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tools/sctk-2.4.10/src/sclite/wilcoxon.c
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/**********************************************************************/
/* */
/* FILE: wilcoxon.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 Wilcoxon Test and generates */
/* a report. */
/* */
/* SOURCE:Statistics: Probability, Inference and Decision */
/* By Robert L. Winkler and William L. Hays, */
/* Page 856 */
/* */
/* See Also: The documentation file "wilcoxon.doc" */
/* */
/**********************************************************************/
#include "sctk.h"
static int wilcoxon_test_analysis(int num_a, int num_b, double sum_a, double sum_b, char *treat1_str, char *treat2_str, double alpha, int verbose, int zero_is_best, double *conf, FILE *fp);
/****************************************************************/
/* main procedure to perform the wilcoxon test on the RANK */
/* structure. */
/****************************************************************/
void perform_wilcoxon(RANK *rank, int verbose, int report, char *formula_str, char formula_id, int ***out_winner, char *outroot, int feedback, double ***out_conf)
{
int comp1, comp2, result, **winner;
double **conf;
FILE *fp = stdout;
if (report || verbose){
char *f = rsprintf("%s.wilc",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(conf,rank->n_trt,rank->n_trt,double,0.0);
*out_winner = winner;
*out_conf = conf;
if (!report) verbose=FALSE;
for (comp1=0; comp1 < rank->n_trt -1; comp1++)
for (comp2=comp1+1; comp2< rank->n_trt ; comp2++){
result = compute_wilcoxon_for_treatment(rank,comp1,comp2,"Spkr",
formula_str,verbose,formula_id=='E',fp,
&(conf[comp1][comp2]));
winner[comp1][comp2] = result;
}
if (report) print_trt_comp_matrix_for_RANK_one_winner(winner,rank,
"Comparison Matrix for the Wilcoxon Test",formula_str,
"Speaker",fp);
if (fp != stdout) fclose(fp);
}
/****************************************************************/
/* Given the two indexes of treatments to compare (in the */
/* RANK Struct) compute the Wilcoxon statistics */
/* vars: */
/* zero_is_best : This identifies the "ideal" value for */
/* the value computed in the rank struct */
/* percentages. */
/****************************************************************/
int compute_wilcoxon_for_treatment(RANK *rank, int treat1, int treat2, char *block_id, char *formula_str, int verbose, int zero_is_best, FILE *fp, double *conf)
{
int sum_plus=0, sum_minus=0, i;
double sum_plus_rank = 0.0, sum_minus_rank = 0.0;
double sum_trt1=0.0, sum_trt2=0.0, sum_trt_diff=0.0;
int block, max_len_block=0, max_len_treat=6;
char *pct_format, thresh_str[140];
TEXT *title_line = (TEXT *)0;
int paper_width = 79, rep_width;
double equal_thresh = 0.05;
double *block_diff, *block_rank;
int *block_sort, tptr[2];
int alternate;
alloc_singarr(block_diff, rank->n_blk ,double);
alloc_singarr(block_rank, rank->n_blk ,double);
alloc_singarr(block_sort, rank->n_blk ,int);
/* change the ordering if necessary */
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;
sum_trt1 = sum_trt2 = 0.0;
/* compute the test */
for (block=0; block <rank->n_blk ; block++)
block_diff[block] = fabs(rank->pcts [ block ][ tptr[0] ] -
rank->pcts [ block ][ tptr[1] ] );
rank_double_arr(block_diff, rank->n_blk ,block_sort,block_rank,INCREASING);
for (block=0; block <rank->n_blk ; block++)
block_diff[block] = rank->pcts [ block ][ tptr[0] ] -
rank->pcts [ block ][ tptr[1] ] ;
sprintf(thresh_str,"(Threshold for equal percentages +- %5.3f)",
equal_thresh);
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 [ tptr[0] ] ))
max_len_treat = strlen(rank->trt_name [ tptr[0] ] );
if (max_len_treat < strlen(rank->trt_name [ tptr[1] ] ))
max_len_treat = strlen(rank->trt_name [ tptr[1] ] );
rep_width = max_len_block + max_len_treat * 2 + 37;
alloc_singarr(pct_format, max_len_treat + 2,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) ));
/* Print a detailed table showing sign differences */
if (verbose) {
fprintf(fp,"%s
",center("Wilcoxon Test Calculations Table",
paper_width));
title_line = TEXT_strdup(rsprintf("Comparing %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("",(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," Signed
");
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,"Difference Rank Rank
");
fprintf(fp,"%s",center("",(paper_width - rep_width)/2));
