<font size="4">Dear Eric,<br><br>Thank you very much for you reply.<br><br>I'm clear about the testing of multiple-way interaction now</font><font size="4">. I suppose the tests I mentioned in the last email is simple effect test. Am I right?<br>
<br>Thanks again.<br><br>Lin<br><br><br></font><br><div class="gmail_quote">2009/11/24 Eric Maris <span dir="ltr"><<a href="mailto:e.maris@donders.ru.nl">e.maris@donders.ru.nl</a>></span><br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<div link="blue" vlink="blue" lang="NL">
<div>
<p class="MsoNormal"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">Dear
Lin,</span></font></p>
<p class="MsoNormal"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB"> </span></font></p>
<p class="MsoNormal"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB"> </span></font></p>
<p class="MsoNormal"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB"> </span></font></p>
<div style="border-style: none none none solid; border-color: -moz-use-text-color -moz-use-text-color -moz-use-text-color blue; border-width: medium medium medium 1.5pt; padding: 0pt 0pt 0pt 4pt;"><div class="im">
<p class="MsoNormal" style="margin-bottom: 12pt;"><font face="Times New Roman" size="4"><span style="font-size: 13.5pt;" lang="EN-GB">Thanks for
your clear answer. </span></font><font size="4"><span style="font-size: 13.5pt;">I
also have a question about the permutation testing of the interactions in the
mixed factorial design.<br>
<br>
Suppose I have three factors, with two levels in each: 2Group(boys,girls)*2A(A1,A2)*2B(B1,B2).
Factor Group is a between-subject factor, while factor A and B are
within-subject factors. What I want to test is whether factors B influences
factor A differently on boys and girls (a three-way interaction).<br>
<br>
Can I test the interaction between factor B and Group separately in B1 and B2
conditions? That is, first split the data into two parts (B1, B2), and then for
each part test the interaction between factor A and Group by subtracting the
observations of A1 from A2 and taking it as a new dependent variable.<br>
<br>
Furthermore, if I have another factor C(C1, C2), and I'm interested in whether
the combination of B and C influences factor A differently on boys and girls.
Can I first split the data into four parts according to the combination of
factor B and C (B1C1, B1C2, B2C1, B2C2) and do the interaction between factor A
and Group separately for each part?<br>
<br>
<font color="blue"><span style="color: blue;"></span></font></span></font></p>
</div><p class="MsoNormal" style="margin-bottom: 12pt;"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">I do not think it is necessary to split the
data and do separate analyses on the different parts.</span></font></p>
<p class="MsoNormal" style="margin-bottom: 12pt;"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">Reformulating an interacting effect null
hypothesis as a main effect null hypothesis for a different dependent variable is
possible if you have at most a single between-subjects variable in your design.
Thus, it also works in the case you describe, with two within-subjects and one
between-subjects variable. The dependent variable that must be calculated is
the two-way interaction effect contrast for the 2-factorial within-subjects design
with the variables A and B: [A1,B1] + [A2,B2] – [A1,B2] – [A2,B1]. You
then perform a independent samples T-test on the interaction contrast variable,
comparing the two levels of your between-subjects variable.</span></font></p>
<p class="MsoNormal" style="margin-bottom: 12pt;"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">This reformulation is also possible when there are
more than two within-subjects variables in the design. The only thing that
changes is the interaction effec contrast.</span></font></p><div class="im">
<p class="MsoNormal" style="margin-bottom: 12pt;"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB"> </span></font></p>
<p class="MsoNormal" style="margin-bottom: 12pt;"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">Best,</span></font></p>
<p class="MsoNormal" style="margin-bottom: 12pt;"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">Eric</span></font></p>
<p class="MsoNormal"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB"> </span></font></p>
<p class="MsoNormal"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">dr.
Eric Maris<br>
Donders Institute for Brain, Cognition and Behavior</span></font></p>
<p class="MsoNormal"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">Center
for Cognition and F.C.
