1 /* PSPP - One way ANOVA. -*-c-*-
3 Copyright (C) 1997-9, 2000 Free Software Foundation, Inc.
4 Author: John Darrington 2004
6 This program is free software; you can redistribute it and/or
7 modify it under the terms of the GNU General Public License as
8 published by the Free Software Foundation; either version 2 of the
9 License, or (at your option) any later version.
11 This program is distributed in the hope that it will be useful, but
12 WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 General Public License for more details.
16 You should have received a copy of the GNU General Public License
17 along with this program; if not, write to the Free Software
18 Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
22 #include <gsl/gsl_cdf.h>
37 #include "value-labels.h"
49 +missing=miss:!analysis/listwise,
50 incl:include/!exclude;
51 contrast= double list;
52 statistics[st_]=descriptives,homogeneity.
59 static int bad_weight_warn = 1;
62 static struct cmd_oneway cmd;
64 /* The independent variable */
65 static struct variable *indep_var;
67 /* Number of dependent variables */
70 /* The dependent variables */
71 static struct variable **vars;
74 /* A hash table containing all the distinct values of the independent
76 static struct hsh_table *global_group_hash ;
78 /* The number of distinct values of the independent variable, when all
79 missing values are disregarded */
80 static int ostensible_number_of_groups=-1;
83 /* Function to use for testing for missing values */
84 static is_missing_func value_is_missing;
87 static void calculate(const struct casefile *cf, void *_mode);
90 /* Routines to show the output tables */
91 static void show_anova_table(void);
92 static void show_descriptives(void);
93 static void show_homogeneity(void);
94 static void show_contrast_coeffs(void);
95 static void show_contrast_tests(void);
104 if ( !parse_oneway(&cmd) )
107 /* If /MISSING=INCLUDE is set, then user missing values are ignored */
108 if (cmd.incl == ONEWAY_INCLUDE )
109 value_is_missing = is_system_missing;
111 value_is_missing = is_missing;
113 multipass_procedure_with_splits (calculate, &cmd);
115 /* Check the sanity of the given contrast values */
116 for (i = 0 ; i < cmd.sbc_contrast ; ++i )
121 if ( subc_list_double_count(&cmd.dl_contrast[i]) !=
122 ostensible_number_of_groups )
125 _("Number of contrast coefficients must equal the number of groups"));
129 for (j=0; j < ostensible_number_of_groups ; ++j )
130 sum += subc_list_double_at(&cmd.dl_contrast[i],j);
133 msg(SW,_("Coefficients for contrast %d do not total zero"),i + 1);
138 /* Show the statistics tables */
139 if ( cmd.sbc_statistics )
141 for (i = 0 ; i < ONEWAY_ST_count ; ++i )
143 if ( ! cmd.a_statistics[i] ) continue;
146 case ONEWAY_ST_DESCRIPTIVES:
149 case ONEWAY_ST_HOMOGENEITY:
159 if (cmd.sbc_contrast)
161 show_contrast_coeffs();
162 show_contrast_tests();
167 for (i = 0 ; i < n_vars ; ++i )
169 struct hsh_table *group_hash = vars[i]->p.ww.group_hash;
171 hsh_destroy(group_hash);
174 hsh_destroy(global_group_hash);
183 /* Parser for the variables sub command */
185 oneway_custom_variables(struct cmd_oneway *cmd UNUSED)
190 if ((token != T_ID || dict_lookup_var (default_dict, tokid) == NULL)
195 if (!parse_variables (default_dict, &vars, &n_vars,
