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Thanks for all of these replies, this was all very helpful. The formulas
Tom suggested seem to have done the trick (effect sizes needed for simple
one-way and two-way t-tests only). Thanks again, very grateful for your
expertise.

On Thu, Feb 14, 2019 at 2:50 PM Glasser, Matthew <[log in to unmask]> wrote:

> Maybe you can use %BOLD instead as a measure of effect size.
>
> Matt.
>
> From: FSL - FMRIB's Software Library <[log in to unmask]> on behalf of
> Thomas Nichols <[log in to unmask]>
> Reply-To: FSL - FMRIB's Software Library <[log in to unmask]>
> Date: Thursday, February 14, 2019 at 5:04 AM
> To: "[log in to unmask]" <[log in to unmask]>
> Subject: Re: [FSL] Converting t-statistics to Cohen's d?
>
> Hi Nicole,
>
> Getting a Cohen's d for an arbitrary contrast out of a GLM is basically
> impossible.  That's because Cohen's d is only precisely defined for
> one-sample and two-sample comparisons.
>
> I can offer three options:
>
> 1. One-sample t-test.  If your design is nothing more than a one-sample
> t-test, then you can use this relationship to compute Cohen's d from the t
> statistic image *_tstat*
>
> d = t / sqrt(N)
>
>
> 2. Two-sample t-test.  If your design is just a two-sample t-test of
> groups of size N1 and N2, and your contrast tests for the difference, then
> you can use
>
> d = t * sqrt( 1/N1 + 1/N2 )
>
>
> 3. For any other contrast, you need to work with R^2 or Cohen's f^2.
> These relationships will get you there.  Make an F test if you don't
> already have it, as F = t^2, and then
>
> f2 = F * v1/v2
> R2 = f2 / ( f2 + 1 )
>
> where v1 is the numerator DF and v2 is the denominator DF of your F-test;
> for a squared t-test, this is v1=1, v2=N-p, where p is the total number of
> regressors in your model.
>
> f2 is the noncentrality parameter used for power analyses, while R2 has
> the more natural "variance explained" interpretation.
>
> -Tom
>
> On Thu, Feb 14, 2019 at 7:31 AM Steve Smith <[log in to unmask]> wrote:
>
>> Hi - Cohen's D is the effect divided by the standard deviation of the
>> errors, whereas varcope is similar but is the stddev is divided by the
>> degrees of freedom, so that it reflects the uncertainty of the cope. To get
>> back to D you would need to divide cope/varcope by the temporal degrees of
>> freedom.   The *exact* calculations here are slightly complicated by
>> adjustmet for temporal smoothness in the prewhitening step.
>>
>> Cheers.
>>
>>
>>
>>
>> On 13 Feb 2019, at 21:09, Nicole Petersen <[log in to unmask]> wrote:
>>
>> Hi Matthew (and others),
>>
>> Thanks for this recommendation. I have done this (finally) and then
>> divided the cope images by sqrt(varcope) to produce what I believe are
>> effect size maps in Cohen's D. However, some of the Cohen's D values seem
>> improbably high -- higher than 4. (These maps are being used to visualize
>> differences that were NOT statistically significant, so I was expecting
>> small Cohen's D values.) Questions:
>>
>> 1. Is my math wrong, and there is another way to get Cohen's D from these
>> images?
>> 2. If my math is right, does this also seem improbably high to you?
>>
>> Thanks in advance for any advice.
>>
>>
>> Best,
>> Nicole
>>
>>
>> On Tue, Nov 27, 2018 at 8:40 AM Matthew Webster <
>> [log in to unmask]> wrote:
>>
>>> Hello,
>>>           You can use the --glm_output option to output this glm info
>>> directly from randomise.
>>>
>>> Kind Regards
>>> Matthew
>>> --------------------------------
>>> Dr Matthew Webster
>>> FMRIB Centre
>>> John Radcliffe Hospital
>>> University of Oxford
>>>
>>> > On 26 Nov 2018, at 20:38, Nicole Petersen <[log in to unmask]> wrote:
>>> >
>>> > Hi FSL experts!
>>> >
>>> > I have been tasked with creating effect size maps in Cohen's d out of
>>> randomise outputs. I understand that this could be done by using film_gls
>>> --noest to produce PE and COPE images, which can then be converted to
>>> Cohen's d through fslmaths. I'd like to try converting the t-statistic
>>> images produced by randomise directly (since those are the analyses we're
>>> reporting on). Do you all have recommendations as to how to compute these
>>> maps?
>>> >
>>> >
>>> > Thanks for any help,
>>> > Nicole Petersen
>>> >
>>> >
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>>
>>
>> --
>> Nicole Petersen, Ph.D
>> Postdoctoral Fellow
>> London Lab
>> Semel Institute for Neuroscience and Human Behavior
>> Department of Psychiatry and Biobehavioral Sciences
>> University of California, Los Angeles
>>
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>>
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>> Head of Analysis,  WIN (FMRIB) Oxford
>>
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>> +44 (0) 1865 610470
>> [log in to unmask]    http://www.fmrib.ox.ac.uk/~steve
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>
>
> --
> __________________________________________________________
> Thomas Nichols, PhD
> Professor of Neuroimaging Statistics
> Nuffield Department of Population Health | University of Oxford
> Big Data Institute | Li Ka Shing Centre for Health Information and
> Discovery
> Old Road Campus | Headington | Oxford | OX3 7LF | United Kingdom
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-- 
Nicole Petersen, Ph.D
Postdoctoral Fellow
London Lab
Semel Institute for Neuroscience and Human Behavior
Department of Psychiatry and Biobehavioral Sciences
University of California, Los Angeles

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