Blame view
tools/sctk-2.4.10/src/sclite/anovar.c
20.3 KB
8dcb6dfcb
first commit
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 |
/**********************************************************************/
/* */
/* FILE: anovar.c */
/* WRITTEN BY: Jonathan G. Fiscus */
/* DATE: April 14 1989 */
/* NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY */
/* SPEECH RECOGNITION GROUP */
/* */
/* USAGE: This uses the rank structure to perform */
/* a Friedman two-way analysis of variance */
/* by ranks and generates a report. */
/* */
/* SOURCE:Applied Non Parametric Statistics by Daniel */
/* */
/**********************************************************************/
#include "sctk.h"
#define FRI_TITLE "Friedman Two-way Analysis of Variance by Ranks"
#define RANK_TITLEA "COMPARISON MATRIX: Comparing All Systems"
#define RANK_TITLEB "COMPARISON MATRIX: Comparing All Speakers"
#define RANK_TITLE_1 "Using a Multiple Comparison Test"
#define ADJUST_THRESH 0.50000
#define MULTI_COMP_ALPHA 0.05
static int analyze_rank_sum(RANK *, int, int, double *, int, int, FILE *);
static void print_result_of_analyze_rank_sum(int, double, double, char *,FILE *);
static double dsum_sqr(double *, int);
static double calc_adjust_for_trt(RANK *);
static double calc_adjust_for_blks(RANK *);
static void do_multi_comp_for_anovar(int, int, char **, double *, double *, char *, int *, int **, int, FILE *);
static void calc_stat_ranks(int, int, int **, double*);
static double calc_comp_value(int, int);
static void print_ANOVAR_comp_matrix(int, int **, char **, char *, int *, FILE *);
/****************************************************************/
/* main procedure to perform a two-way analysis of variance by*/
/* ranks. first the sum of the treatment and block ranks */
/* are summed then if there is a difference between at least */
/* one of the blocks or treatments, then a multiple comparison*/
/* is performed */
/****************************************************************/
void compute_anovar(RANK *rank, int verbose, int report, int ***out_sys_winner, char *outroot, int feedback, double ***out_conf)
{
double *sum_trt_rank, *sum_blk_rank;
char pad[FULL_SCREEN];
int i,j, **trt_winner, **blk_winner;
double **conf;
FILE *fp = stdout;
if (report || verbose){
char *f = rsprintf("%s.anovar",outroot);
if ((fp=(strcmp(outroot,"-") == 0) ? stdout : fopen(f,"w")) ==
(FILE *)0){
fprintf(stderr,"Warning: Open of %s for write failed. "
"Using stdout instead.
",f);
fp = stdout;
} else
if (feedback >= 1) printf(" Output written to '%s'
",f);
}
alloc_2dimZ(conf,rank->n_trt,rank->n_trt,double,0.0);
alloc_2dimZ(trt_winner,rank->n_trt,rank->n_trt,int,NO_DIFF);
alloc_2dimZ(blk_winner,rank->n_blk,rank->n_blk,int,NO_DIFF);
*out_sys_winner = trt_winner;
*out_conf = conf;
alloc_singZ(sum_trt_rank,rnk_trt(rank),double,0.0);
alloc_singZ(sum_blk_rank,rnk_blks(rank),double,0.0);
/* sum the ranks */
for (i=0;i<rnk_blks(rank);i++)
for (j=0;j<rnk_trt(rank);j++){
sum_trt_rank[j] += Vrnk_t_rank(rank,i,j);
sum_blk_rank[i] += Vrnk_b_rank(rank,i,j);
