct group_statistics *) hsh_first(hash[v],&hi);
438 gs = (struct group_statistics *) hsh_next(hash[v],&hi) )
442 cmp = compare_values(&gs->id, &key->id, 0);
444 assert( cmp != 0 ); /* or else the hash would have found something */
447 ( gs->criterion == CMP_GT || gs->criterion == CMP_GE )
452 ( gs->criterion == CMP_LT || gs->criterion == CMP_LE )