for (i=0; i<rep_width; i++)
fprintf(fp,"-");
fprintf(fp,"
");
}
alternate=0;
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," ");
fprintf(fp,"%6.2f %5.1f ",block_diff[block],block_rank[block]);
sum_trt1 += rank->pcts [ block ][ tptr[0] ] ;
sum_trt2 += rank->pcts [ block ][ tptr[1] ] ;
sum_trt_diff += block_diff[block];
}
if (block_diff[block] < 0.0 && (fabs(block_diff[block]) > 0.005)){
if (verbose) fprintf(fp,"%5.1f
",(-1.0) * block_rank[block]);
sum_minus++;
sum_minus_rank += block_rank[block];
}
else if (block_diff[block] > 0.0 &&(fabs(block_diff[block]) > 0.005)){
if (verbose) fprintf(fp,"%5.1f
",block_rank[block]);
sum_plus++;
sum_plus_rank += block_rank[block];
} else {
if (verbose) fprintf(fp,"%5.1f
",block_rank[block]);
if ((alternate++ % 2) == 0){
sum_plus++;
sum_plus_rank += block_rank[block];
} else {
sum_minus++;
sum_minus_rank += block_rank[block];
}
}
}
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," ");
fprintf(fp,"%6.2f",sum_trt_diff /rank->n_blk );
fprintf(fp,"
");
sprintf(title_line,"Sum of %2d positive ranks = %4.1f",
sum_plus,sum_plus_rank);
fprintf(fp,"%s
",center(title_line,paper_width));
sprintf(title_line,"Sum of %2d negative ranks = %4.1f",
sum_minus,sum_minus_rank);
fprintf(fp,"%s
",center(title_line,paper_width));
fprintf(fp,"
");
}
free_singarr(block_diff,double);
free_singarr(block_rank,double);
free_singarr(block_sort,int);
free_singarr(pct_format,char);
if (title_line != (TEXT *)0)
free_singarr(title_line, TEXT);
/* Analyze the Results */
{ int result;
result = wilcoxon_test_analysis(sum_plus,sum_minus,sum_plus_rank,
sum_minus_rank,rank->trt_name[tptr[0]],
rank->trt_name[tptr[1]],0.05,verbose,
zero_is_best,conf,fp);
/* 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 */
/****************************************************************/
static int wilcoxon_test_analysis(int num_a, int num_b, double sum_a, double sum_b, char *treat1_str, char *treat2_str, double alpha, int verbose, int zero_is_best, double *conf, FILE *fp)
{
double test_stat;
int i, z_ind=0, dbg=0;
char better;
for (i=0; i <= PER90; i++)
if (Z2tail[i].perc_interior-(1.0 - alpha) > -0.001){
z_ind=i;
if (dbg) printf("Z score %d %f %f
",i,Z2tail[i].perc_interior,
Z2tail[i].perc_interior-(1.0 - alpha));
}
/* compute the Z statistic */
{ double W, E;
double var;
int n;
if (num_a < num_b)
W = sum_a;
else
W = sum_b;
n = num_a + num_b;
better = (num_a < num_b) ? 'b' : 'a';
if (zero_is_best) /* make an adjustment for direction of PCTS*/
better = (better == 'a') ? 'b' : 'a';
E = ((double)n * (double)(n+1) / 4.0);
var = (double)(n * (n+1) * (2*n + 1)) / 24.0;
test_stat = ((W - E) / (double)sqrt(var));
/* W will be rounded to the nearest whole number */
if (dbg){
printf(" Z Approximation for Wilcoxon Signed-Rank test
");
printf(" W = %f
",W);
printf(" n = %d
",n);
printf(" E(W) = %f
",E);
printf(" var = %f
",var);
printf(" Z_stat = %f
",test_stat);
printf(" Better = %c
",better);
printf(" Better S = %s
",
(better == 'a') ? treat1_str : treat2_str);
}
}
*conf = 1.0 - (2.0 * (normprob((double) (fabs(test_stat))) - 0.50));
if (verbose){
fprintf(fp," The Null Hypothesis:
");
fprintf(fp," The two populations represented by the respective matched
");
fprintf(fp," pairs are identical.
");
fprintf(fp," Alternate Hypothesis:
");
fprintf(fp," The two populations are not equal and therfore
");
fprintf(fp," there is a difference between systems.
");
fprintf(fp," Decision Analysis:
");
fprintf(fp," Assumptions:
");
fprintf(fp," The distribution of signed ranks is approximated
");
fprintf(fp," by the normal distribution if the number of Blocks
");
fprintf(fp," is greater than equal to 8.
");
fprintf(fp," Rejection Threshold:
");
fprintf(fp," Based on a %2.0f%% confidence interval, the Z-score should
",
Z2tail[z_ind].perc_interior*100.0);
fprintf(fp," be greater than %4.2f or less than -%4.2f.
",Z2tail[z_ind].z,
Z2tail[z_ind].z);
fprintf(fp," Decision:
");
fprintf(fp," The Z statistic = %4.2f, therefore the Hypothesis
",test_stat);
if (fabs(test_stat) > Z2tail[z_ind].z){
fprintf(fp," is REJECTED in favor of the Null Hypothesis.
");
fprintf(fp," Further, %s is the better System.
",
(better == 'a') ? treat1_str : treat2_str);
} else
fprintf(fp," is ACCEPTED.
");
form_feed(fp);
}
if (fabs(test_stat) > Z2tail[z_ind].z)
return(TEST_DIFF * ((better == 'a') ? (-1) : 1));
return(NO_DIFF);
}
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