197 | PV_NUMERIC | PV_NO_SCRATCH) )
205 if ( ! lex_match(T_BY))
209 indep_var = parse_variable();
213 msg(SE,_("`%s' is not a variable name"),tokid);
222 /* Show the ANOVA table */
224 show_anova_table(void)
228 int n_rows = n_vars * 3 + 1;
233 t = tab_create (n_cols,n_rows,0);
234 tab_headers (t, 2, 0, 1, 0);
235 tab_dim (t, tab_natural_dimensions);
242 n_cols - 1, n_rows - 1);
244 tab_hline (t, TAL_2, 0, n_cols - 1, 1 );
245 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
246 tab_vline (t, TAL_0, 1, 0, 0);
248 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Sum of Squares"));
249 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df"));
250 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Mean Square"));
251 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("F"));
252 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
255 for ( i=0 ; i < n_vars ; ++i )
257 struct group_statistics *totals = &vars[i]->p.ww.ugs;
258 struct hsh_table *group_hash = vars[i]->p.ww.group_hash;
259 struct hsh_iterator g;
260 struct group_statistics *gs;
264 for (gs = hsh_first (group_hash,&g);
266 gs = hsh_next(group_hash,&g))
268 ssa += (gs->sum * gs->sum)/gs->n;
271 ssa -= ( totals->sum * totals->sum ) / totals->n ;
273 const char *s = (vars[i]->label) ? vars[i]->label : vars[i]->name;
276 tab_text (t, 0, i * 3 + 1, TAB_LEFT | TAT_TITLE, s);
277 tab_text (t, 1, i * 3 + 1, TAB_LEFT | TAT_TITLE, _("Between Groups"));
278 tab_text (t, 1, i * 3 + 2, TAB_LEFT | TAT_TITLE, _("Within Groups"));
279 tab_text (t, 1, i * 3 + 3, TAB_LEFT | TAT_TITLE, _("Total"));
282 tab_hline(t, TAL_1, 0, n_cols - 1 , i * 3 + 1);
285 const double sst = totals->ssq - ( totals->sum * totals->sum) / totals->n ;
286 const double df1 = vars[i]->p.ww.n_groups - 1;
287 const double df2 = totals->n - vars[i]->p.ww.n_groups ;
288 const double msa = ssa / df1;
290 vars[i]->p.ww.mse = (sst - ssa) / df2;
293 /* Sums of Squares */
294 tab_float (t, 2, i * 3 + 1, 0, ssa, 10, 2);
295 tab_float (t, 2, i * 3 + 3, 0, sst, 10, 2);
296 tab_float (t, 2, i * 3 + 2, 0, sst - ssa, 10, 2);
299 /* Degrees of freedom */
300 tab_float (t, 3, i * 3 + 1, 0, df1, 4, 0);
301 tab_float (t, 3, i * 3 + 2, 0, df2, 4, 0);
302 tab_float (t, 3, i * 3 + 3, 0, totals->n - 1, 4, 0);
305 tab_float (t, 4, i * 3 + 1, TAB_RIGHT, msa, 8, 3);
306 tab_float (t, 4, i * 3 + 2, TAB_RIGHT, vars[i]->p.ww.mse, 8, 3);
310 const double F = msa/vars[i]->p.ww.mse ;
313 tab_float (t, 5, i * 3 + 1, 0, F, 8, 3);
315 /* The significance */
316 tab_float (t, 6, i * 3 + 1, 0, gsl_cdf_fdist_Q(F,df1,df2), 8, 3);
324 tab_title (t, 0, _("ANOVA"));
330 /* Show the descriptives table */
332 show_descriptives(void)
339 const double confidence=0.95;
340 const double q = (1.0 - confidence) / 2.0;
347 for ( v = 0 ; v < n_vars ; ++v )
348 n_rows += vars[v]->p.ww.n_groups + 1;
350 t = tab_create (n_cols,n_rows,0);
351 tab_headers (t, 2, 0, 2, 0);
352 tab_dim (t, tab_natural_dimensions);
355 /* Put a frame around the entire box, and vertical lines inside */
360 n_cols - 1, n_rows - 1);
362 /* Underline headers */
363 tab_hline (t, TAL_2, 0, n_cols - 1, 2 );
364 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
366 tab_text (t, 2, 1, TAB_CENTER | TAT_TITLE, _("N"));
