This document was successfully checked as XHTML 1.0 Transitional!

Result: Passed
:
Modified:(undefined)
Server:Apache/2.4.38 (Debian)
Size:4930
Content-Type:text/html
: utf-8
: XHTML 1.0 Transitional
Root Element: html
Root Namespace: http://www.w3.org/1999/xhtml
Options

Help on the options is available.

Congratulations

The document located at <http://web.tecnico.ulisboa.pt/~mcasquilho/compute/errtheory/Fx-errors.php> was successfully checked as XHTML 1.0 Transitional. This means that the resource in question identified itself as "XHTML 1.0 Transitional" and that we successfully performed a formal validation of it. The parser implementations we used for this check are based on OpenSP (SGML/XML) and libxml2 (XML).

"valid" Icon(s) on your Web page

To show your readers that you have taken the care to create an interoperable Web page, you may display this icon on any page that validates. Here is the HTML you could use to add this icon to your Web page:

Valid XHTML 1.0 Transitional 
  <p>
    <a href="http://validator.w3.org/check?uri=referer"><img
      src="http://www.w3.org/Icons/valid-xhtml10" alt="Valid XHTML 1.0 Transitional" height="31" width="88" /></a>
  </p>

A full list of icons, with links to alternate formats and colors, is available: If you like, you can download a copy of the icons to keep in your local web directory, and change the HTML fragment above to reference your local image rather than the one on this server.

Linking to this result

If you would like to create a link to this page (i.e., this validation result) to make it easier to revalidate this page in the future or to allow others to validate your page, the URI is <http://validator.w3.org/check?uri=http%3A%2F%2Fweb.tecnico.ulisboa.pt%2F~mcasquilho%2Fcompute%2Ferrtheory%2FFx-errors.php;ss=1;verbose=1> (or you can just add the current page to your bookmarks or hotlist).

Validating CSS Style Sheets

If you use CSS in your document, you can check it using the W3C CSS Validation Service.

↑ Top

Source Listing

Below is the source input I used for this validation:

  1. <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
  2. "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
  3. <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"><head>
  4. <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
  5. <meta name="Author" lang="en" content="Miguel Casquilho" />
  6. <title>M&middot;C, IST: errors, outliers</title>
  7. <link rel="stylesheet" type="text/css"
  8. href="http://web.tecnico.ulisboa.pt/~mcasquilho/commonstyle.css" />
  9. </head> <!-- 04-Aug-2008 -->
  10. <body class="sm">
  11. <form method="post" action=
  12. "http://web.tecnico.ulisboa.pt/~mcasquilho/cgi-bin/interfacepng.php?errtheory">
  13. <input name="executable" type="hidden" value="errtheory.exe" />
  15. <table width="90%" bgcolor="#eeeeee" align="center" border="1" class="sm">
  16. <tr><td colspan="3">
  17. <table width="100%" class="sm">
  18. <tr><td width="50px"><a href='https://fenix.ist.utl.pt/departamentos/deq'><img alt='&copy;'
  19. src="http://web.tecnico.ulisboa.pt/~mcasquilho/depot/MC.gif" border='0'
  20. width='40' height='41' /></a>
  21. </td><!-- title -->
  22. <td><div style="font-size: 13.5pt; text-align: center"><!-- title --><b
  23. onmouseout="this.style.color='blue', this.style.fontStyle='normal'"
  24. onmouseover="this.style.color='red',
  25. this.style.fontStyle='bold'">
  26. Errors,
  27. outliers</b></div>&emsp;
  28. From a generated or supplied sample, calculates some common statistics
  29. and detects a possible outlier.<!-- b>Under construction</b --></td>
  30. <td width="112px"><table width='100%'>
  31. <tr><td align='center' bgcolor='white'>
  32. <input type="submit"
  33. value="&nbsp; Execute &nbsp;" style="background-color: #00bfff"
  34. onmouseout="this.style.fontStyle='normal', this.style.fontWeight='normal'"
  35. onmouseover="this.style.fontStyle='normal', this.style.fontWeight='bold'" /></td>
  36. </tr><tr><td align='center'><span style='font-size:
  37. xx-small'>2021.Mar.16 03:49:57</span></td></tr>
  38. </table>
  39. </td></tr></table>
  40. </td></tr> <!-- ................................................... -->
  42. <tr><td width="15%" align="center"><i>n</i></td>
  43. <td width="45%"><input name="isize" type="text" value="6" size="5"
  44. maxlength="5" /></td>
  45. <td width="40%">Sample <i>size</i> (number of observations).</td></tr>
  47. <tr><td align="center">Data source</td>
  48. <td><select name="igensup"><option value="1"
  49. selected="selected">generate (G)</option><option
  50. value="2">supply (S)</option></select>
  51. (&ldquo;G&rdquo; or &ldquo;S&rdquo;)</td>
  52. <td>Data: <i>generated</i>; or <i>supplied</i> by user. &bull;</td></tr>
  54. <tr><td align="center"><i>&mu;</i>, <i>&sigma;</i> (for G)</td>
  55. <td><input name="zmu" type="text" value="10" size="5"
  56. maxlength="5" /><input name="sigma" type="text" value=".5" size="5"
  57. maxlength="5" /></td>
  58. <td><i>Mean</i> and <i>standard deviation</i> &mdash;
  59. ignored if&nbsp;"S".</td></tr>
  61. <tr><td align="center">ntrial, .seed (for G)</td>
  62. <td><input name="ntrial" type="text" value="100000" size="6"
  63. maxlength="6" /><input name="iseed" type="text" value="0" size="6"
  64. maxlength="10" /></td>
  65. <td>No. of <i>trials</i> and <i>seed</i> &mdash;
  66. ignored if&nbsp;"S". &bull;</td></tr>
  68. <tr><td align="center">Supplied data, <i>X</i> (for&nbsp;S)</td>
  69. <td style="font-size: 95%; color: blue"><textarea name="data"
  70. style="font-size: smaller; color: red" cols="38"
