<font size="4">Dear Eric,<br><br>Thanks for your clear answer. 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: </font><font size="4">2Group(boys,girls)</font><font size="4">*</font><font size="4">2A(A1,A2)*2B(B1,B2). Factor </font><font size="4">Group is a between-subject factor</font><font size="4">, while factor </font><font size="4">A and B are within-subject factors. What I want to test is whether factors B influences factor A differently on boys and girls</font><font size="4"> (a three-way interaction)</font><font size="4">.<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 </font><font size="4">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>Thank you in advance.<br><br>Lin<br></font>
<font size="4"><br><br></font><br><div class="gmail_quote">2009/11/24 Eric Maris <span dir="ltr"><<a href="mailto:e.maris@donders.ru.nl" target="_blank">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="purple" lang="NL">
<div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">Dear Stephan,</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;" 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;" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;" 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;" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;" lang="EN-GB">Best,</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;" lang="EN-GB">Eric</span></font></p><div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;" lang="EN-GB"> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> -----Oorspronkelijk bericht-----</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> 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;">> Stephan Moratti</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> Verzonden: dinsdag 24 november 2009 10:20</span></font></p><div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> 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;">> 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;">> in a two by two design</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> </span></font></p>
</div><p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> Hi all,</span></font></p><div><div></div><div>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> 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;">> 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;">> 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;">> 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;">> 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;">> 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;">> 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;">> 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;">> 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;">> 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;">> 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;">> resample condition, we would destroy the
condition structure.</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> 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;">> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> Best,</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> Stephan</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> </span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> ----------------------------------</span></font></p>
<p><font face="Bookman Old Style" size="3"><span style="font-size: 12pt;">> 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;">> 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;">> 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;">> <a href="http://www.ru.nl/neuroimaging/fieldtrip" target="_blank">http://www.ru.nl/neuroimaging/fieldtrip</a>.</span></font></p>
</div></div></div>
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<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>
</div></div><p> <a href="http://listserv.surfnet.nl/archives/fieldtrip.html" target="_blank">http://listserv.surfnet.nl/archives/fieldtrip.html</a></p>
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</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>
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<p> http://www.ru.nl/fcdonders/fieldtrip/</p>