Hi Mark,
You can transform a t-statistic to a correlation coefficient using the
expression:
r = t / sqrt(t^2+v)
where v are the (error) degrees of freedom of the t-statistic. I
haven't checked, but I guess that should correspond to something like
this
fslmaths t -sqr -add v -sqrt -recip -mul t r
where t is the input image, e.g. your_tstat.nii, and r would be the
output image, like your_rstat.nii, and v is replaced in the command
with the actual numerical value of your degrees of freedom.
I hope that helps,
Ged
P.S. If you (or anyone else reading) are interested in deriving the
above formula, it's easiest to derive the relationship between
R-squared and the F-statistic expressed in terms of sum squared errors
and then use the fact that a t-statistic is the square root of a
(single numerator degree of freedom) F-statistic.
On 13 May 2010 17:53, Mark Shen <[log in to unmask]> wrote:
> Thank you. Does anyone know how to obtain the actual r correlations
> (between FA and demeaned ages) from each voxel, since the resulting stat
> maps give only t-values and p-values?
> Thanks in advance!
>
> On May 13, 2010, at 1:25 AM, Stephen Smith wrote:
> Hi - this is a huge fractional age range - if you have checked your
> registrations are all ok then I would think probably that this result is
> valid.
> Cheers.
>
>
> On 13 May 2010, at 09:16, Mark Shen wrote:
>
> I do not think the correlation could possibly be so high that the
> correlation between Group1's FA and age survives at corrected 1-p=.995 for
> nearly every voxel (#46000) in the mean_FA_skeleton. Group2's correlation
> between FA and age is a little more reasonable but still very high
> (corrected 1-p=.96 for 4600 voxels).
> Perhaps I should elaborate that Group1 has a developmental disorder and
> Group2 is controls, both ranging in age from 2-5 years old. I include the
> .con and .mat files below for clarification. Thanks for all your assistance
> and patience!
> .con file
> /NumWaves 4
> /NumContrasts 2
> /PPheights 1 1
> /Matrix
> 0 0 1 0
> 0 0 0 1
> .mat file
> /NumWaves 4
> /NumPoints 76
> /PPheights 2.72 2.72
> /Matrix
> 1 0 0.49 0
> 1 0 1.24 0
> 1 0 0.01 0
> 1 0 -0.60 0
> 1 0 0.66 0
> 1 0 1.21 0
> 1 0 1.30 0
> 1 0 1.42 0
> 1 0 0.59 0
> 1 0 -0.06 0
> 1 0 0.44 0
> 1 0 0.68 0
> 1 0 0.18 0
> 1 0 0.33 0
> 1 0 0.19 0
> 1 0 0.46 0
> 1 0 -0.19 0
> 1 0 -0.47 0
> 1 0 0.27 0
> 1 0 -0.29 0
> 1 0 0.60 0
> 1 0 0.05 0
> 1 0 -0.34 0
> 1 0 -0.41 0
> 1 0 -0.43 0
> 1 0 -0.45 0
> 1 0 0.02 0
> 1 0 0.16 0
> 1 0 0.43 0
> 1 0 0.08 0
> 1 0 -0.18 0
> 1 0 -0.49 0
> 1 0 0.36 0
> 1 0 -0.34 0
> 1 0 0.35 0
> 1 0 1.16 0
> 1 0 -0.08 0
> 1 0 0.11 0
> 1 0 -0.87 0
> 1 0 -1.02 0
> 1 0 0.21 0
> 1 0 -0.62 0
> 1 0 0.37 0
> 1 0 -0.60 0
> 1 0 -0.22 0
> 1 0 -0.40 0
> 1 0 -0.90 0
> 1 0 -0.91 0
> 1 0 -0.70 0
> 1 0 -0.52 0
> 1 0 -0.73 0
> 1 0 -0.81 0
> 1 0 -0.50 0
> 0 1 0 -0.31
> 0 1 0 -0.22
> 0 1 0 1.70
> 0 1 0 1.29
> 0 1 0 0.93
> 0 1 0 0.16
> 0 1 0 -0.46
> 0 1 0 -0.32
> 0 1 0 -0.02
> 0 1 0 -0.54
> 0 1 0 0.14
> 0 1 0 -0.16
> 0 1 0 -0.98
> 0 1 0 -0.15
> 0 1 0 0.28
> 0 1 0 -0.61
> 0 1 0 -0.12
> 0 1 0 -0.26
> 0 1 0 0.24
> 0 1 0 -0.03
> 0 1 0 -0.67
> 0 1 0 0.07
> 0 1 0 -0.04
>
>
> On May 13, 2010, at 12:58 AM, Stephen Smith wrote:
> Hi
> On 13 May 2010, at 08:39, Mark Shen wrote:
>
> Thank you for your response. I confirmed that age is indeed demeaned (sum
> of each group's demeaned age equals 0, average equals 0). The age should be
> demeaned within each group and then padded with zeros, correct?
