<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:st1="urn:schemas-microsoft-com:office:smarttags" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv=Content-Type content="text/html; charset=us-ascii">
<meta name=Generator content="Microsoft Word 11 (filtered medium)">
<o:SmartTagType namespaceuri="urn:schemas-microsoft-com:office:smarttags"
name="PersonName"/>
<!--[if !mso]>
<style>
st1\:*{behavior:url(#default#ieooui) }
</style>
<![endif]-->
<style>
<!--
/* Font Definitions */
@font-face
{font-family:"Bookman Old Style";
panose-1:2 5 6 4 5 5 5 2 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
a:link, span.MsoHyperlink
{color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{color:purple;
text-decoration:underline;}
p.MsoPlainText, li.MsoPlainText, div.MsoPlainText
{margin:0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Bookman Old Style";}
@page Section1
{size:595.3pt 841.9pt;
margin:70.85pt 42.25pt 70.85pt 42.25pt;}
div.Section1
{page:Section1;}
-->
</style>
</head>
<body lang=NL link=blue vlink=purple>
<div class=Section1>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>Dear Stephan,<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'>It is sometimes possible to reformulate an interaction
effect null hypothesis such that it becomes a main effect null hypothesis (however,
for a different dependent variable, obtained be calculating the difference
between conditions). Such a reformulation is possible for a two-factorial
design in which one independent variable is manipulated within subjects (in
your case, this is condition), and the other between subjects (in your case,
this is group). You do this by calculating subject-specific difference scores,
[condition1 - condition2], and using these as the dependent variable in a
between-groups comparison. This is possible by means of the standard independent-samples
T-test, but also by means of a permutation test (involving permutation of the difference
scores), which allows you to deal with the multiple comparison problem.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'>For a factorial design that only involves
between-subject independent variables, such a reformulation is not possible (at
least, I am not aware of it). <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'>Best,<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'>Eric<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span lang=EN-GB
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> -----Oorspronkelijk bericht-----</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> Van: <st1:PersonName w:st="on">FieldTrip
discussion list</st1:PersonName> [mailto:FIELDTRIP@NIC.SURFNET.NL] Namens</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> Stephan Moratti</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> Verzonden: dinsdag 24 november 2009 10:20</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> Aan: FIELDTRIP@NIC.SURFNET.NL</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> Onderwerp: Re: [FIELDTRIP] Question about
permutation testing of an interaction</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> in a two by two design</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> </span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> Hi all,</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> </span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> Thanks for the interesing discussion about the
interaction with respect to</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> permutation. I have been also struggling with
this question. As we want to</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> test the interaction (and not the main effect
condition), I am not sure if</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> resampling condition would produce the
distribution of our null hypothesis.</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> Regarding the interaction, we want to check if
the mean values across</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> conditions follow the same pattern in two groups
(if we consider a group x</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> condition interaction). If we make a line plot an
interaction would be indicated</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> by a line crossing if each line represents a
group (ideally). No interaction</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> would be represented by parallel lines for each
group. So I wonder if by</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> resampling the subject values between the groups
keeping the condition</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> structure intact, would create our null
distribution for the interaction. If we</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> resample condition, we would destroy the
condition structure.</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> </span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> What do you think? I would be happy for any
input.</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> </span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> Best,</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> </span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> Stephan</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> </span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> ----------------------------------</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> The aim of this list is to facilitate the
discussion between users of the FieldTrip</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> toolbox, to share experiences and to discuss new
ideas for MEG and EEG analysis.</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> See also http://listserv.surfnet.nl/archives/fieldtrip.html
and</span></font></p>
<p class=MsoPlainText><font size=3 face="Bookman Old Style"><span
style='font-size:12.0pt'>> http://www.ru.nl/neuroimaging/fieldtrip.</span></font></p>
</div>
</body>
</html>
<p>----------------------------------</p>
<p>The aim of this list is to facilitate the discussion between users of the FieldTrip toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis.</p>
<p> http://listserv.surfnet.nl/archives/fieldtrip.html</p>
<p> http://www.ru.nl/fcdonders/fieldtrip/</p>