  71. rows="1" >26.1 25.8 26.3 26.8 25.9 26.2</textarea></td>
  72. <td>User-supplied <i>data</i> (<i>n</i> must <i>always</i> match them !)
  73. &mdash; ignored if&nbsp;"G". &bull;</td></tr>
  75. <tr><td align="center">Outlier ?</td>
  76. <td><select name="ioutlier"><option value="-1">smallest</option>
  77. <option value="+1" selected="selected">largest</option></select></td>
  78. <td>Outlier (?), <i>smallest</i> or <i>largest</i>, to be
  79. assessed.</td></tr>
  81. <tr><td align="center"><i>P</i></td>
  82. <td><input name="prob" type="text" value="95" size="5"
  83. maxlength="5" /> %</td>
  84. <td><i>Probability</i> for interval for <i>&mu;</i>. &bull;</td></tr>
  86. <tr><td align="center">Show values</td>
  87. <td><select name="ishow"><option value="0" selected="selected">No</option>
  88. <option value="1">Yes</option></select></td>
  89. <td>Shows the coordinates of the graph. &bull;</td></tr>
  91. <!-- ...fonts/freefont/florence luxembrg muriel PARKAVE.pfb -->
  92. <!-- png linetype: my designations
  93. 1 red ff0000, 2 green 00c000, 3 blue 0080ff, 4 c000ff, 5 00eeee, 6 brown c04000,
  94. 7 beige eeee00, 8 dark blue 2020c0, 9 peach ffc020, 10 dark green 008040,
  95. 11 violeta a080ff, 12 dark brown 804000, 13 pink ff80ff, 14 turquesa 00c060,
  96. 15 turquesa 00c0c0, 16 turq. escuro 006080, 17 escarlate c06080,
  97. 18 dark green 008000, 19 green 40ff80, 20 dark blue 306080, 21 dark red 806000,
  98. 22 dark gray 404040, 23 olive green 408000, 24 navy blue 000080, 25 806010,
  99. 26 806060, 27 ~806080, 28 ~5050c0, 29 0000ff, 30 006000, 31 ~eb0c0,
  100. 32 40c080, 33 60a0c0 -->
  101. <!-- plot gnudata.dat \ (or anything: this line is a MANDATORY dummy) -->
  103. <tr><td colspan="3"><input name="gnuplot" type="hidden"
  104. value="set terminal png enhanced font 'FreeSerif, 13'
  105. set timestamp font 'FreeSerif, 10' offset 5, -0.7
  106. set nokey; set title 'Delta or x' offset 0, +.5
  107. set xlabel 'i' offset 12, .1; set ylabel 'y'
  108. plot 'anyname.dat' \
  109. using 1:2 with lines linetype 2 linewidth 3, \
  110. '' using 1:3 with linespoints linetype 1 linewidth 3 ps 2" />
  111. <table width="100%" class="sm">
  112. <tr><td valign="top" colspan="2">&emsp; From a randomly
  113. <i>generated</i> (G) or <i>user-supplied</i> (S) sample (set of observations),
  114. calculates some common <i>statistics</i>: average (<i>x</i>-bar),
  115. standard deviation (<i>s</i>), average deviation (<i>&delta;</i>).
  116. <br />&emsp;The graph shows: for G, <i>&delta;</i> simulated
  117. for random samples of size 2<sup><i>k</i></sup> trials, with (integer)
  118. <i>k</i> = 1<big><b>..</b></big>log<sub>2</sub>(ntrial)
  119. (log<sub>2</sub>100000 = 16.6 &rarr; 16); for S, the user data,
  120. without the (possible) outlier.
  121. <br />&emsp;An extreme (smallest or largest) value in the sample is
  122. assessed to estimate whether it is an <i>outlier</i> (to be rejected).
  123. <br />&emsp;The decision on what is an outlier is a delicate question.
  124. See, for example, Barnett and Lewis [1998].
  125. <br />&emsp;Excel:&nbsp;
  126. <i>t</i> = Stud<sup>inv</sup>([(1+prob)/2, <i>&nu;</i>] becomes
  127. TINV[(1-prob, <i>&nu;</i>]&emsp;Typically,
  128. <i>&nu;</i> = <i>n</i> &minus; 1. (Here, <i>n</i> had already been
  129. reduced, so <i>&nu;</i>&nbsp;=&nbsp;<i>n</i><sup>original</sup> &minus; 2 .)
  130. <br />&emsp;Other suggested data:
  131. 26.6 26.8 26.2 26.9 27.1 27.0 (smallest) &emsp;
  132. 26.6 26.9 26.7 26.6 26.7 26.6 (largest)</td>
