<div dir="ltr"><font color="#000000" face="Times New Roman" size="3">
</font><p style="margin:0in 0in 8pt"><font color="#000000" face="Calibri" size="3">Hi Son,</font></p><font color="#000000" face="Times New Roman" size="3">
</font><p style="margin:0in 0in 8pt"><font color="#000000" face="Calibri" size="3">What you are explaining sounds like resampling to build a
distribution under the null hypothesis. You would need to make sure that your
random draws are representative in some way of an instance where the test
statistic (graph theoretic measure) is truly zero, i.e. representative of the
null hypothesis. There is no info on your measure, so one can't comment any further
on how one would achieve this. </font></p><font color="#000000" face="Times New Roman" size="3">
</font><p style="margin:0in 0in 8pt"><font color="#000000" face="Calibri" size="3">Once you have the bootstrapped distribution you compute the
proportion of values above the test statistic and those below the test
statistic--the test statistic is the measure you got from the actual sample,
not the bootstrapped distribution. </font></p><font color="#000000" face="Times New Roman" size="3">
</font><p style="margin:0in 0in 8pt"><font color="#000000" face="Calibri" size="3">Then it depends whether you use a two-tail or one-tail test
and the direction of the hypothesized effect: for a one-tail test you could potentially
take the proportion of the distribution above equal to the test statistic, that
would be your p-value. For two tailed-tests take the min value of the
two-proportions as your p-value and remember to divide alpha by 2 to test for
significance. </font></p><font color="#000000" face="Times New Roman" size="3">
</font><p style="margin:0in 0in 8pt"><font color="#000000" face="Calibri" size="3">That, in a nutshell, is a simple approach; however, there
are other ways to go about this. </font></p><font color="#000000" face="Times New Roman" size="3">
</font><p style="margin:0in 0in 8pt"><font color="#000000" face="Calibri" size="3">Matthew<span></span></font></p><font color="#000000" face="Times New Roman" size="3">
</font></div><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Oct 5, 2016 at 6:54 AM, Ta Dinh, Son <span dir="ltr"><<a href="mailto:son.ta.dinh@tum.de" target="_blank">son.ta.dinh@tum.de</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div lang="DE" link="#0563C1" vlink="#954F72">
<div class="m_9202272115444020451WordSection1">
<p class="MsoNormal">Dear Fieldtrippers,<u></u><u></u></p>
<p class="MsoNormal"> <u></u><u></u></p>
<p class="MsoNormal">the general problem we are facing is one of statistics. In particular, we are trying to test the robustness of a graph measure when reducing the amount of nodes it is computed with. In our case, we use the EEG electrodes as nodes.<u></u><u></u></p>
<p class="MsoNormal"> <u></u><u></u></p>
<p class="MsoNormal">We are trying to find out whether a graph measure differs significantly from zero over a group of subjects. The exact calculation of the measure is rather complicated to explain, suffice it to say that every subject has exactly one scalar
value in the end. Computation of this measure using 64 electrodes is straightforward and we can easily calculate a p-value and/or a confidence interval.<u></u><u></u></p>
<p class="MsoNormal">When we calculate based on only 32 electrodes however, we draw 32 electrodes randomly. Therefore, we need to repeat this computation many times (let’s say 1000 times). So we then get [1000 x number of subjects] values, or 1000 p-values/confidence
intervals.<u></u><u></u></p>
<p class="MsoNormal">How do we statistically test whether the measure is robustly different from 0? Is it too naive to simply assume that if the confidence interval does not contain 0 in at least 950 of the 1000 computations then it is robustly different from
0?<u></u><u></u></p>
<p class="MsoNormal"> <u></u><u></u></p>
<p class="MsoNormal">Any help would be greatly appreciated!<u></u><u></u></p>
<p class="MsoNormal"> <u></u><u></u></p>
<p class="MsoNormal">Best regards,<u></u><u></u></p>
<p class="MsoNormal">Son<u></u><u></u></p>
<p class="MsoNormal"><u></u> <u></u></p>
<p class="MsoNormal"><span style="color:rgb(136,136,136);font-family:"Times New Roman",serif;font-size:7.5pt">Son Ta Dinh, M.Sc.</span><span style="color:rgb(136,136,136);font-family:"Times New Roman",serif;font-size:12pt"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="color:rgb(136,136,136);font-family:"Times New Roman",serif;font-size:7.5pt">PhD student in Human Pain Research</span><span style="color:rgb(136,136,136);font-family:"Times New Roman",serif;font-size:12pt"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="color:rgb(136,136,136);font-family:"Times New Roman",serif;font-size:7.5pt">Klinikum rechts der Isar</span><span style="color:rgb(136,136,136);font-family:"Times New Roman",serif;font-size:12pt"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="color:rgb(136,136,136);font-family:"Times New Roman",serif;font-size:7.5pt">Technische Universität München<br>
Munich, Germany<br>
Phone: <a href="tel:%2B49%2089%204140%207664" target="_blank"><span style="color:blue">+49 89 4140 7664</span></a><br>
<a href="http://www.painlabmunich.de/" target="_blank"><span style="color:blue">http://www.painlabmunich.de/</span></a></span><span style="color:rgb(136,136,136);font-family:"Times New Roman",serif;font-size:12pt"><u></u><u></u></span></p>
<p class="MsoNormal"><u></u> <u></u></p>
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