367 tab_text (t, 3, 1, TAB_CENTER | TAT_TITLE, _("Mean"));
368 tab_text (t, 4, 1, TAB_CENTER | TAT_TITLE, _("Std. Deviation"));
369 tab_text (t, 5, 1, TAB_CENTER | TAT_TITLE, _("Std. Error"));
372 tab_vline(t, TAL_0, 7, 0, 0);
373 tab_hline(t, TAL_1, 6, 7, 1);
374 tab_joint_text (t, 6, 0, 7, 0, TAB_CENTER | TAT_TITLE | TAT_PRINTF, _("%g%% Confidence Interval for Mean"),confidence*100.0);
376 tab_text (t, 6, 1, TAB_CENTER | TAT_TITLE, _("Lower Bound"));
377 tab_text (t, 7, 1, TAB_CENTER | TAT_TITLE, _("Upper Bound"));
379 tab_text (t, 8, 1, TAB_CENTER | TAT_TITLE, _("Minimum"));
380 tab_text (t, 9, 1, TAB_CENTER | TAT_TITLE, _("Maximum"));
383 tab_title (t, 0, _("Descriptives"));
387 for ( v=0 ; v < n_vars ; ++v )
393 struct hsh_iterator g;
394 struct group_statistics *gs;
395 struct group_statistics *totals = &vars[v]->p.ww.ugs;
398 char *s = (vars[v]->label) ? vars[v]->label : vars[v]->name;
400 struct hsh_table *group_hash = vars[v]->p.ww.group_hash;
403 tab_text (t, 0, row, TAB_LEFT | TAT_TITLE, s);
405 tab_hline(t, TAL_1, 0, n_cols - 1 , row);
408 for (gs = hsh_first (group_hash,&g);
410 gs = hsh_next(group_hash,&g))
412 const char *s = val_labs_find(indep_var->val_labs, gs->id );
415 tab_text (t, 1, row + count,
416 TAB_LEFT | TAT_TITLE ,s);
417 else if ( indep_var->width != 0 )
418 tab_text (t, 1, row + count,
419 TAB_LEFT | TAT_TITLE, gs->id.s);
421 tab_text (t, 1, row + count,
422 TAB_LEFT | TAT_TITLE | TAT_PRINTF, "%g", gs->id.f);
425 /* Now fill in the numbers ... */
427 tab_float (t, 2, row + count, 0, gs->n, 8,0);
429 tab_float (t, 3, row + count, 0, gs->mean,8,2);
431 tab_float (t, 4, row + count, 0, gs->std_dev,8,2);
433 std_error = gs->std_dev/sqrt(gs->n) ;
434 tab_float (t, 5, row + count, 0,
437 /* Now the confidence interval */
439 T = gsl_cdf_tdist_Qinv(q,gs->n - 1);
441 tab_float(t, 6, row + count, 0,
442 gs->mean - T * std_error, 8, 2);
444 tab_float(t, 7, row + count, 0,
445 gs->mean + T * std_error, 8, 2);
449 tab_float(t, 8, row + count, 0, gs->minimum, 8, 2);
450 tab_float(t, 9, row + count, 0, gs->maximum, 8, 2);
455 tab_text (t, 1, row + count,
456 TAB_LEFT | TAT_TITLE ,_("Total"));
458 tab_float (t, 2, row + count, 0, totals->n, 8,0);
460 tab_float (t, 3, row + count, 0, totals->mean, 8,2);
462 tab_float (t, 4, row + count, 0, totals->std_dev,8,2);
464 std_error = totals->std_dev/sqrt(totals->n) ;
466 tab_float (t, 5, row + count, 0, std_error, 8,2);
468 /* Now the confidence interval */
470 T = gsl_cdf_tdist_Qinv(q,totals->n - 1);
472 tab_float(t, 6, row + count, 0,
473 totals->mean - T * std_error, 8, 2);
475 tab_float(t, 7, row + count, 0,
476 totals->mean + T * std_error, 8, 2);
480 tab_float(t, 8, row + count, 0, totals->minimum, 8, 2);
481 tab_float(t, 9, row + count, 0, totals->maximum, 8, 2);
483 row += vars[v]->p.ww.n_groups + 1;
492 /* Show the homogeneity table */
494 show_homogeneity(void)
498 int n_rows = n_vars + 1;
503 t = tab_create (n_cols,n_rows,0);
504 tab_headers (t, 1, 0, 1, 0);
505 tab_dim (t, tab_natural_dimensions);
507 /* Put a frame around the entire box, and vertical lines inside */
512 n_cols - 1, n_rows - 1);
515 tab_hline(t, TAL_2, 0, n_cols - 1, 1);
516 tab_vline(t, TAL_2, 1, 0, n_rows - 1);
519 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("Levene Statistic"));
