<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>FAQ/percentile</title><revhistory><revision><revnumber>10</revnumber><date>2013-03-08 10:17:24</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>9</revnumber><date>2007-11-07 15:44:48</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2007-11-07 15:44:01</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2007-11-07 15:37:38</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2007-11-07 15:08:30</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2007-11-07 15:07:10</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2007-01-25 15:59:58</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2006-07-20 13:31:38</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>2</revnumber><date>2006-07-20 13:29:08</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>1</revnumber><date>2006-07-20 13:28:55</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision></revhistory></articleinfo><section><title>Percentiles of exponential data and use in outlier detection</title><para>If the data follows an exponential distribution (test this by using Kolmogorov-Smirnov test in SPSS and choosing the exponential option). Then </para><para>- (Mean score) (LN(1- PERC/100 ))  gives the threshold of the PERC% percentile. </para><para>This follows from  </para><para>P(X &lt; x) = 1 – EXP(-R*x)  where rate, R, is estimated from the sample data by 1/mean.  </para><para>These percentiles may be <ulink url="http://www.statsoft.com/textbook/glose.html">used</ulink> to classify a  data point as extreme since outliers are defined as either  </para><para>&gt; 75th percentile + 1.5 * (75th perc - 25th perc) </para><para>or  </para><para>&lt; 25th percentile - 1.5 * (75th perc - 25th perc) </para></section></article>