}
if (verbose){
set_pad(pad,FRI_TITLE, FULL_SCREEN);
fprintf(fp,"
%s%s
",pad,FRI_TITLE);
fprintf(fp,"%s----------------------------------------------
",pad);
set_pad_cent_n(pad,SCREEN_WIDTH, FULL_SCREEN);
fprintf(fp,"%s\tHo: Testing the hypothesis that all recognizers are the same",
pad);
}
/* if at least one difference, do multiple comparison */
if (analyze_rank_sum(rank,rnk_trt(rank),rnk_blks(rank),
sum_trt_rank,
FOR_TREATMENTS,verbose,fp) == TEST_DIFF)
clear_2dim(trt_winner,rank->n_trt,rank->n_trt,NO_DIFF);
do_multi_comp_for_anovar(rnk_trt(rank),rnk_blks(rank),
rnk_t_name(rank),sum_trt_rank,
ovr_t_rank(rank),RANK_TITLEA,
srt_t_rank(rank),trt_winner,verbose,fp);
if (verbose) form_feed(fp);
if (verbose){
set_pad(pad,FRI_TITLE, FULL_SCREEN);
fprintf(fp,"
%s%s
",pad,FRI_TITLE);
fprintf(fp,"%s----------------------------------------------
",pad);
set_pad_cent_n(pad,SCREEN_WIDTH, FULL_SCREEN);
fprintf(fp,"%s\tHo: Testing the hypothesis that all speakers are the same",
pad);
}
/* if at least one difference, do multiple comparison */
if (analyze_rank_sum(rank,rnk_blks(rank),rnk_trt(rank),sum_blk_rank,
FOR_BLOCKS,verbose,fp) == TEST_DIFF)
clear_2dim(blk_winner,rank->n_blk,rank->n_blk,NO_DIFF);
do_multi_comp_for_anovar(rnk_blks(rank),rnk_trt(rank),
rnk_b_name(rank),sum_blk_rank,
ovr_b_rank(rank),RANK_TITLEB,
srt_b_rank(rank),blk_winner, verbose,fp);
if (verbose && (fp == stdout)) form_feed(fp);
free_2dimarr(blk_winner,rank->n_blk,int);
free_singarr(sum_trt_rank,double);
free_singarr(sum_blk_rank,double);
if (fp != stdout) fclose(fp);
}
/*****************************************************************/
/* X2_r formula: */
/* k */
/* 12 --. 2 */
/* ------- * \ R - 3b(t+1) */
/* bt(t+1) / j */
/* --' */
/* j = 1 */
/* */
/* b = num_blk */
/* t = num_trt */
/* R = Sum of the ranks for that column */
/* */
/* this is the initial test to see if the treatment or ranks */
/* are different */
/*****************************************************************/
static int analyze_rank_sum(RANK *rank, int trt_num, int blk_num, double *sum_arr, int orient, int verbose,FILE *fp)
{
int df;
double X2_r, adjust;
char *subject_blk = "speaker";
char *subject_trt = "recognition system";
/* calculate the test statistic */
df = trt_num - 2; /* #trt is one based so subtract 2 */
/* make sure df isn't negative */;
if (df < 0) df = 0;
/* make sure df isn't greater than MAX_DF */
if (df > MAX_DF) df = MAX_DF;
X2_r = (12.00000 /
(double)(blk_num*trt_num*(trt_num+1))) *
(dsum_sqr(sum_arr,trt_num)) -
3.00000 * (double)blk_num * (double)(trt_num+1);
if (orient == FOR_TREATMENTS)
adjust = calc_adjust_for_trt(rank);
else
adjust = calc_adjust_for_blks(rank);
/* if two identical systems are entered, adjust will be 0.0 and core*/
/* dump. this avoids this */
if (adjust == 0.0)
X2_r = 0.0;
else
X2_r /= adjust;
if (verbose)
if (orient == FOR_TREATMENTS)
print_result_of_analyze_rank_sum(df, X2_r, adjust, subject_trt,fp); else
print_result_of_analyze_rank_sum(df, X2_r, adjust, subject_blk,fp);
/* return the result */