520 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("df1"));
521 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df2"));
522 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
525 tab_title (t, 0, _("Test of Homogeneity of Variances"));
527 for ( v=0 ; v < n_vars ; ++v )
529 char *s = (vars[v]->label) ? vars[v]->label : vars[v]->name;
531 tab_text (t, 0, v + 1, TAB_LEFT | TAT_TITLE, s);
540 /* Show the contrast coefficients table */
542 show_contrast_coeffs(void)
545 int n_cols = 2 + ostensible_number_of_groups;
546 int n_rows = 2 + cmd.sbc_contrast;
547 struct hsh_iterator g;
548 union value *group_value;
555 t = tab_create (n_cols,n_rows,0);
556 tab_headers (t, 2, 0, 2, 0);
557 tab_dim (t, tab_natural_dimensions);
559 /* Put a frame around the entire box, and vertical lines inside */
564 n_cols - 1, n_rows - 1);
580 tab_hline(t, TAL_1, 2, n_cols - 1, 1);
583 tab_hline(t, TAL_2, 0, n_cols - 1, 2);
584 tab_vline(t, TAL_2, 2, 0, n_rows - 1);
587 tab_title (t, 0, _("Contrast Coefficients"));
589 tab_text (t, 0, 2, TAB_LEFT | TAT_TITLE, _("Contrast"));
591 s = (indep_var->label) ? indep_var->label : indep_var->name;
593 tab_joint_text (t, 2, 0, n_cols - 1, 0, TAB_CENTER | TAT_TITLE, s);
595 for (group_value = hsh_first (global_group_hash,&g);
597 group_value = hsh_next(global_group_hash,&g))
602 lab = val_labs_find(indep_var->val_labs,*group_value);
605 tab_text (t, count + 2, 1,
606 TAB_CENTER | TAT_TITLE ,lab);
608 tab_text (t, count + 2, 1,
609 TAB_CENTER | TAT_TITLE | TAT_PRINTF, "%g", group_value->f);
611 for (i = 0 ; i < cmd.sbc_contrast ; ++i )
613 tab_text(t, 1, i + 2, TAB_CENTER | TAT_PRINTF, "%d", i + 1);
614 tab_text(t, count + 2, i + 2, TAB_RIGHT | TAT_PRINTF, "%g",
615 subc_list_double_at(&cmd.dl_contrast[i],count)
627 /* Show the results of the contrast tests */
629 show_contrast_tests(void)
633 int n_rows = 1 + n_vars * 2 * cmd.sbc_contrast;
637 t = tab_create (n_cols,n_rows,0);
638 tab_headers (t, 3, 0, 1, 0);
639 tab_dim (t, tab_natural_dimensions);
641 /* Put a frame around the entire box, and vertical lines inside */
646 n_cols - 1, n_rows - 1);
654 tab_hline(t, TAL_2, 0, n_cols - 1, 1);
655 tab_vline(t, TAL_2, 3, 0, n_rows - 1);
658 tab_title (t, 0, _("Contrast Tests"));
660 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Contrast"));
661 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Value of Contrast"));
662 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Std. Error"));
663 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("t"));
664 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("df"));
665 tab_text (t, 7, 0, TAB_CENTER | TAT_TITLE, _("Sig. (2-tailed)"));
667 for ( v = 0 ; v < n_vars ; ++v )
670 int lines_per_variable = 2 * cmd.sbc_contrast;
673 tab_text (t, 0, (v * lines_per_variable) + 1, TAB_LEFT | TAT_TITLE,
674 vars[v]->label?vars[v]->label:vars[v]->name);
678 for ( i = 0 ; i < cmd.sbc_contrast ; ++i )
681 double contrast_value = 0.0;
682 double coef_msq = 0.0;
683 struct oneway_proc *ww = &vars[v]->p.ww ;
684 struct hsh_table *group_hash = ww->group_hash;
685 struct hsh_iterator g;
686 struct group_statistics *gs;
689 double std_error_contrast ;
694 /* Note: The calculation of the degrees of freedom in the variances
695 not equal case is painfull!!
