NWA-PCUG Newsletter Article
Basic Answers
by Ed Maxey - September 97
(click to email author)

The print out read, "The odds are 125,000 to one against 267 or less HEADS when a basket of 624 coins is overturned." This was GWBasic's answer when asked to set up trials of 624 random numbers and then tally odds and evens in a million trials. Why are these odds of interest?

Martha S. Linet etal. (RESIDENTIAL EXPOSURE TO MAGNETIC FIELDS AND ACUTE LYMPHOBLASTIC LEUKEMIA IN CHILDREN) found "little evidence that living in homes characterized by high measured time-weighted average magnetic-field levels ... increases the risk of ALL in children (N Engl J Med 1997;337:1-7.)." This report found that there were 624 cases of acute lymphoblastic leukemia (ALL) in a matched analysis. Only 267 of these had a residential electromagnetic field exposures of under 0.065 µT (microTesla). It seemed unlikely that chance alone would have been at play when so few cases occurred in those residences with the lowest category of exposure.

If the median residential EMF exposure in the United States were known one could predict that chance alone would distribute 50% of ALL cases on each side of the median value. This follows the WEBSTER'S COLLEGIATE DICTIONARY definition; "Designating a point so chosen in a series that half of the individuals in the series are on one side of it, and half on the other."

The median residential EMF has been recognized by law. Judge Michael Galvin (Decision 93-11-013 November 2, 1993, BEFORE THE PUBLIC UTILITIES COMMISSION OF THE STATE OF CALIFORNIA) noted "...the 0.35 milligauss median United States residential EMF level generated by electric power facilities...." This value equates to 0.035 µT, about half of the 0.065 µT in the Linet paper. Judge Galvin also noted that high fields may come from individual appliances. The greatest offenders were hair dryers and electric shavers. Few children sleep within a meter of blowing hair dryers or buzzing shavers.

Judge Galvin additionally stated,
"The most often found source of magnetic fields in residential
and commercial property is the grounding system. The
grounding system includes water pipes, television cables, gas
pipelines, and other metallic paths that are grounded."

Many children are exposed to such fields. Parents can turn off electric household appliances. They can not turn off EMFs from the grounding system.

The Linet paper does not depict 0.065 µT as being higher than the national median residential electromagnetic field exposure. Even so, 0.065 µT was treated as the median in this computer program. If the actual median were to be lower than 0.065 µT the odds of acute ALL being linked to power line EMFs would be even greater than 125,000 to one.

Here is the program in case you would like to have your computer confirm these odds. Those with scanners may simply scan the program into their computers. ANSWERS.BAS is suggested as a name.

The command line would be:
and then press the enter key.
10 E1 = 312: O1 = 312' REM E1 gets lowest EVEN & O1 gets lowest ODD count
20 M = .5' REM M = Mid point; determines if number is ODD or EVEN
30 C=267' REM record any hits at or below 267
40 C1 = 265' REM Cutoff point minus 2 for array coverage
50 DEFDBL T' REM All "T" variables are double precision
60 TT =1:TE =1000000!' Rem counting 1 to 1,000,000
70 P$="**###,###,###,###,###":P1$="###,###"
80 P2$ = " to one against 267 or less being"
90 P3$= "HEADS when a basket of 624 coins is overturned."
100 DIM OS(94)' REM array holds individual ODDS & EVENS trials sums
110 CLS
120 PRINT "Trial number"TT" Evens - Odds ="TEVEN-TODD'REM show tally
130 FOR V = 1 TO 624 ' REM Flip 624 pennies for heads or tails
150 IF RND < M THEN E = E + 1 ELSE O = O +1' REM Count evens and odds
160 NEXT V
170 IF E < E1 THEN E1 = E ' REM Find lowest even value in 1,000,000 trials
180 IF O < O1 THEN O1 = O ' REM Find lowest odd value in 1,000,000 trials
190 IF E =< C THEN E2 = E2 + 1 'REM Find number of even 267 or lower hits
200 IF O =< C THEN O2 = O2 + 1 'REM Find number of odd 267 or lower hits
210 OS(E-C1)=OS(E-C1)+1 ' REM Tally hits in each distribution category
230 TT = TT +1' REM Tally trials up to 1,000,000
240 E = 0: O = 0' REM Reset count variables to zero
250 IF TT < TE THEN GOTO 120' Rem loop until 1,000,000
260 REM Data determined. Now display it and save it on hard drive.
270 PRINT "There were "TT" trials."
280 OPEN "O", #1, "DISTRIB.TXT"'REM Save data using Print #1
290 PRINT #1,"There were "TT" trials."
300 PRINT "The EVENs totaled" USING P$;TEVEN
310 PRINT #1, "The EVENs totaled" USING P$;TEVEN 320 PRINT "The ODDs totaled " USING P$;TODD
330 PRINT #1 ,"The ODDs totaled " USING P$;TODD
340 PRINT "The minimum number of EVENs was"E1" and ODDs was "O1".
350 PRINT #1,"The minimum number for EVENs was"E1" and for ODDs was "O1".
360 PRINT "There were "E2" 267 or less EVEN hits and "O2" 267 or less ODD hits."
370 PRINT #1,"There were "E2" 267 or less EVEN hits and "O2" 267 or less ODD hits."
380 PRINT "The odds are "USING P1$;TE/E2;:PRINT P2$:PRINT P3$
390 PRINT #1,"The odds are "USING P1$;TE/E2;:PRINT #1,P2$:PRINT #1,P3$
400 FOR V=0 TO 94: TF=TF+OS(V):NEXT V 'REM Tally the array as a check
410 PRINT "Total odd and even trials ="TF
420 PRINT #1,"Total odd and even trials ="TF
430 FOR V = 0 TO 94: 'REM Now print array to screen and disk
440 PRINT C1+V"="OS(V);
450 PRINT #1,C1+V"="OS(V);
460 IF V>0 AND (V/6)=INT(V/6) THEN PRINT
470 IF V>0 AND (V/6)=INT(V/6) THEN PRINT #1,
480 NEXT V
490 CLOSE #1

May BASIC's ANSWERS favor you.

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