# [FieldTrip] calculating behavioural-power correlation -- follow-up questions

Xiaoming Du XDu at mprc.umaryland.edu
Tue Oct 20 00:56:51 CEST 2015

```For example, our power values ranged from 1 to 3 (after log transform); my behavioral data ranged from 20 to 90;

by using above mentioned script, there are 14 negative clusters were reported in variable stat.

stat =

prob: [30x50 double]
posclusters: []
posclusterslabelmat: [30x50 double]
posdistribution: [1x1000 double]
negclusters: [1x14 struct]
negclusterslabelmat: [30x50 double]
negdistribution: [1x1000 double]
cirange: [30x50 double]
stat: [30x50 double]
ref: [30x50 double]
rho: [30x50 double]
dimord: 'chan_freq'
freq: [1x50 double]
label: {30x1 cell}
time: 2.5000
cfg: [1x1 struct]

However, the p values of those clusters (i.e., stat.negclusters.prob) are all ones. The smallest value in  stat.negdistribution is way larger than the largest negative cluster t-sum. This could be real. However, it is more likely due to the shuffle between power and behavioral group. For example, design matrix  [1 1 1 1 2 2 2 2; 1 2 3 4 1 2 3 4] was shuffled to [1 2 2 1 2 2 1 1; 1 2 3 4 1 2 3 4].  After each permutation, for some subjects, their power data was labeled as behavioral data and vice versa. Because of the scale difference between power and behavioral data, large negative correlations were generated by permutation. This further biased the cluster distribution.
My limited understanding is that, for correlation, each permutation should fix cfg.ivar and only shuffle half of the cfg.uvar. For example, permute design matrix [1 1 1 1 2 2 2 2; 1 2 3 4 1 2 3 4]  to [1 1 1 1 2 2 2; 1 2 3 4 4 2 3 1]. THerefore, after permutation, one subject's power data corresponds to another subject's behavioral data.

I am not good at statistics. It will be really appreciated if you have any suggestions or comments.

Xiaoming

>>> Arjen Stolk <a.stolk8 at gmail.com> 10/19/2015 6:01 PM >>>
Hey Xiaoming,

Not sure if I understand, but shouldn't the directions of the correlations be independent of the scaling of the two variables? Looking at the code of ft_statfun_correlationT it doesn't seem the conversion from correlation to T value (tstat = rho*(sqrt(max(nunits)-2))/sqrt((1-rho^2))) would result in a direction change either. Perhaps you could try to first manually calculate a correlation between signal power and behavioral power, and see whether anything is behaving unexpectedly?

Yours,
Arjen

2015-10-19 14:25 GMT-07:00 Xiaoming Du <XDu at mprc.umaryland.edu>:

Dear FieldTrip users,
This is Xiaoming from University of Maryland Baltimore. My current project requires to calculate behavioral-power correlation across subjects. Similar topic was discussed here early this year. http://mailman.science.ru.nl/pipermail/fieldtrip/2015-February/008953.html
According to the suggestions in above mentioned thread, I duplicate my power dataset and replace the power values at each time-frequency point with behavioral data. Therefore, those two datasets have same structure and dimension. I used the following script to test if there are significant clusters of correlations.
cfg = [];
cfg.parameter = 'powspctrm';
cfg.method = 'montecarlo';
cfg.statistic = 'ft_statfun_correlationT';
...
etc
...
design = zeros(2, n1 * 2); % n1 is the number of subjects.
design(1,1:n1) = 1;
design(1,(n1 + 1):(n1 * 2)) = 2;
design(2, :) = [[1:n1 ] [1 : n1]];
cfg.design = design;

cfg.ivar = 1;
cfg.uvar = 2;
However, it seems when each time the design matrix is permuted, FieldTrip is using the same method as for 'ft_statfun_depsamplesT', meaning cfg.uvar remains the same while cfg.ivar (1 or 2) is randomly assigned to each subject in design matrix. Although I confirmed this by uncommenting line 313 (i.e., tmpdesign = design(:,resample(i,:))) in ft_statistics_montecarlo.m which allows to display the permuted design matrix in command line, please correct me if this is not the case.
In my mind, this kind of permutation will cause trouble when dealing with correlation. For example, in my case, the behavioral data and power data have different scales. The power data are much larger than behavioral data in general. When assigning behavioral data into power group or vice versa, it will induce huge negative correlations between power and behavioral measurement. Therefore, no negative clusters will survive from permutation test.
Please let me know if I have mis-understanding or if I did anything wrong. Any suggestions will be highly appreciated!
Thanks.

Xiaoming

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