if (X2_r > X2.df[df].level[GEN_X2_PER])
return(TEST_DIFF);
else
return(NO_DIFF);
}
/*****************************************************************/
/* print to stdout the results of the rank_sum test */
/*****************************************************************/
static void print_result_of_analyze_rank_sum(int df, double X2_r, double adjust, char *subject, FILE *fp)
{
char pad[FULL_SCREEN];
int i;
set_pad_cent_n(pad,SCREEN_WIDTH, FULL_SCREEN);
fprintf(fp,"
%s%35sReject if
",pad,"");
fprintf(fp,"%s%26sX2_r > X2 of %s %s (%2.3f)
", pad, "",
X2_pct_str(GEN_X2_PER),
X2_df_str(df),
X2_score(df,GEN_X2_PER));
fprintf(fp,"
");
fprintf(fp,"%s%26sadjustment = %2.3f
",pad,"",adjust);
fprintf(fp,"%s%30s X2_r = %2.3f
",pad,"",X2_r);
if (adjust < ADJUST_THRESH){
fprintf(fp,"
%s\t\t*** Warning: ties adjustment may have severely
",
pad);
fprintf(fp,"%s\t\t exagerated the X2_r value
",pad);
}
fprintf(fp,"%sANALYSIS:
%s--------
",pad,pad);
if (X2_r > X2_score(df,GEN_X2_PER)){
fprintf(fp,"%s\tThe test statistic X2_r shows, with %s confidence, that at
"
,pad,X2.neg_per_str[GEN_X2_PER]),
fprintf(fp,"%s\tleast one %s is significantly different.
",pad,subject);
fprintf(fp,"
");
fprintf(fp,"%s\tFurther, the probablity of there being a difference is
",
pad);
for (i=GEN_X2_PER;i<MAX_X2_PER;i++)
if (X2_r < X2_score(df,i+1))
break;
if (i==MAX_X2_PER)
fprintf(fp,"%s\tgreater that %s.
",pad,X2_neg_pct_str(i));
else
fprintf(fp,"%s\tbetween %s to %s.
",pad,X2_neg_pct_str(i),
X2_neg_pct_str(i+1));
fprintf(fp,"
");
}
else{
fprintf(fp,"%s\tThe test statistic X2_r shows that at the %s confidence
"
,pad,X2_neg_pct_str(GEN_X2_PER)),
fprintf(fp,"%s\tinterval, the %ss are not significantly
",pad,subject);
fprintf(fp,"%s\tdifferent.
",pad);
fprintf(fp,"%s\tFurther, the probablity of there being a difference is
"
,pad);
for (i=GEN_X2_PER;i>MIN_X2_PER;i--)
if (X2_r > X2_score(df,i-1))
break;
if (i==MIN_X2_PER)
fprintf(fp,"%s\tless than %s.
",pad,X2_neg_pct_str(i));
else
fprintf(fp,"%s\tbetween %s to %s.
",pad,X2_neg_pct_str(i-1),
X2_neg_pct_str(i));
fprintf(fp,"
");
}
}
/********************************************************************/
/* return the doubleing point value of the sum of the squares */
/********************************************************************/
static double dsum_sqr(double *arr, int len)
{
int i;
double tot=0.000000;
for (i=0;i<len;i++)
tot += (arr[i]*arr[i]);
return(tot);
}
/********************************************************************/
/* Ties adjustments */
/* b */
/* --. */
/* 1 - \ T */
/* / i */
/* --' */
/* ----------- */
/* 2 */
/* bt(t -1) */
/* */
/* 3 */
/* T = Sum t - Sum t where t = num ties in ith block */
/* i i i */
/* */
/* to adjust for ties, the test statistic must be taken down */
/* by a certain factor, this function returns it */
/********************************************************************/
static double calc_adjust_for_trt(RANK *rank)
{
double *sort_arr;
int sort_num, *sort_count, i, j, sum_T=0;
alloc_singarr(sort_arr,rnk_trt(rank),double);
