Blame view
tools/sctk-2.4.10/src/sclite/signtest.c
14 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 |
/**********************************************************************/
/* */
/* FILE: signtest.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 */
/* the non-parametric Sign Test and generates */
/* a report. */
/* */
/* SOURCE:Statistics: Basic Techniques for Solving */
/* Applied Problems, by Stephen A. Book, 1977 */
/* */
/* See Also: The documentation file "signtest.doc" */
/* */
/**********************************************************************/
#include "sctk.h"
/****************************************************************/
/* main procedure to perform the sign test on the RANK */
/* structure. */
/****************************************************************/
void perform_signtest(RANK *rank, int verbose, int report, char *formula_str, char formula_id, int ***out_winner, char *outroot, int feedback, double ***out_confidence)
{
int comp1, comp2, **winner;
double **confidence;
FILE *fp = stdout;
if (report || verbose){
char *f = rsprintf("%s.sign",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(winner,rank->n_trt,rank->n_trt,int,NO_DIFF);
alloc_2dimZ(confidence,rank->n_trt,rank->n_trt,double,0.0);
*out_confidence = confidence;
*out_winner = winner;
for (comp1=0; comp1 < rank->n_trt -1; comp1++)
for (comp2=comp1+1; comp2< rank->n_trt ; comp2++){
winner[comp1][comp2] =
compute_signtest_for_treatment(rank,comp1,comp2,"Spkr",
formula_str,verbose,
formula_id=='E',fp,
&(confidence[comp1][comp2]));
}
if (report) print_trt_comp_matrix_for_RANK_one_winner(winner,rank,
"Comparison Matrix for the Sign Test",formula_str,
"Speaker",fp);
if (fp != stdout) fclose(fp);
}
/****************************************************************/
/* Given the two indexes of treatments to compare (in the */
/* RANK Struct) compute the Rank Sum statistics */
/* vars: */
/* zero_is_best : This identifies the "ideal" value for */
/* the value computed in the rank struct */
/* percentages. */
/****************************************************************/
int compute_signtest_for_treatment(RANK *rank, int treat1, int treat2, char *block_id, char *formula_str, int verbose, int zero_is_best, FILE *fp, double *confidence)
{
int sum_plus=0, sum_minus=0, sum_equal=0, i;
int block, max_len_block=0, max_len_treat=6;
int tptr[2]; /* a sorting pointer array for the treatment numbers */
char *pct_format, thresh_str[140];
TEXT *title_line = (TEXT *)0;
char *diff_line;
int paper_width = 79, rep_width, diff_col_len;
double equal_thresh = 0.005;
double sum_trt1=0.0, sum_trt2=0.0;
/* compute the maximum block title length */
max_len_block = strlen(block_id);
for (block=0; block <rank->n_blk ; block++)
if (strlen(rank->blk_name [ block ] ) > max_len_block)
max_len_block = strlen(rank->blk_name [ block ] );
if (max_len_treat < strlen(rank->trt_name [ treat1 ] ))
max_len_treat = strlen(rank->trt_name [ treat1 ] );
if (max_len_treat < strlen(rank->trt_name [ treat2 ] ))
max_len_treat = strlen(rank->trt_name [ treat2 ] );
/* set the treatment sorting array */
for (block=0; block <rank->n_blk ; block++){
sum_trt1 += rank->pcts [ block ][ treat1 ] ;
sum_trt2 += rank->pcts [ block ][ treat2 ] ;
}
if (sum_trt1 > sum_trt2)
tptr[0] = treat1, tptr[1] = treat2;
else
tptr[0] = treat2, tptr[1] = treat1;
/* set up format strings and titles */
sprintf(thresh_str,"(Threshold for equal percentages +- %5.3f)",
equal_thresh);
alloc_singarr(pct_format, max_len_treat + 2,char);
alloc_singarr(diff_line, max_len_treat*2 + 7,char);
pct_format[0] = '\0';
strcat(pct_format,center("",(max_len_treat-6)/2));
strcat(pct_format,"%6.2f");