  133. </tr></table></td></tr>
  135. <tr><td align="center"><input type="reset" style="font-size: smaller"
  136. value=" Reset " /></td><td><i>References:</i></td>
  137. <td align="center">Plate: Errth08804</td></tr>
  138. <tr><td colspan="3"><p class="ref">&bull;&nbsp;<a href=
  139. "http://www.physics.tamu.edu/people/showpeople.php?name=
  140. Sante%20R.%20Scuro&amp;userid=sante"><span class="sc">Scuro</span></a>,
  141. Sante R.: <a href="http://web.tecnico.ulisboa.pt/~mcasquilho/compute/errtheory/,basics/ScuroErrTheo.pdf">Error
  142. theory</a>.<i>pdf</i> (<a href=
  143. "http://www.physics.tamu.edu/">Texas A&amp;M Univ.</a>).
  144. &bull;&nbsp;<a href=
  145. "http://class.phys.psu.edu/p559/experiments/html/error.html">Err.
  146. analysis</a> (P. C. Eklund, <a href=
  147. "http://class.phys.psu.edu/">PennState U.</a>).
  148. &bull;&nbsp;<a href=
  149. "http://www.drake.edu/artsci/physics/ERROR_THEORY.htm">Petridis</a>, A.
  150. (<a href="http://www.drake.edu/artsci/">Drake Univ.</a>).
  151. &bull;&nbsp;<a href=
  152. "http://teacher.nsrl.rochester.edu/PHY_LABS/Labs_121.html">Wolfs</a>,
  153. F., see "Error analysis" (Univ. of
  154. <a href="http://www.rochester.edu/">Rochester</a>).</p>
  156. <p class="ref">&bull;&nbsp;<span class="sc">Weisstein</span>, Eric W.,
  157. "<a href="http://mathworld.wolfram.com/ErrorPropagation.html">Error
  158. propagation</a>". From <i>MathWorld</i> &mdash; a Wolfram Web Resource
  159. (accessed 2008-08-04).</p>
  161. <p class="ref">&bull;&nbsp;<span class="sc">Barnett</span>, Vic and
  162. Toby <span class="sc">Lewis</span>, <acronym title="Amazon"><a href=
  163. "http://www.amazon.com/Outliers-Statistical-Wiley-Probability-Statistics/
  164. dp/0471930946/ref=sr_1_2?ie=UTF8&amp;s=books&amp;qid=
  165. 1219876491&amp;sr=1-2">1998</a></acronym>, "Outliers in statistical data",
  166. 3.rd ed. (=1994, <acronym title="BibIST"><a href=
  167. "http://thesaurus.reitoria.utl.pt/search~S3*por?/cQA278-279%2F1.BAR.30829/
  168. cqa++278+279+1+bar30829/-3,-1,0,B/frameset&amp;FF=
  169. cqa++278+279+1+bar30829&amp;1,1,">1978</a></acronym>), Wiley,
  170. New York, NY (USA). (At ISEG Library: <a href=
  171. "http://thesaurus.reitoria.utl.pt/search~S2*por?/
  172. cQA276.B37+1994/cqa++276+b37+1994/-3,-1,0,B/exact&amp;FF=
  173. cqa++276+b37+1994&amp;1,2,">1994</a>.)</p>
  175. <p class="ref">&bull;&nbsp;<span class="sc">Bevington</span>, Philip R. and
  176. D. Keith <span class="sc">Robinson</span>, <acronym title="BibIST"><a href=
  177. "http://thesaurus.reitoria.utl.pt/search~S8*por/?searchtype=
  178. c&amp;searcharg=00.BR.61056&amp;searchscope=3&amp;SORT=D&amp;extended=
  179. 0&amp;SUBMIT=Pesquisar&amp;searchlimits=&amp;searchorigarg=
  180. c00.BR.61056">2003</a></acronym>, "<acronym title="Amazon"><a href=
  181. "http://www.amazon.com/Reduction-Error-Analysis-Physical-Sciences/dp/
  182. 0072472278/ref=pd_bbs_sr_1?ie=UTF8&amp;s=books&amp;qid=1219893338&amp;sr=
  183. 1-1">Data reduction and error analysis for the physical
  184. sciences</a></acronym>", 3.rd ed., McGraw-Hill, New York, NY (USA).</p>
  186. <p class="ref">&bull;&nbsp;Google search: <a href=
  187. "http://www.google.com/search?hl=en-US&amp;safe=off&amp;q=
  188. simulation+%22Monte+Carlo%22+%22chemical+engineering%22+%22random+number%22+site%3A.edu&amp;btnG=Search&amp;meta=">simulation
  189. "Monte Carlo" "Chemical Engineering"&hellip;</a></p>
  191. <p class="ref">&bull;&nbsp;<a href=
  192. "./,basics/KurtSkew.xls">Kurtosis, skewness</a>.<i>xls</i>