Donders Center
for Cognitive Neuroimaging</span></font></p>
<p class="MsoNormal"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">Radboud</span></font><font color="blue" face="Bookman Old Style"><span style="font-family: "Bookman Old Style"; color: blue;" lang="EN-GB"> University</span></font><br>
<font color="blue" face="Bookman Old Style"><span style="font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">P.O. Box</span></font><font color="blue" face="Bookman Old Style"><span style="font-family: "Bookman Old Style"; color: blue;" lang="EN-GB"> 9104</span></font><br>
<font color="blue" face="Bookman Old Style"><span style="font-family: "Bookman Old Style"; color: blue;" lang="EN-GB">6500 HE Nijmegen<br>
The Netherlands<br>
T:+31 24 3612651<br>
Mobile: 06
39584581</span></font></p>
<p class="MsoNormal"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="DE">F:+31
24 3616066<br>
E: e.</span></font><font color="blue" face="Bookman Old Style"><span style="font-family: "Bookman Old Style"; color: blue;"><a href="mailto:e.maris@donders.ru.nl" title="blocked::mailto:maris@nici.kun.nl" target="_blank"><span lang="DE">maris@donders.ru.nl</span></a></span></font><font color="blue" face="Bookman Old Style"><span style="font-family: "Bookman Old Style"; color: blue;" lang="DE"></span></font></p>
<p class="MsoNormal"><font color="blue" face="Times New Roman" size="3"><span style="font-size: 12pt; color: blue;" lang="DE"> </span></font></p>
<p class="MsoNormal"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-US">MSc
Cognitive Neuroscience: </span></font><font color="blue" face="Verdana" size="1"><span style="font-size: 9pt; font-family: Verdana; color: blue;"><a href="http://www.ru.nl/master/cns/" title="http://www.ru.nl/master/cns/" target="_blank"><font title="http://www.ru.nl/master/cns/" face="Bookman Old Style" size="3"><span title="http://www.ru.nl/master/cns/"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-US">www.ru.nl/master/cns/</span></span></font></a></span></font><font face="Verdana" size="1"><span style="font-size: 9pt; font-family: Verdana;" lang="EN-US"></span></font></p>
<p class="MsoNormal" style="margin-bottom: 12pt;"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-US"> </span></font></p>
<p class="MsoNormal" style="margin-bottom: 12pt;"><font color="blue" face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style"; color: blue;" lang="EN-GB"> </span></font></p>
</div><p class="MsoNormal" style="margin-bottom: 12pt;"><font face="Times New Roman" size="4"><span style="font-size: 13.5pt;" lang="EN-GB"><br>
</span></font></p><div><div></div><div class="h5"><font size="4"><span style="font-size: 13.5pt;">Thank you in advance.<br>
<br>
Lin<br>
<br>
<br>
</span></font></div></div><div><div></div><div class="h5">
<div>
<p class="MsoNormal"><font face="Times New Roman" size="3"><span style="font-size: 12pt;">2009/11/24 Eric Maris
<<a href="mailto:e.maris@donders.ru.nl" target="_blank">e.maris@donders.ru.nl</a>></span></font></p>
<div link="blue" vlink="purple">
<div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">Dear Stephan,</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB">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.</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB">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). </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB">Best,</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB">Eric</span></font></p>
<div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> -----Oorspronkelijk bericht-----</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> Van: FieldTrip
discussion list [mailto:<a href="mailto:FIELDTRIP@NIC.SURFNET.NL" target="_blank">FIELDTRIP@NIC.SURFNET.NL</a>]
Namens</span></font></p>
</div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> Stephan Moratti</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> Verzonden: dinsdag 24 november 2009 10:20</span></font></p>
<div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> Aan: <a href="mailto:FIELDTRIP@NIC.SURFNET.NL" target="_blank">FIELDTRIP@NIC.SURFNET.NL</a></span></font></p>
</div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> Onderwerp: Re: [FIELDTRIP] Question about
permutation testing of an interaction</span></font></p>
<div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> in a two by two design</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> </span></font></p>
</div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> Hi all,</span></font></p>
<div>
<div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> Thanks for the interesing discussion
about the interaction with respect to</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> permutation. I have been also struggling
with this question. As we want to</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> test the interaction (and not the main
effect condition), I am not sure if</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> resampling condition would produce the
distribution of our null hypothesis.</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> Regarding the interaction, we want to
check if the mean values across</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> conditions follow the same pattern in two
groups (if we consider a group x</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> condition interaction). If we make a line
plot an interaction would be indicated</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> by a line crossing if each line
represents a group (ideally). No interaction</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> would be represented by parallel lines
for each group. So I wonder if by</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> resampling the subject values between the
groups keeping the condition</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> structure intact, would create our null
distribution for the interaction. If we</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> resample condition, we would destroy the
condition structure.</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> What do you think? I would be happy for
any input.</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> Best,</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> Stephan</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> ----------------------------------</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> The aim of this list is to facilitate the
discussion between users of the FieldTrip</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> toolbox, to share experiences and to
discuss new ideas for MEG and EEG analysis.</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> See also <a href="http://listserv.surfnet.nl/archives/fieldtrip.html" target="_blank">http://listserv.surfnet.nl/archives/fieldtrip.html</a>
and</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt; font-family: "Bookman Old Style";">> <a href="http://www.ru.nl/neuroimaging/fieldtrip" target="_blank">http://www.ru.nl/neuroimaging/fieldtrip</a>.</span></font></p>
</div>
</div>
</div>
</div>
<div>
<div>
<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;">----------------------------------</span></font></p>
<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;">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.</span></font></p>
</div>
</div>
<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;"><a href="http://listserv.surfnet.nl/archives/fieldtrip.html" target="_blank">http://listserv.surfnet.nl/archives/fieldtrip.html</a></span></font></p>
<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;"><a href="http://www.ru.nl/fcdonders/fieldtrip/" target="_blank">http://www.ru.nl/fcdonders/fieldtrip/</a></span></font></p>
</div>
<p class="MsoNormal"><font face="Times New Roman" size="3"><span style="font-size: 12pt;"> </span></font></p>
<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;">----------------------------------</span></font></p>
<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;">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.</span></font></p>
<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;"><a href="http://listserv.surfnet.nl/archives/fieldtrip.html" target="_blank">http://listserv.surfnet.nl/archives/fieldtrip.html</a></span></font></p>
<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;"><a href="http://www.ru.nl/fcdonders/fieldtrip/" target="_blank">http://www.ru.nl/fcdonders/fieldtrip/</a></span></font></p>
</div></div></div>
</div>
</div><div><div></div><div class="h5">
<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> <a href="http://listserv.surfnet.nl/archives/fieldtrip.html" target="_blank">http://listserv.surfnet.nl/archives/fieldtrip.html</a></p>
<p> <a href="http://www.ru.nl/fcdonders/fieldtrip/" target="_blank">http://www.ru.nl/fcdonders/fieldtrip/</a></p>
</div></div></blockquote></div><br>
<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>