[FieldTrip] Statistical test of robustness of a graph measure based on reduced amount of nodes

[Matt Gerhold]

Hi Son,

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.

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.

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.

That, in a nutshell, is a simple approach; however, there are other ways to
go about this.

Matthew

On Wed, Oct 5, 2016 at 6:54 AM, Ta Dinh, Son <son.ta.dinh at tum.de> wrote:

> Dear Fieldtrippers,
>
>
>
> 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.
>
>
>
> 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.
>
> 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.
>
> 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?
>
>
>
> Any help would be greatly appreciated!
>
>
>
> Best regards,
>
> Son
>
>
>
> Son Ta Dinh, M.Sc.
>
> PhD student in Human Pain Research
>
> Klinikum rechts der Isar
>
> Technische Universität München
> Munich, Germany
> Phone: +49 89 4140 7664
> http://www.painlabmunich.de/
>
>
>
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