strcat(pct_format,center("",max_len_treat - ((max_len_treat-6)/2 + 6) ));
sprintf(diff_line,"[%s - %s]",rank->trt_name[tptr[0]],
rank->trt_name[tptr[1]]);
diff_col_len = 15;
if (strlen(diff_line) > diff_col_len) diff_col_len=strlen(diff_line);
rep_width = max_len_block + max_len_treat * 2 + 4 * 3 + diff_col_len;
/* Print a detailed table showing sign differences */
if (verbose) {
sum_trt1 = sum_trt2 = 0.0;
fprintf(fp,"%s
",center("Sign Test Calculations Table Comparing",
paper_width));
title_line = TEXT_strdup(rsprintf("%s %s Percentages for Systems %s and %s",
block_id, formula_str,rank->trt_name[tptr[0]],
rank->trt_name [ tptr[1] ] ));
fprintf(fp,"%s
",center(title_line,paper_width));
fprintf(fp,"%s
",center(thresh_str,paper_width));
fprintf(fp,"%s",center("",(paper_width - rep_width)/2));
fprintf(fp,"%s",center("",max_len_block));
fprintf(fp," "); fprintf(fp,"%s",center("",max_len_treat));
fprintf(fp," "); fprintf(fp,"%s",center("",max_len_treat));
fprintf(fp," ");
fprintf(fp,"%s
",center("Difference Sign",diff_col_len));
fprintf(fp,"%s",center("",(paper_width - rep_width)/2));
fprintf(fp,"%s",center(block_id,max_len_block));
fprintf(fp," ");
fprintf(fp,"%s",center(rank->trt_name [ tptr[0] ] ,max_len_treat));
fprintf(fp," ");
fprintf(fp,"%s",center(rank->trt_name [ tptr[1] ] ,max_len_treat));
fprintf(fp," ");
fprintf(fp,"%s
",center(diff_line,diff_col_len));
fprintf(fp,"%s",center("",(paper_width - rep_width)/2));
for (i=0; i<rep_width; i++)
fprintf(fp,"-");
fprintf(fp,"
");
}
for (block=0; block <rank->n_blk ; block++){
if (verbose) {
fprintf(fp,"%s",center("",(paper_width - rep_width)/2));
fprintf(fp,"%s",center(rank->blk_name [ block ] ,max_len_block));
fprintf(fp," ");
fprintf(fp,pct_format,rank->pcts [ block ][ tptr[0] ] );
fprintf(fp," ");
fprintf(fp,pct_format,rank->pcts [ block ][ tptr[1] ] );
fprintf(fp," ");
}
if (fabs(rank->pcts [ block ][ tptr[0] ] - rank->pcts [ block ][ tptr[1] ] ) <=
equal_thresh){
if (verbose) fprintf(fp,"%s
",center("0",diff_col_len));
sum_equal++;
}
else if (rank->pcts [ block ][ tptr[0] ] < rank->pcts [ block ][ tptr[1] ] ){
if (verbose) fprintf(fp,"%s
",center("-",diff_col_len));
sum_minus++;
}
else {
if (verbose) fprintf(fp,"%s
",center("+",diff_col_len));
sum_plus++;
}
sum_trt1 += rank->pcts [ block ][ tptr[0] ] ;
sum_trt2 += rank->pcts [ block ][ tptr[1] ] ;
}
if (verbose){
fprintf(fp,"%s",center("",(paper_width - rep_width)/2));
for (i=0; i<rep_width; i++)
fprintf(fp,"-");
fprintf(fp,"
");
/* an Average line */
fprintf(fp,"%s",center("",(paper_width - rep_width)/2));
fprintf(fp,"%s",center("Avg.",max_len_block));
fprintf(fp," ");
fprintf(fp,pct_format,sum_trt1 /rank->n_blk );
fprintf(fp," ");
fprintf(fp,pct_format,sum_trt2 /rank->n_blk );
fprintf(fp,"
");
sprintf(title_line,"No. Speakers with Positive %s Differences = N(+) = %2d",formula_str,sum_plus);
fprintf(fp,"%s
",center(title_line,paper_width));
sprintf(title_line,"No. Speakers with Negative %s Differences = N(-) = %2d",formula_str,sum_minus);
fprintf(fp,"%s
",center(title_line,paper_width));
sprintf(title_line,"No. Speakers with No %s Differences = N(0) = %2d",formula_str,sum_equal);
fprintf(fp,"%s
",center(title_line,paper_width));
fprintf(fp,"
");
}
free_singarr(pct_format,char);
free_singarr(diff_line,char);
if (title_line != (TEXT *)0)
free_singarr(title_line, TEXT);
/* Analyze the Results */
{ int result;
result = sign_test_analysis(sum_plus,sum_minus,sum_equal,"+","-",0,
0.05,verbose, rank->trt_name [ tptr[0] ] ,
rank->trt_name [ tptr[1] ] ,
tptr,zero_is_best,fp,confidence);
/* if the result is significant, system which is better depends on if */
