[VoxBo] Orthogonal contrasts including conditions labeled as zero

[Charan Ranganath]

Hi Ranjani, this makes perfect sense. Let's make the example concrete.

Say your betas are A=.1, B=.2, C=.3, and call your baseline condition "X".

As I said before, when you do a t-test, your output will be the t-value 
for the test of a linear combination of betas. If you weight each beta 
in the t-test at .33, then you are testing the following null hypothesis:
.33(A-X)+.33(B-X)+.33(C-X)=0, which is  mathematically equivalent to 
testing .33A+.33B+.33C-x=0. That is also mathematically equivalent to
testing the hypothesis (A+B+C)-3X=0, which is what you are doing when 
you weight each at +1.

However, when you set the scale for raw betas, you are instead just 
asking voxbo to give you a weighted sum. So, in our example, when you 
set the wights to .33, you get .198, whereas when you set the weights to 
+1, you get .6 as the weighted sum.

So the discrepancy is because asking for the raw betas gives you a 
weighted sum, whereas the t-test option gives you the result of a 
statistical test that is computed on the weighted sum.

I hope this helps. CR

Ranjani Prabhakaran wrote:
> Hi,
> 
> If I'm trying to do a region of interest analysis and want to compare 
> all conditions (A,B, and C) versus baseline within a masked region, I 
> found that if I set my weights for conditions A, B, C as +1, +1, +1 OR 
> as +.33, +.33, +.33: I get the same t value from vbdumpstats.
> But, if I want to get a beta value rather than a t-value, I found that I 
> get different beta values depending on whether I set the weights as 
> +1,+1,+1 or +.33,+.33,+.33.
> 
> What would be the appropriate weights for this contrast if I want to get 
> a beta value?
> 
> Thanks!
> 
> Ranjani
> On Jan 24, 2008, at 5:16 PM, Charan Ranganath wrote:
> 
>> Lila, I think this is the answer to your question. When you do a 
>> t-test in voxbo (or spm, etc.) you are testing whether the value of a 
>> linear combination of beta values is significantly different from 
>> zero. So, if you weight A, B, and C as +1, +1, +1, you are testing the 
>> null hypothesis that (A+B+C)=0. Now, because "0" is your baseline 
>> condition, the beta values (parameter estimates) can be be interpreted 
>> as a measure of a change from this baseline. For convenience, let's 
>> call the baseline as "X". Therefore in this example, you are really 
>> testing (A-X+B-X+C-X)=0 or (A+B+C)-3X=0. If you multiply all of the 
>> parameters by some constant (say .33), then mathematically, it makes 
>> no difference. e.g., if (A+B+C)-3X=0, then .33A+.33B+.33C=0.
>>
>> I hope this helps. CR
>>
>> Lila Chrysikou wrote:
>>> Hello,
>>> I was wondering how VoxBo treats any condition coded as zero (0) in 
>>> one's condition function if that condition is entered in a contrast.
>>> For example, if I have three conditions A, B, and C and the null 
>>> coded as 0 in the condition function and I want to compare (A+B+C) 
>>> with the null, should I enter in my contrast.txt file the contrast 
>>> coefficients as 1 1 1 and assume that VoxBo will code the null as -3 
>>> to set up an orthogonal contrast?
>>> Or does VoxBo code the null as -1, hence I should enter my contrast 
>>> as .33 .33 .33 ?
>>> Many thanks in advance for your help-
>>> ~Lila
>>> -- 
>>> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>>> Evangelia G. Chrysikou, Ph.D.
>>> Post Doctoral Research Fellow
>>> Thompson-Schill Lab
>>> Office address: 3810 Walnut St.,Room 307, Philadelphia, PA 19104
>>> 215. 573.6726  (phone)
>>> 215. 898.1982  (fax)
>>> E-mail: evangelg at psych.upenn.edu <mailto:evangelg at psych.upenn.edu>
>>
>> -- 
>> Charan Ranganath, Ph.D.
>> Associate Professor
>> Center for Neuroscience and Dept. of Psychology
>> University of California at Davis
>> 1544 Newton Ct.
>> Davis, CA 95616
>>
>> phone: 530-757-8750
>> fax: 530-757-8640
>>
>> http://DynamicMemoryLab.org
> 
> 

-- 
Charan Ranganath, Ph.D.
Associate Professor
Center for Neuroscience and Dept. of Psychology
University of California at Davis
1544 Newton Ct.
Davis, CA 95616

phone: 530-757-8750
fax: 530-757-8640

http://DynamicMemoryLab.org