alloc_singarr(sort_count,rnk_trt(rank),int);
/* find the ties ans sum Ti */
for (i=0;i<rnk_blks(rank);i++){
for (j=0;j<rnk_trt(rank); j++){
sort_arr[j]=0.0;
sort_count[j]=0;
}
for (j=0;j<rnk_trt(rank); j++){
sort_num = 0;
while ((sort_arr[sort_num] != 0.0) &&
(Vrnk_t_rank(rank,i,j) != sort_arr[sort_num]))
sort_num++;
sort_arr[sort_num] = Vrnk_t_rank(rank,i,j);
sort_count[sort_num]++;
}
for (j=0;j<rnk_trt(rank); j++)
if (sort_count[j] > 0)
sum_T += (sort_count[j] * sort_count[j] * sort_count[j])
- sort_count[j];
}
free_singarr(sort_arr,double);
free_singarr(sort_count,int);
/* return the adjustment number */
return( 1.000000 - (sum_T/
(double)(rnk_blks(rank)*
rnk_trt(rank)*
((rnk_trt(rank) * rnk_trt(rank)) - 1))));
}
/********************************************************************/
/* see calc_adjust_for_trt but substitute B for t */
/********************************************************************/
static double calc_adjust_for_blks(RANK *rank)
{
double *sort_arr;
int sort_num, *sort_count, i, j, sum_T=0;
alloc_singarr(sort_arr,rnk_blks(rank),double);
alloc_singarr(sort_count,rnk_blks(rank),int);
/* find the ties ans sum Ti */
for (i=0;i<rnk_trt(rank);i++){
for (j=0;j<rnk_blks(rank); j++){
sort_arr[j]=0.0;
sort_count[j]=0;
}
for (j=0;j<rnk_blks(rank); j++){
sort_num = 0;
while ((sort_arr[sort_num] != 0.0) &&
(Vrnk_b_rank(rank,j,i) != sort_arr[sort_num]))
sort_num++;
sort_arr[sort_num] = Vrnk_b_rank(rank,j,i);
sort_count[sort_num]++;
}
for (j=0;j<rnk_trt(rank); j++)
if (sort_count[j] > 0)
sum_T += (sort_count[j] * sort_count[j] * sort_count[j])
- sort_count[j];
}
free_singarr(sort_arr,double);
free_singarr(sort_count,int);
/* return the adjustment number */
return( 1.000000 - (sum_T/
(double)(rnk_trt(rank)*
rnk_blks(rank)*
((rnk_blks(rank) * rnk_blks(rank)) - 1))));
}
/********************************************************************/
/* for the treatments, calculate and do the MULTIPLE comparison */
/* print everything out if requested */
/********************************************************************/
static void do_multi_comp_for_anovar(int trt_num, int blk_num, char **trt_names, double *sum_arr, double *ovr_rank_arr, char *title, int *srt_ptr, int **stat_sum, int verbose, FILE *fp)
{
calc_stat_ranks(trt_num,blk_num,stat_sum,sum_arr);
if (verbose)
print_ANOVAR_comp_matrix(trt_num,stat_sum,trt_names,title,srt_ptr,fp);
}
/*********************************************************************/
/* Multiple comparison test to rank the systems */
/* ________ */
/* / bt(t+1) */
/* | R - R | >= z / -------- */
/* j i V 6 */
/* */
/* R = the Sum of the nth column ranks */
/* z = Z score the alpha = 0.05 */
/* ---- */
/* t(t-1) */
/* */
/* go through all possible comparisons and rank the treatments for */
/* according to the number of treatments beaten or beaten by */
/* */
/*********************************************************************/
static void calc_stat_ranks(int trt_num, int blk_num, int **stat_sum, double *sum_arr)
{
int comp1, comp2, result;
double Zcomp_value, compare_value;
