<?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/absdiff</title><revhistory><revision><revnumber>9</revnumber><date>2013-03-08 10:17:37</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>8</revnumber><date>2011-11-02 16:37:15</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2011-11-02 16:36:34</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2011-11-02 16:36:05</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2011-11-02 16:35:46</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2011-11-02 16:35:21</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2011-11-02 16:34:41</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2011-11-02 16:34:20</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2011-11-02 16:31:56</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Difference in errors adjusted for overall number when the errors have different signs</title><para>Suppose we have error scores which can take positive or negative values, of equal importance, on two conditions, baseline (B) and treatment (T) then assuming at least one of B and T are non-zero the difference in the errors adjusted for total number can be expressed using absolute values, abs(), as </para><screen><![CDATA[sgn(T-B)[abs(T-B)] / [(abs(B) + abs(T)] if T and B have different signs or
]]><![CDATA[
[abs(T) - abs(B)] / [(abs(B) + abs(T)] if T and B have the same sign]]></screen><para>Alternatively, provided B is nonzero, we can express the difference in errors as a percentage change (PC) by </para><screen><![CDATA[sgn(T-B) 100[abs(T-B)] / abs(B) if T and B have different signs or
]]><![CDATA[
100[abs(T) - abs(B)]/abs(B) = 100(SF - 1) if T and B have the same sign]]></screen><para>where SF is the scaling factor relating to T and B. </para><para>For example if T and B both have the same sign and the number of errors doubles (SF=2) it follows abs(T) - abs(B) = 2 abs(B) so abs(T) = 2 abs(B) which gives a 100 (2abs(B)- abs(B))/abs(B) = 100% increase in errors from baseline. </para><para>If we ignore the absolute values in the above formulae we can end up with misleading values due to failing to ignore the signs of B and T. For example if we have scores of -3 for B and +2 for T then the total number of errors equal to B+A equals -1 when in fact there are 5 errors made in total. </para></section></article>