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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Hey Matthew,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Thanks for the answer, but the question is exactly how to actually build a representative null distribution. As the calculation using
all (64) electrodes is deterministic, it can’t really be used to create a distribution, it would just be a vector of 1000 x 1 exact same value.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">The graph measure is called hub disruption index and was introduced here: Achard, S., et al. (2012). "Hubs of brain functional networks
are radically reorganized in comatose patients." PNAS.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">To put it in a nutshell, it compares a subject against a group of controls, thereby giving a single value for every subject (in comparison
to the control group).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">I hope this has cleared up the context a bit.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Best<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Son<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:7.5pt;color:#888888">Son Ta Dinh, M.Sc.</span><span lang="EN-US" style="color:#888888"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:7.5pt;color:#888888">PhD student in Human Pain Research</span><span lang="EN-US" style="color:#888888"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:7.5pt;color:#888888">Klinikum rechts der Isar</span><span style="color:#888888"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:7.5pt;color:#888888">Technische Universität München<br>
Munich, Germany<br>
Phone: </span><a href="tel:%2B49%2089%204140%207664" target="_blank"><span style="font-size:7.5pt">+49 89 4140 7664</span></a><span style="font-size:7.5pt;color:#888888"><br>
</span><a href="http://www.painlabmunich.de/" target="_blank"><span style="font-size:7.5pt">http://www.painlabmunich.de/</span></a><span style="color:#888888"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">Von:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> Nickel, Moritz
<br>
<b>Gesendet:</b> Mittwoch, 12. </span><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Oktober 2016 16:37<br>
<b>An:</b> Ta Dinh, Son <son.ta.dinh@tum.de><br>
<b>Betreff:</b> Fwd: [FieldTrip] Statistical test of robustness of a graph measure based on reduced amount of nodes<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span lang="EN-US">---------- Forwarded message ----------<br>
From: <b>Matt Gerhold</b> <</span><a href="mailto:matt.gerhold@gmail.com"><span lang="EN-US">matt.gerhold@gmail.com</span></a><span lang="EN-US">><br>
Date: 2016-10-05 13:31 GMT+02:00<br>
Subject: Re: [FieldTrip] Statistical test of robustness of a graph measure based on reduced amount of nodes<br>
To: FieldTrip discussion list <</span><a href="mailto:fieldtrip@science.ru.nl"><span lang="EN-US">fieldtrip@science.ru.nl</span></a><span lang="EN-US">><br>
<br>
<o:p></o:p></span></p>
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<span lang="EN-US" style="font-family:"Calibri",sans-serif;color:black">Hi Son,</span><span lang="EN-US"><o:p></o:p></span></p>
<p style="mso-margin-top-alt:0cm;margin-right:0cm;margin-bottom:8.0pt;margin-left:0cm">
<span lang="EN-US" style="font-family:"Calibri",sans-serif;color:black">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.
</span><span lang="EN-US"><o:p></o:p></span></p>
<p style="mso-margin-top-alt:0cm;margin-right:0cm;margin-bottom:8.0pt;margin-left:0cm">
<span lang="EN-US" style="font-family:"Calibri",sans-serif;color:black">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. </span><span lang="EN-US"><o:p></o:p></span></p>
<p style="mso-margin-top-alt:0cm;margin-right:0cm;margin-bottom:8.0pt;margin-left:0cm">
<span lang="EN-US" style="font-family:"Calibri",sans-serif;color:black">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.
</span><span lang="EN-US"><o:p></o:p></span></p>
<p style="mso-margin-top-alt:0cm;margin-right:0cm;margin-bottom:8.0pt;margin-left:0cm">
<span lang="EN-US" style="font-family:"Calibri",sans-serif;color:black">That, in a nutshell, is a simple approach; however, there are other ways to go about this.
</span><span lang="EN-US"><o:p></o:p></span></p>
<p style="mso-margin-top-alt:0cm;margin-right:0cm;margin-bottom:8.0pt;margin-left:0cm">
<span lang="EN-US" style="font-family:"Calibri",sans-serif;color:black">Matthew</span><span lang="EN-US"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US">On Wed, Oct 5, 2016 at 6:54 AM, Ta Dinh, Son <</span><a href="mailto:son.ta.dinh@tum.de" target="_blank"><span lang="EN-US">son.ta.dinh@tum.de</span></a><span lang="EN-US">> wrote:<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Dear Fieldtrippers,<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">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?<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Any help would be greatly appreciated!<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Best regards,<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Son<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:7.5pt;color:#888888">Son Ta Dinh, M.Sc.</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:7.5pt;color:#888888">PhD student in Human Pain Research</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:7.5pt;color:#888888">Klinikum rechts der Isar</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:7.5pt;color:#888888">Technische Universität München<br>
Munich, Germany<br>
Phone: </span><a href="tel:%2B49%2089%204140%207664" target="_blank"><span style="font-size:7.5pt">+49 89 4140 7664</span></a><span style="font-size:7.5pt;color:#888888"><br>
</span><a href="http://www.painlabmunich.de/" target="_blank"><span style="font-size:7.5pt">http://www.painlabmunich.de/</span></a><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span lang="EN-US">_______________________________________________<br>
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<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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