696 The following formula may help to understand it:
697 \frac{\left(\sum_{i=1}^k{c_i^2\frac{s_i^2}{n_i}}\right)^2}
700 \frac{\left(c_i^2\frac{s_i^2}{n_i}\right)^2} {n_i-1}
705 double df_denominator = 0.0;
706 double df_numerator = 0.0;
711 tab_text (t, 1, (v * lines_per_variable) + i + 1,
712 TAB_LEFT | TAT_TITLE,
713 _("Assume equal variances"));
715 tab_text (t, 1, (v * lines_per_variable) + i + 1 + cmd.sbc_contrast,
716 TAB_LEFT | TAT_TITLE,
717 _("Does not assume equal"));
720 tab_text (t, 2, (v * lines_per_variable) + i + 1,
721 TAB_CENTER | TAT_TITLE | TAT_PRINTF, "%d",i+1);
724 tab_text (t, 2, (v * lines_per_variable) + i + 1 + cmd.sbc_contrast,
725 TAB_CENTER | TAT_TITLE | TAT_PRINTF, "%d",i+1);
727 /* FIXME: Potential danger here.
728 We're ASSUMING THE array is in the order corresponding to the
730 for (ci = 0, gs = hsh_first (group_hash,&g);
732 ++ci, gs = hsh_next(group_hash,&g))
735 const double coef = subc_list_double_at(&cmd.dl_contrast[i],ci);
736 const double winv = (gs->std_dev * gs->std_dev) / gs->n;
738 contrast_value += coef * gs->mean;
740 coef_msq += (coef * coef) / gs->n ;
742 sec_vneq += (coef * coef) * (gs->std_dev * gs->std_dev ) /gs->n ;
744 df_numerator += (coef * coef) * winv;
745 df_denominator += pow2((coef * coef) * winv) / (gs->n - 1);
748 sec_vneq = sqrt(sec_vneq);
751 df_numerator = pow2(df_numerator);
754 tab_float (t, 3, (v * lines_per_variable) + i + 1,
755 TAB_RIGHT, contrast_value, 8,2);
757 tab_float (t, 3, (v * lines_per_variable) + i + 1 + cmd.sbc_contrast,
758 TAB_RIGHT, contrast_value, 8,2);
761 std_error_contrast = sqrt(vars[v]->p.ww.mse * coef_msq);
764 tab_float (t, 4, (v * lines_per_variable) + i + 1,
765 TAB_RIGHT, std_error_contrast,
768 T = fabs(contrast_value / std_error_contrast) ;
772 tab_float (t, 5, (v * lines_per_variable) + i + 1,
776 df = ww->ugs.n - ww->n_groups;
778 /* Degrees of Freedom */
779 tab_float (t, 6, (v * lines_per_variable) + i + 1,
784 /* Significance TWO TAILED !!*/
785 tab_float (t, 7, (v * lines_per_variable) + i + 1,
786 TAB_RIGHT, 2 * gsl_cdf_tdist_Q(T,df),
790 /* Now for the Variances NOT Equal case */
794 (v * lines_per_variable) + i + 1 + cmd.sbc_contrast,
799 T = contrast_value / sec_vneq;
801 (v * lines_per_variable) + i + 1 + cmd.sbc_contrast,
806 df = df_numerator / df_denominator;
809 (v * lines_per_variable) + i + 1 + cmd.sbc_contrast,
813 /* The Significance */
815 tab_float (t, 7, (v * lines_per_variable) + i + 1 + cmd.sbc_contrast,
816 TAB_RIGHT, 2 * gsl_cdf_tdist_Q(T,df),
823 tab_hline(t, TAL_1, 0, n_cols - 1, (v * lines_per_variable) + 1);
831 /* ONEWAY ANOVA Calculations */
833 static void postcalc ( struct cmd_oneway *cmd UNUSED );
835 static void precalc ( struct cmd_oneway *cmd UNUSED );
837 int compare_group_id (const struct group_statistics *a,
838 const struct group_statistics *b, int width);
840 unsigned int hash_group_id(const struct group_statistics *v, int width);
842 void free_group_id(struct group_statistics *v, void *aux UNUSED);
848 compare_group_id (const struct group_statistics *a,
849 const struct group_statistics *b, int width)
851 return compare_values(&a->id, &b->id, width);
855 hash_group_id(const struct group_statistics *v, int width)
857 return hash_value ( &v->id, width);
861 free_group_id(struct group_statistics *v, void *aux UNUSED)
867 /* Pre calculations */
869 precalc ( struct cmd_oneway *cmd UNUSED )
873 for(i=0; i< n_vars ; ++i)
875 struct group_statistics *totals = &vars[i]->p.ww.ugs;
877 /* Create a hash for each of the dependent variables.
