Subject: C++ (fwd) "Linet" study probabilities......
Date: Wed, 10 Jun 1998 150545 -0500 (CDT)
From: "Roy L. Beavers" <rbeavers@llion.org>
To: emfguru@hotmail.com
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---------- Forwarded message ----------
Date: Wed, 10 Jun 1998 14:28:48 -0500
From: Edward Maxey
To: "Roy L. Beavers"
Subject: C++ "Linet" study probabilities.........
Hello Roy Beavers,
Several months ago results from a BASIC study showing that the
probability of 60 Hz EMFs being causal to childhood leukemia (the Linet
study) was 200,000 to one. Recently questions have come up about the
integrity of the random number function in MICROSOFT's BASIC.
Accordingly the program was written in C++ using the "rand" function.
This function "uses a multiplicative congruential random number generator"
with a period of 2^32. It is available on UNIX and is defined in ANSI
C.
Here is a result when 10,000,000 baskets of 624 coins was overturned.
It took 141 minutes to run on an 80 MHZ Pentium machine.
Heads categories are numbered 248 through 376.
The values following "=" give the hits per category.
***This run showed a 5,408 to one probability that EMFs are causal
to childhood acute lymphoblastic leukemia.***
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Probability is 5,408 to one.
Total Heads = 3,120,196,185
248 = 0 249 = 1 250 = 0 251 = 2
252 = 4 253 = 3 254 = 13 255 = 8
256 = 10 257 = 12 258 = 31 259 = 38
260 = 58 261 = 87 262 = 117 263 = 143
264 = 194 265 = 265 266 = 377 267 = 486
268 = 647 269 = 862 270 = 1091 271 = 1441
272 = 1876 273 = 2347 274 = 3084 275 = 3982
276 = 5035 277 = 6426 278 = 7949 279 = 9637
280 = 11920 281 = 14693 282 = 17967 283 = 21701
284 = 25907 285 = 30601 286 = 36274 287 = 42714
288 = 50426 289 = 58240 290 = 67746 291 = 77464
292 = 88722 293 = 100185 294 = 112743 295 = 126644
296 = 140536 297 = 155491 298 = 170592 299 = 185101
300 = 200137 301 = 216604 302 = 231233 303 = 247164
304 = 260253 305 = 272072 306 = 283909 307 = 294456
308 = 303258 309 = 309793 310 = 315141 311 = 317997
312 = 318977 313 = 318239 314 = 315719 315 = 309634
316 = 303506 317 = 295276 318 = 284460 319 = 273346
320 = 260468 321 = 246585 322 = 232185 323 = 216749
324 = 201712 325 = 186761 326 = 170540 327 = 155626
328 = 140872 329 = 127199 330 = 112916 331 = 100078
332 = 89116 333 = 78043 334 = 68225 335 = 58649
336 = 50915 337 = 43404 338 = 37179 339 = 31008
340 = 26074 341 = 21691 342 = 17715 343 = 14704
344 = 12230 345 = 9967 346 = 7579 347 = 6368
348 = 5073 349 = 3952 350 = 3176 351 = 2426
352 = 1839 353 = 1467 354 = 1138 355 = 847
356 = 678 357 = 471 358 = 357 359 = 266
360 = 188 361 = 136 362 = 119 363 = 61
364 = 58 365 = 31 366 = 30 367 = 18
368 = 13 369 = 10 370 = 6 371 = 5
372 = 6 373 = 1 374 = 0 375 = 0
376 = 1
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Here is the program in case some of your readers who have C++
compilers wish to see for themselves.
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/*program NCIRAND.C Calculates the probability of 267 heads
when a basked of 624 coins is overturned.
by
E. Stanton Maxey, M.D., F.A.C.S.
2811 Joyce Street
Fayetteville, AR 72703
Phone (501) 443 7699*/
#include
#include
#include
#include
#include
#include
FILE *textfile; /*pointer to recording file*/
int L,H,U,V,Z;
float G,F;
long I; /*counts up to
10,000,000*/
double T; /*counts up to
3,120,000,000*/
long Head[130]; /*array to hold 130 hit
categories*/
int main()
{T = 0;
U = 0;
H = 0;
L = 0;
clrscr();
randomize();
for(V = 0; V < 129; V++)
{ Head[V] = 0;} /*zero hit array*/
G = 0;
for(I=1; I < 10000001; I++) /*Number of 634 coin baskets dumped*/
{
H = 0; F =0;
for(V = 1; V < 625; V++) /*get # of heads from 624 coins*/
{if ((rand() % 10) < 5) H = H + 1;} /*tally hits per basket*/
T = T + H; /*tally total hits*/
Z = H - 248; /*get Z factor*/
Head[Z] = Head[Z] + 1; /*log hit in Head[Z]*/
if (H<268) L = L + 1; /*tally hits below 268*/
}
G = 10000000/L; /*determine probability*/
printf("\nProbability is %3.0f",G); /*print probability*/
printf(" to one.\n");
printf("\nTotal Heads = %3.0lf",T);
printf("\n");
Z = 247;
if ((textfile = fopen("NCIRAND.TXT","w")) == NULL) /*open data file*/
{printf("Error opening text file for writing\n");
exit(0);}
fprintf(textfile,"\nProbability is %3.0f",G);/*file print
probability*/
fprintf(textfile," to one.\n");
fprintf(textfile,"\nTotal Heads = %3.0lf",T);
fprintf(textfile,"\n");
for(V = 1; V < 130; V++) /*Z -1 and V +1 for file print*/
{printf("%3hd",V+Z);
fprintf(textfile,"%3hd",V+Z);
printf(" = ");
fprintf(textfile," = ");
printf("%ld",Head[V-1]);
fprintf(textfile,"%ld",Head[V-1]);
printf(" ");
fprintf(textfile," ");
if ((V%4) == 0) printf("\n");
if ((V%4) == 0) fprintf(textfile,"\n"); /*four categories per line*/
}
fclose(textfile); /*close file*/
return(0);
}
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All good wishes,
Ed
Archive provided courtesy of WaveGuide, http://www.wave-guide.org
Reprinted with permission of Roy Beavers, http://www.feb.se/EMF-L/EMF-L.html