  193. &bull;&nbsp;<a href=
  194. "http://www.okstate.edu/sas/v7/sashtml/books/qc/chap1/sect17.htm">Descriptive
  195. statistics</a> (SAS v7 doc., Oklahoma State Univ., Stillwater).</p>
  197. <p class="ref">&bull;&nbsp;<a href=
  198. "http://web.ist.utl.pt/mcasquilho/compute/qc/Fx-Student.php">Student's
  199. <i>t</i></a> (this site).</p>
  201. <p class="ref">&bull;&nbsp;<span class="sc">Taylor</span>, John R.,
  202. <acronym title="BibIST"><a href=
  203. "http://thesaurus.reitoria.utl.pt/search~S3*por?/cQC39.TAY.67208/
  204. cqc+++39+tay67208/-3,-1,0,B/
  205. frameset&amp;FF=cqc+++39+tay67208&amp;1,1,">1997</a></acronym>,
  206. "An introduction to error analysis", 2.nd ed., <acronym title="Amazon"><a href=
  207. "http://www.amazon.co.uk/In
  208. troduction-Error-Analysis-Uncertainties-Measurements/
  209. dp/093570275X/ref=sr_1_1?ie=UTF8&amp;s=books&amp;qid=1217804330&amp;sr=1-1"
  210. >Univ. Sci. Books</a></acronym>
  211. (<a href="http://www.uscibooks.com">USB</a>), Sausalito, CA (USA)
  212. (<a href="http://physics.gac.edu/~mellema/Taylor/
  213. Taylor_files/frame.htm">intro</a> IE).</p>
  215. <p class="ref">&bull;&nbsp;[<acronym
  216. title="Lyons, 1991,&nbsp;
  217. 'A practical guide to data analysis for physical science students'"><a href=
  218. "http://web.tecnico.ulisboa.pt/~mcasquilho/acad/errors/bibliography.php">Lyons, 1991</a></acronym>]
  219. &bull;&nbsp;[<acronym title="Taylor, 1987,&nbsp;
  220. 'Quality assurance of chemical measurements'"><a href=
  221. "http://web.tecnico.ulisboa.pt/~mcasquilho/acad/errors/bibliography.php">J. K. Taylor, 1987</a></acronym>]</p>
  223. <p class="ref">&bull;&nbsp;<span class="sc">Weisstein</span>, Eric W.,
  224. "<a href="http://mathworld.wolfram.com/Studentst-Distribution.html">Student's
  225. t-distribution</a>". From <i>MathWorld</i> &mdash; a Wolfram
  226. Web Resource (accessed 2008-08-04).</p>
  228. <p class="ref">&bull;&nbsp;<a href=
  229. "http://www-groups.dcs.st-and.ac.uk/~history/Biographies/
  230. Chauvenet.html">Chauvenet</a>, William, 1820&ndash;1870
  231. (<acronym title="Google">"<a href=
  232. "http://www.google.pt/search?hl=en&amp;q=
  233. %22Chauvenet%27s+criterion%22+site%3A.edu&amp;meta=">Chauvenet's
  234. criterion</a></acronym>").</p>
  236. <p class="ref">&bull;&nbsp;1805-08-04: <a href=
  237. "http://www-groups.dcs.st-and.ac.uk/~history/Biographies/
  238. Hamilton.html">Hamilton</a>, Sir William Rowan, birthday.</p>
  239. </td></tr>
  240. </table>
  241. </form>
  243. <div style="line-height: 6pt">&nbsp;</div>
  244. <div style="line-height: 1.5pt; color: black;
  245. background-color: red">&nbsp;</div>
  247. <table width="100%" class="sm"><tr>
  248. <td width="58px"><a href="http://validator.w3.org/check?uri=
  249. http://web.tecnico.ulisboa.pt/~mcasquilho/compute/errtheory/Fx-errors.php;verbose=1;ss=1"><img
  250. src="http://web.tecnico.ulisboa.pt/~mcasquilho/depot/valid-xhtml10s.png"
  251. alt="Valid HTML 4.01!" border="0" width="55px" height="19px" /></a></td>
  252. <td width="15%" align="left"><a href="http://www.tecnico.ulisboa.pt"><img
  253. src="http://web.tecnico.ulisboa.pt/~mcasquilho/depot/wwwist.png"
  254. alt="IST" align="middle" border="0" width="88px" height="34px" /></a></td>
  255. <td width="70%" align=
  256. "right"><i>http://web.tecnico.ulisboa.pt/~mcasquilho/compute/errtheory/Fx-errors.php</i><br />
  257. <i>Created:</i> 2008-08-04 &mdash; <i>Last modified:</i>
  258. 2009-09-17</td></tr></table>
  259. </body></html>

↑ Top