Dear Mayank,



Incomplete answer now but we can follow up next week. Have a look at the

examples described here:

  https://en.wikibooks.org/wiki/SPM/Group_Analysis

and the articles linked at the end of the page, in particular about the

difference between pooled and partitioned error variances. This would

explain, in part, the difference in results between your two models.



If you had only one single within-subject factor with two levels, you

would get identical results whether you use a paired t-test with a [1

-1] contrast vs using a one-sample t-test of the difference between the

two levels.



For a short explanation of whitening, have a look at slide 15 here:

  https://www.fil.ion.ucl.ac.uk/spm/course/slides19-oct/02_GLM.pptx

Importantly you need to whiten both design and data - could it be that

you didn't whiten the data when you did your own computations?



In the simple case of a two-sample t-test, the effect of whitening when

assuming unequal variance (as a violation of non-sphericity) will be

equivalent to the difference between using this equation:



https://en.wikipedia.org/wiki/Student%27s_t-test#Equal_or_unequal_sample_sizes,_equal_variance

vs using this one:



https://en.wikipedia.org/wiki/Student%27s_t-test#Equal_or_unequal_sample_sizes,_unequal_variances



As for how these things are computed in SPM, have a look here to see how

beta are ResMS are computed:

  https://github.com/spm/spm12/blob/r7487/spm_spm.m#L582-L633

and here for how they are used to form a t-statistic:

  https://github.com/spm/spm12/blob/r7487/spm_contrasts.m#L215-L219



Best regards,

Guillaume.





On 08/11/2019 15:12, Mayank Jog wrote:

> Dear Experts,

> I had a conceptual question that came up during the course of analyzing

> data. The question takes a little bit to set up : 

> 

> I'm looking to analyze ASL data, collected pre-post for subjects

> enrolled in our study with two treatments (type1, type2) , both of which

> have their individual placebos

> 

> My design matrix looks like : 

> Screen Shot 2019-11-08 at 7.01.31 AM.png

> 

> with columns 1-8 as follows:

> 1 = pre,'placebo','treatment#1'

> 2 = post,'placebo', 'treatment#1'

> 3 = pre,'placebo','treatment#2'

> 4 = post,'placebo', 'treatment#2'

> 5 = pre,'Active','treatment#1'

> 6 = post,'Active', 'treatment#1'

> 7 = pre,'Active','treatment#2'

> 8 = post,'Active', 'treatment#2' 

> *I specified unequal variances for all factors, and independence for all

> except "pre/post' factor

> (I can provide more details on the study if needed, let me know!)

> 

> The final filtered/prewhitened design matrix looks like :

> Screen Shot 2019-11-08 at 7.01.49 AM.png

> 

> 

> 

> One of the contrasts I was interested in was : 

> [0 0 0 0 -1 1 -1 1]

> (basically, looking at the pre-post differences between the two treatments)

> When I looked at the t-contrast set up; and compared it to a 2-sample

> t-test run separately (with input = pre-post differences for one

> treatment vs the other), the results were different. 

> 

> Why should this be so? 

> 

> First, I dug around a bit within spm.mat, trying to figure out how

> t-values in the spmT map are derived: 

> 

> Question 1. 

> I noticed in the spm structure that pre-whitening was being performed. (

> SPM.xX.xKXs is different from SPM.xX.X)

> 

> What does pre-whitening mean for a 2nd level analysis ? I mean, there

> doesn't seem to be an analogue of it in the steps one takes to do a

> 2-sample t-test .... Is there something fundamentally different between

> the t-contrast as set up here, and doing a 2 sample t-test 

> (with input = pre-post differences for one treatment vs the other). 

> 

> Question 2. 

> Next I tried to understand the outputs of an analysis, the spmT images,

> and the ResMS image in particular. The ResMS image seems to store 

> 

> ResMS = Var(e)* (c' * (X'X)^-1 * c)

> 

> where c = [1 1 1 1 1 1 1 1]', and X is the filtered and whitened design

> matrix "SPM.xX.xKXs". The way I tried to verify this was : I used

> different c's (corresponding to different contrasts), con-images and

> ResMs to calculate t-values, and compared them to the t-values in the

> spmT maps. They seem to be slightly off for all contrasts by the same

> number ... by a factor 1.02 or 2% ... I was curious where this factor

> came from. More concisely, given a con-image, ResMS, and a contrast

> vector "c", what is the formula to generate the exact T-value that spm

> stores in the spmT maps?

> 

> Apologies if the questions are really simple!

> Thank you,

> Mayank



-- 

Guillaume Flandin, PhD

Wellcome Centre for Human Neuroimaging

UCL Queen Square Institute of Neurology

London WC1N 3BG