/* the treatments have been swapped, a negative result means tprt[0] is */
/* better, positive one tprt[1] is better */
return(result * ((tptr[0] == treat1) ? 1 : (-1)));
}
}
/****************************************************************/
/* Given the vital numbers for computing a rank sum test, */
/* Compute it, and if requested, print a verbose analysis */
/****************************************************************/
int sign_test_analysis(int num_a, int num_b, int num_z, char *str_a, char *str_b, int str_z, double alpha, int verbose, char *treat1_str, char *treat2_str, int *tptr, int zero_is_best, FILE *fp, double *confidence)
{
double test_stat, p=0.5;
int i;
num_b += (num_z / 2) + (num_z % 2);
num_a += (num_z / 2);
num_z = 0;
/* multiplication by 2 means it's a two-tailed test */
if (num_a != num_b)
test_stat = 2.0 * compute_acc_binomial(MIN(num_a,num_b),num_a+num_b,p);
else
test_stat = 1.0;
*confidence = test_stat;
if (verbose){
fprintf(fp,"The NULL Hypothesis:
");
fprintf(fp," The number of speakers for which the differences is positive
");
fprintf(fp," equals the number of speakers for which the differences is
");
fprintf(fp," negative.
");
fprintf(fp," P(N(+)) = P(N(-)) = 0.50
");
fprintf(fp,"Alternate Hypothesis:
");
fprintf(fp," The number of speakers for which the differences is positive
");
fprintf(fp," is NOT equal to the number of speakers for which the difference
");
fprintf(fp," is negative.
");
fprintf(fp,"Decision Analysis:
");
fprintf(fp," Assumptions:
");
fprintf(fp," A1: The distibution of positive and negative differences
");
fprintf(fp," follows the binomial distribution for N fair coin tosses.
");
fprintf(fp,"
");
fprintf(fp," A2: In order to resolve the complication caused by cases where the
");
fprintf(fp," difference in Word Accuracy is zero, half of the cases will
");
fprintf(fp," be assigned to N(+) and half to N(-). In the event of an
");
fprintf(fp," odd number of zero differences, N(-) will get one extra, this
");
fprintf(fp," reduces the probability of there being a difference between
");
fprintf(fp," the two systems.
");
fprintf(fp," Rejection criterion:
");
fprintf(fp," Reject the null hypothesis at the 95%% confidence level based
");
fprintf(fp," on the following critical values table. N is the number of
");
fprintf(fp," speakers being compared and N(-) is the number of negative
");
fprintf(fp," differences.
");
/* print a table of critical values */
fprintf(fp," MIN(N(-),N(+)) P(MIN(N(-),N(+)) | N=%2d)
",num_a+num_b);
fprintf(fp," -------------- ------------------------
");
for (i=0; i <= (num_a+num_b)/2 && (i - 3) <= num_b; i++){
double val = 2.0*compute_acc_binomial(i,num_a+num_b,p),
valp1 = 2.0*compute_acc_binomial(i+1,num_a+num_b,p);
if (val >= 0.0005)
fprintf(fp," %3d %5.3f", i,val);
else
fprintf(fp," %3d <0.001 ", i);
if ((val < alpha) && (valp1 > alpha))
fprintf(fp," <--- Null Hypothesis rejected at or below this point
");
else
fprintf(fp,"
");
}
fprintf(fp,"
");
fprintf(fp," Decision:
");
fprintf(fp," There were N(-)=%d negative differences , the probability of
",num_b);
fprintf(fp," it occuring is %5.3f, therefore the null hypothesis ",test_stat);
if (test_stat < alpha){
fprintf(fp,"is REJECTED
");
fprintf(fp," in favor of the Alternate Hypothesis. Further, %s is the
",
(zero_is_best) ? treat2_str : treat1_str);
fprintf(fp," better System.
");
} else{
fprintf(fp,"is ACCEPTED
");
fprintf(fp," There is no statistical difference between %s and %s
",treat1_str,treat2_str);
}
form_feed(fp);
}
if (test_stat < alpha){
if (0) fprintf(fp,"Returning Result %d
",TEST_DIFF * ((zero_is_best) ? 1 : -1));
return(TEST_DIFF * ((zero_is_best) ? 1 : -1));
}
return(NO_DIFF);
}
|