double sqr_root;
/* calculate the comparison value for the confidence interval */
Zcomp_value = calc_comp_value(trt_num,blk_num);
sqr_root = sqrt(blk_num * trt_num * (trt_num - 1) / 6.000000);
compare_value = (double)Zcomp_value * (double)sqr_root;
/* go through the comparison and build an array to rank */
for (comp1=0; comp1 <(trt_num-1); comp1++)
for (comp2=comp1+1; comp2<(trt_num); comp2++){
if (fabs(sum_arr[comp1] - sum_arr[comp2]) >= compare_value)
if (sum_arr[comp1] > sum_arr[comp2])
result = 1;
else
result = -1;
else
result = 0;
stat_sum[comp1][comp2] += result;
stat_sum[comp2][comp1] += result * (-1);
}
}
/*********************************************************************/
/* Given the alpha, find the closest approximate Z index to that */
/* percentage */
/*********************************************************************/
static double calc_comp_value(int trt_num, int blk_num)
{
double Z_area;
int i;
Z_area = MULTI_COMP_ALPHA / (double)(trt_num * (trt_num-1));
if (Z_area < Z_exter(Z1tail,MAX_Z_PER))
return(Z_score(Z1tail,MAX_Z_PER));
for (i=MAX_Z_PER+1; i< MIN_Z_PER ; i++)
if (Z_area < Z_exter(Z1tail,i))
return(Z_score(Z1tail,i));
return(Z_score(Z1tail,MIN_Z_PER));
}
static void print_ANOVAR_comp_matrix(int trt_num, int **stat_sum, char **trt_names, char *title, int *srt_ptr, FILE *fp)
{
char pad[FULL_SCREEN],name_format[50],*hyphens="--------------------";
char *spaces=" ";
int t, t2;
int max_trt_name_len=4, hy_l=20;
set_pad(pad,title, FULL_SCREEN);
fprintf(fp,"
%s%s
",pad,title);
set_pad(pad,RANK_TITLE_1, FULL_SCREEN);
fprintf(fp,"%s%s
",pad,RANK_TITLE_1);
for (t=0; t<trt_num; t++)
if (max_trt_name_len < strlen(trt_names[t]))
max_trt_name_len = strlen(trt_names[t]);
set_pad_cent_n(pad,(trt_num+1) * (max_trt_name_len+2+1), FULL_SCREEN);
sprintf(name_format,"| %%-%ds ",max_trt_name_len);
/* first line */
fprintf(fp,"%s|%s",pad,(hyphens+(hy_l-(max_trt_name_len+2))));
for (t=0; t<trt_num; t++)
fprintf(fp,"%s",(hyphens+(hy_l-(max_trt_name_len+3))));
fprintf(fp,"|
");
/* systems on top */
fprintf(fp,"%s|%s",pad,(spaces+(hy_l-(max_trt_name_len+2))));
for (t=0; t<trt_num; t++)
fprintf(fp,name_format,trt_names[srt_ptr[t]]);
fprintf(fp,"|
");
/* separation line */
fprintf(fp,"%s|%s+",pad,(hyphens+(hy_l-(max_trt_name_len+2))));
for (t=0; t<trt_num-1; t++)
fprintf(fp,"%s",(hyphens+(hy_l-(max_trt_name_len+3))));
fprintf(fp,"%s|
",(hyphens+(hy_l-(max_trt_name_len+2))));
/* systems */
for (t=0; t<trt_num; t++){
fprintf(fp,"%s",pad);
fprintf(fp,name_format,trt_names[srt_ptr[t]]);
for (t2=0; t2<trt_num; t2++){
if (t < t2)
switch (stat_sum[srt_ptr[t]][srt_ptr[t2]]) {
case -1: fprintf(fp,name_format,trt_names[srt_ptr[t]]);
break;
case 1: fprintf(fp,name_format,trt_names[srt_ptr[t2]]);
break;
default: fprintf(fp,name_format,"same");
break;
}
else
fprintf(fp,name_format,"");
}
fprintf(fp,"|
");
}
/* last line */
fprintf(fp,"%s|%s",pad,(hyphens+(hy_l-(max_trt_name_len+2))));
for (t=0; t<trt_num; t++)
fprintf(fp,"%s",(hyphens+(hy_l-(max_trt_name_len+3))));
fprintf(fp,"|
");
}
|