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<div class=3DSection1>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt'>A Quick Evaluation of the Quality of Random Numb=
ers
Produced by OpenEpi&#8217;s Random Module,<span style=3D'mso-spacerun:yes'>=
&nbsp;
</span>December 2003<o:p></o:p></span></b></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Andy Dean, EpiInformatics.com</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Random.htm merely passes though to the user in a conve=
nient
form the random numbers produced by the JavaScript Math.random() function.<=
span
style=3D'mso-spacerun:yes'>&nbsp; </span>Hence a completely separate analys=
is of
their quality is not necessary.<span style=3D'mso-spacerun:yes'>&nbsp;
</span>They are merely scaled to fit the range requested and placed in the
required number of columns.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>According to the literature on the Internet, the JavaS=
cript
random number generator is adequate for many purposes, and at least one
commercial product built around it is offered (http://www.randomizer.org/ab=
out.htm).<span
style=3D'mso-spacerun:yes'>&nbsp; </span>It is, however, a &#8220;pseudoran=
dom
number generator,&#8221; and not suitable for exacting applications such as
cryptography.<span style=3D'mso-spacerun:yes'>&nbsp; </span>I could not fin=
d any
systematic summary of tests done on the JavaScript Math.random function in
various browsers, which would have been important information.<span
style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>I made some crude attempts to assess the quality of the
random numbers produced by OpenEpi&#8217;s Random module, by generating 100=
00
numbers between 1 and 999 in a single column with OmitText set to
&#8220;Yes.&#8221;<span style=3D'mso-spacerun:yes'>&nbsp; </span>Since the =
file
is in HTML, it has a lot of HTML table cells and attributes&#8212;more in
volume than the numbers.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Micr=
osoft
Word read the file and I was able to save it as a text file, and then to RE=
AD
it in Epi Info&#8217;s Analysis program.<span style=3D'mso-spacerun:yes'>&n=
bsp;
</span>It indeed had 10000 numbers, with the following statistics:</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<div align=3Dcenter>

<table class=3DMsoNormalTable border=3D0 cellspacing=3D3 cellpadding=3D0
 style=3D'mso-cellspacing:1.5pt'>
 <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes'>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal><o:p>&nbsp;</o:p></p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Obs</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Total </p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Mean</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal><span style=3D'mso-spacerun:yes'>&nbsp; </span>Varia=
nce</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Std Dev <=
/p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:1;mso-yfti-lastrow:yes'>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal><o:p>&nbsp;</o:p></p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'>10000</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'>5013275.000=
0</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'>501.3275</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'><span
  style=3D'mso-spacerun:yes'>&nbsp; </span>82032.8867</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'>286.4138 </=
p>
  </td>
 </tr>
</table>

</div>

<p class=3DMsoNormal><span style=3D'display:none;mso-hide:all'><o:p>&nbsp;<=
/o:p></span></p>

<div align=3Dcenter>

<table class=3DMsoNormalTable border=3D0 cellspacing=3D3 cellpadding=3D0
 style=3D'mso-cellspacing:1.5pt'>
 <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes'>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal><o:p>&nbsp;</o:p></p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Minimum</=
p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>25%</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Median</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>75%</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Maximum</=
p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Mode </p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:1;mso-yfti-lastrow:yes'>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal><o:p>&nbsp;</o:p></p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'>1.0000</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'>255.0000</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'>504.0000</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'>747.5000</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'>999.0000</p>
  </td>
  <td style=3D'padding:.75pt .75pt .75pt .75pt'>
  <p class=3DMsoNormal align=3Dright style=3D'text-align:right'>35.0000 </p>
  </td>
 </tr>
</table>

