Dear Dr. Anderson

Thank you very much for your answer. I am most grateful.

I can promote better understanding about the statistics.

I thought that beta was almost similar to r.

beta=Sxy/Sx^2

correlation coefficient (r)=Sxy/SxYx

I understood that former standardized method was adopted for calculating the correlation in FSL-GLM. Am I right?

One using another software might suggest that calculation for the correlation with this formula. 

Perhaps it may be transformed significance test for correlation.

R^2=t^2(t^2+DF)

I would be grateful if you provide me the information about the formula which FSL adopted when you have a time.

Best regards,

S Fujii

----- Original Message -----
From: Anderson M. Winkler <[log in to unmask]>
To: [log in to unmask]

Date: 2015/12/28, Mon 20:35
Subject: Re: [FSL] multiple regression and permutation

Hi,

All cases you describe are solved in the exact same way:

- If there is one continuous regressor of interest and no nuisance regressors, the test statistic is the t-statistic, which gives the same p-value as if it were a correlation, that is, they are permutationally equivalent (the t statistic and the correlation coefficient are monotonically related, and even in the parametric case, give the same p-value).

- If there is one continuous regressor of interest and one or more nuisance regressors, the test statistic is also the t-statistic, which in this case gives the same p-value as if it were a partial correlation, that is, the t-statistic is permutationally equivalent to the partial correlation coefficient.

- If there are more than one regressor of interest, and the contrast has more than one column (or row as shown in the program interface), that is, if the contrast has rank larger than 1, then the test statistic is no longer the t-statistic, but the F-statistic. There isn't a direct correspondence to a partial correlation in this case, although one can compute the coefficient of determination (R^2) that tells something about how much of the variance of the data is explained by the regressors used in the contrast.

Hope this helps.

All the best,

Anderson

On 25 December 2015 at 09:48, 藤井 さやか <[log in to unmask]> wrote:

Hi Anderson,

Thank you so much for extremely helpful and detailed response to my questions!

I understand that randomise can select the most appropriate statistic methods (Simulation sｃenario 1 to 8) (Anderson et al, 2014) and below.

First, If I select only one continuous regressor (phyisiological data), the statistic method will be selected by randomise as the correlation with the permutation among the continuous regressor (N!) like bootstrap by central limit theorem, which show positive and negative relationship. 

Second, if I select some continuous regressors, one interest covariate (phyisiological data) and some nuisance covariates (age and education), the  statistic method will be selected by randomise as the association with permutation among one interest covariate and among each nuisance covariates (N!) like partial correlation with positive association, which do not detect negative association.

Third, if I divide two group (0 or 1 blocks) and select nuisance covariates, the statistic method will be selected by randomise as ANOVA and the association like ANCOVA and permutation among each continuous regressors in the blocks among nominal scales (N!+N!).

Shamefully enough, I tried to perform F-test for second case, but a error occured. 

That is why F-test is available for ANOVA and second case is not multiple regression but correlation.

Sorry to be peppering you with emails and my English is not good enough.

I would be most grateful if you could provide me with the information when you have a time.

Best wishes for the holiday season and a very Happy New Year.

S Fujii

ginal Message -----

From: Anderson M. Winkler <[log in to unmask]>
To: [log in to unmask]
Date: 2015/12/23, Wed 22:58
Subject: Re: [FSL] multiple regression and permutation

Hi,

Please see below:

On 22 December 2015 at 04:56, S. Fujii <[log in to unmask]> wrote:

Dear experts



Thank you so much for your all help during your FSL course.

I would like to ask you a question about Single-Group Average with Additional Covariate on FSLwiki, GLM.

On FSLwiki, I read that how to use one-sample T test is only for fMRI data, which was restricted.

The one-sample t-test tests whether the average across all images is different than zero. For most non FMRI images, this is always true, and we don't need to test. For instance: in VBM, everywhere in the cortex, there is some gray matter, i.e., a positive quantity, thus the average is always different than zero. Likewise for FA and most other measurements.

 

However, there is a few paper about the association when they use TBSS recently.

Also, when I had read this mailing list, someone might have asked a question about multiple regression for TBSS and written the script. And a user might upload the scripts as multiple regression for TBSS.

Multiple regression includes other variables that can be tested, not just the average, which doesn't need to be tested, as we know it's always positive and thus different than zero.

 

So, I have analyzed FA and physiological data in healthy participants using ANOVA for devided tertile of physiological data and onesample T test with physiological data as EV1 (contrast: 1, line break, -1) like mean activation on Single-Group Average with Additional Covariate, GLM, FSLwiki.

My results using these two methods overlapped partially.

It seems you split the physiological data into 3 groups and run an ANOVA (?). I'm not sure I follow, but it seems the most correct way is to use a one-sample t-test with additional covariate as described in the manual, but don't test the intercept, just the continuous regressor, i.e., the physiological data. The result in randomise is equivalent to having computed a correlation between the physiological data and FA, which is probably the result that matters in this case.

All the best,

Anderson

 

Is the latter analysis wrong? Or is the methods using Monte Carlo test MCMC-regression?

I can not fully understand the permutation. That is why I will select the former results using ANOVA.

Do you have a way to identify association or correlation when I use TBSS, FA and physiological data in healthy participants?



I would be grateful if you could help me.


S Fujii