>
> Correct
>
> And the PPheights should be the difference between the max and min demeaned
> value of whichever group gives the highest difference?
>
> Sure - though this isn't used by randomise anyway.
> So - is it possible that you have a strong widespread age correlation then?
> Cheers.
>
>
>
>
> Thanks again for your expertise.
>
> On May 12, 2010, at 11:11 PM, Stephen Smith wrote:
> Getting weird distributions in t that don't look like they have a sensible
> amount of null values in them (i.e. roughly gaussian mean 0 std 1) can be
> caused by two things in general:
> - You don't have much null effect in the data - e.g. in VBM or TBSS when you
> have a global / widespread correlation against your model
> - There's a problem with the data not being demeaned but the model being
> zero mean, etc.
> Cheers.
>
>
>
> On 12 May 2010, at 16:16, Mark Shen wrote:
>
> Hi, I have a follow-up question to this post. Are the outputs from this
> correlational analysis (below) still interpreted as t-statistic for the
> correlation between each group and age, the corresponding incorrect 1-p
> value, and the corresponding corrected 1-p value? If so, I have some
> strange results I would like feedback on.
>
> contrasts:
>
> [0 0 1 0 0 0] -- patients
>
> [0 0 0 1 0 0] -- controls
>
>
> The resulting tstat map looks randomly distributed around .8 and has a range
> of -2.5-4. The p stat map ranges from 0-1 but has all frequency (#6000
> voxels) near 1. The corrp map ranges from 0-1 and has the highest frequency
> near 1 (#2000 voxels).
>
> Does this seem plausible? How could the 1-p value for the correlation
> between age and FA be so highly significant for almost every voxel?
>
> Thank you!
> Mark
>
> On May 6, 2010, at 4:51 AM, DRC SPM wrote:
>
> Hi Amelia,
>
> If your design is:
>
> EV1=Patients
>
> EV2=Controls
>
> EV3=Patients_age_demeaned (I subtracted the mean age of all patients from
>
> each patient’s age. I put 0s for all Controls in this EV.)
>
> EV4=Controls_age_demeaned ((I subtracted the mean age of all controls from
>
> each controls’s age. I put 0s for all Patients in this EV.)
>
> EV5=gender_demeaned (I subtracted the mean gender of all subjects - both
>
> patients and controls - from each subject's gender.)
>
> EV6=handedness_demeaned (I subtracted the mean handnessness of all subject -
>
> both patients and controls - from each subject's handedness.)
>
> Then you can test for relationships with age within each group with:
> [0 0 1 0 0 0] -- patients
> [0 0 0 1 0 0] -- controls
> and test for the slope with age being steeper in one group than the other
> with
> [0 0 1 -1 0 0] -- patients > controls
> [0 0 -1 1 0 0] -- controls > patients
> where an F-test over either of these will test for different age
> slopes between the groups.
>
> Note that these can't be interpreted as stronger or weaker
> age-correlations between the groups. In a simple or multiple
> regression model, a t-contrast with a single 1 over a variable is
> equivalent to testing the (partial) correlation with that variable,
> but in more complicated models, you can't assume intuitively similar
> equivalences. For example, you could have a steeper slope in patients,
> but a lower correlation, if the patients are more variable around the
> slope; the contrast above tests just for the steeper slope, not for
> the different correlation.
>
> I hope that helps,
> Ged
>
>
>
> ---------------------------------------------------------------------------
> Stephen M. Smith, Professor of Biomedical Engineering
> Associate Director, Oxford University FMRIB Centre
>
> FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
> +44 (0) 1865 222726 (fax 222717)
> [log in to unmask] http://www.fmrib.ox.ac.uk/~steve
> ---------------------------------------------------------------------------
>
>
>
>
>
>
> ---------------------------------------------------------------------------
> Stephen M. Smith, Professor of Biomedical Engineering
> Associate Director, Oxford University FMRIB Centre
>
> FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
> +44 (0) 1865 222726 (fax 222717)
> [log in to unmask] http://www.fmrib.ox.ac.uk/~steve
> ---------------------------------------------------------------------------
>
>
>
>
>
>
> ---------------------------------------------------------------------------
> Stephen M. Smith, Professor of Biomedical Engineering
> Associate Director, Oxford University FMRIB Centre
>
> FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
> +44 (0) 1865 222726 (fax 222717)
> [log in to unmask] http://www.fmrib.ox.ac.uk/~steve
> ---------------------------------------------------------------------------
>
>
>
>
>
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