878 The hash contains a group_statistics structure,
879 and is keyed by value of the independent variable */
881 vars[i]->p.ww.group_hash =
883 (hsh_compare_func *) compare_group_id,
884 (hsh_hash_func *) hash_group_id,
885 (hsh_free_func *) free_group_id,
886 (void *) indep_var->width );
893 totals->maximum = - DBL_MAX;
894 totals->minimum = DBL_MAX;
900 calculate(const struct casefile *cf, void *cmd_)
902 struct casereader *r;
906 struct cmd_oneway *cmd = (struct cmd_oneway *) cmd_;
908 global_group_hash = hsh_create(4,
909 (hsh_compare_func *) compare_values,
910 (hsh_hash_func *) hash_value,
912 (void *) indep_var->width );
916 for(r = casefile_get_reader (cf);
917 casereader_read (r, &c) ;
922 const double weight =
923 dict_get_case_weight(default_dict,&c,&bad_weight_warn);
925 const union value *indep_val = case_data (&c, indep_var->fv);
927 hsh_insert ( global_group_hash, (void *) indep_val );
930 for ( i = 0 ; i < n_vars ; ++i )
932 const struct variable *v = vars[i];
934 const union value *val = case_data (&c, v->fv);
936 struct hsh_table *group_hash = vars[i]->p.ww.group_hash;
938 struct group_statistics *gs;
940 gs = hsh_find(group_hash, (void *) indep_val );
944 gs = (struct group_statistics *)
945 xmalloc (sizeof(struct group_statistics));
952 gs->minimum = DBL_MAX;
953 gs->maximum = -DBL_MAX;
955 hsh_insert ( group_hash, (void *) gs );
958 if (! value_is_missing(val,v) )
960 struct group_statistics *totals = &vars[i]->p.ww.ugs;
963 totals->sum+=weight * val->f;
964 totals->ssq+=weight * val->f * val->f;
966 if ( val->f * weight < totals->minimum )
967 totals->minimum = val->f * weight;
969 if ( val->f * weight > totals->maximum )
970 totals->maximum = val->f * weight;
973 gs->sum+=weight * val->f;
974 gs->ssq+=weight * val->f * val->f;
976 if ( val->f * weight < gs->minimum )
977 gs->minimum = val->f * weight;
979 if ( val->f * weight > gs->maximum )
980 gs->maximum = val->f * weight;
983 vars[i]->p.ww.n_groups = hsh_count ( group_hash );
987 casereader_destroy (r);
991 ostensible_number_of_groups = hsh_count (global_group_hash);
996 /* Post calculations for the ONEWAY command */
998 postcalc ( struct cmd_oneway *cmd UNUSED )
1003 for(i = 0; i < n_vars ; ++i)
1005 struct hsh_table *group_hash = vars[i]->p.ww.group_hash;
1006 struct group_statistics *totals = &vars[i]->p.ww.ugs;
1008 struct hsh_iterator g;
1009 struct group_statistics *gs;
1011 for (gs = hsh_first (group_hash,&g);
1013 gs = hsh_next(group_hash,&g))
1015 gs->mean=gs->sum / gs->n;
1016 gs->s_std_dev= sqrt(
1017 ( (gs->ssq / gs->n ) - gs->mean * gs->mean )
1022 ( (gs->ssq / gs->n ) - gs->mean * gs->mean )
1025 gs->se_mean = gs->std_dev / sqrt(gs->n);
1026 gs->mean_diff= gs->sum_diff / gs->n;
1032 totals->mean = totals->sum / totals->n;
1033 totals->std_dev= sqrt(
1034 totals->n/(totals->n-1) *
1035 ( (totals->ssq / totals->n ) - totals->mean * totals->mean )
1038 totals->se_mean = totals->std_dev / sqrt(totals->n);