</div>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>After considerable maneuvering, I was able to draw 30
samples, using<span style=3D'mso-spacerun:yes'>&nbsp; </span>number mod 30.=
</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The means of the 30 samples plotted as follows, with a
little reordering to put the larger values in the middle. Not quite good en=
ough
for Dr. Gauss, but a tolerable resemblance to the normal curve.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>Clever people can take this analys=
is
much further, more as a teaching exercise than an evaluation, since we know=
 the
randomness is not perfect.<span style=3D'mso-spacerun:yes'>&nbsp; </span></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shapetype id=3D"_x0000_t75" coor=
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  <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/>
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  <v:f eqn=3D"prod @7 21600 pixelHeight"/>
  <v:f eqn=3D"sum @10 21600 0"/>
 </v:formulas>
 <v:path o:extrusionok=3D"f" gradientshapeok=3D"t" o:connecttype=3D"rect"/>
 <o:lock v:ext=3D"edit" aspectratio=3D"t"/>
</v:shapetype><v:shape id=3D"_x0000_i1025" type=3D"#_x0000_t75" alt=3D"" st=
yle=3D'width:351pt;
 height:272.4pt'>
 <v:imagedata src=3D"RandomTests_files/image001.jpg" o:href=3D"../RandomNum=
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</v:shape><![endif]--><![if !vml]><img width=3D468 height=3D363
src=3D"RandomTests_files/image002.jpg" v:shapes=3D"_x0000_i1025"><![endif]>=
</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><img width=3D468 height=3D364 id=3D"_x0000_i1026"
src=3D"file:///C:\Epi_Info\OUT88_12.JPG"></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Here is a moving average of the counts of the 10000 1-=
999
numbers.<span style=3D'mso-spacerun:yes'>&nbsp; </span>It seems to be quite
consistent across the range.<span style=3D'mso-spacerun:yes'>&nbsp; </span>=
The
blocky appearance is mostly due to artifacts in the &#8220;pixilation&#8221;
since it disappears if fewer numbers are selected.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>I downloaded two programs designed specifically to tes=
t the
quality of random numbers.<span style=3D'mso-spacerun:yes'>&nbsp; </span>On=
e is a
DOS program called ENT.exe.<span style=3D'mso-spacerun:yes'>&nbsp; </span>H=
ere
are the results.</p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_i1027" type=
=3D"#_x0000_t75"
 style=3D'width:405pt;height:2in'>
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</v:shape><![endif]--><![if !vml]><img width=3D540 height=3D192
src=3D"RandomTests_files/image004.jpg" v:shapes=3D"_x0000_i1027"><![endif]>=
</p>

<p class=3DMsoNormal>Unfortunately, I can&#8217;t say what they mean, but I=
 know
that the average mean value of databytes in an ASCII file filled with digits
can never be 127.5, since that would mean including all the ASCII character=
s,
including those above 128.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Go=
od for
white noise or subatomic particles, perhaps, but not really pertinent to
epidemiology.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<span style=3D'font-size:12.0pt;font-family:"Times New Roman";mso-fareast-f=
ont-family:
"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:EN-US;
mso-bidi-language:AR-SA'><br clear=3Dall style=3D'mso-special-character:lin=
e-break;
page-break-before:always'>
</span>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The second test suite is called RNGmeter 0.9, from
ComScire.<span style=3D'mso-spacerun:yes'>&nbsp; </span>It has a nice Windo=
ws
interface.<span style=3D'mso-spacerun:yes'>&nbsp; </span>After running it f=
or 5
minutes, it gave results suggesting that my file of numbers did not pass the
more rigid tests.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Those who e=
njoy
such things will find a lot of software and hardware&#8212;generated random
numbers on the Internet and may wish to characterize the numbers produced by
various browsers.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Since the b=
rowser
suppliers apparently do not make public their tests, it would be a continui=
ng
task to keep up with new browsers as they come out.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Evaluation of the Microsoft .NET framework for random =
bit
quality has been done, with excellent results, but it is not clear whether =
this
is the one used by JavaScript in IE.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><a
href=3D"http://www.atstake.com/research/reports/eval_ms_ibm/analysis/2.3.4.=
html">http://www.atstake.com/research/reports/eval_ms_ibm/analysis/2.3.4.ht=
ml</a></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>I generated 80 numbers from 1 to 100 and entered them =
in a
test available on the net at</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>http://ubmail.ubalt.edu/~harsham/Business-stat/otherap=
plets/Randomness.htm</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>by Professor Hossein Arsham.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>The module performed the Runs Test=
 with
45 Runs, produced a p-value of 0.18238, and gave the conclusion, &#8220;Lit=
tle
or no evidence against randomness.&#8221;<span style=3D'mso-spacerun:yes'>&=
nbsp;
</span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>It is clear, however, that Random.htm produces differe=
nt
numbers each time it is run, that the numbers can be saved to a file by run=
ning
OpenEpi from OpenEpiSave.hta on the a local disk, or by copying and pasting=
 the
output to a word processor or Excel.<span style=3D'mso-spacerun:yes'>&nbsp;=
&nbsp;
</span>They should be useful for most epidemiologic purposes.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Comments prepared by Andy Dean, who confesses that thi=
s was
fun, but not really a professional evaluation.<span
style=3D'mso-spacerun:yes'>&nbsp; </span></p>

</div>

</body>

</html>

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