Thank you very much for the reply. I am uncertain whether I understand correctly.

"No. The positive and negative slopes have a perfect correlation. Just use the ones with a positive slope. To test negative slopes invert the contrast."
 At the first level, I specified four conditions, with one parametric modulator for each. Then in the contrast manager, I defined (apart from the contrasts between conditions) two contrasts for each parameter, a negative and a postive one (e.g., [0 1 0 0 0 0 0 0] and [0 -1 0 0 0 0 0 0], as suggested in this list. Therefore, I have 4 con images for the condition contrasts and in total 8 for the parametric modulators. 
> I assume that I have to use both the resulting positive and negative parametric modulation con image in the second level analysis? 
> If the two are perfectly correlated, why is it necessary to make both contrasts at the first level?  

"But you only need one factor as described above."
> In the design I used now, there was only one difficulty factor (with two levels, refering to the two con images for each parametric modulator). However, the condition itself was another factor. If I use only one factor, how can I ever define the 8 con images from the first level? 
> Should I use a flexible factorial design at this point at all? 

 "'Is it correct to interpret the results as representing regions in which there was a significant interaction between a given condition and difficulty?
In the new model yes. Make sure you have columns for each subject as well."
> Do you mean by including a subject factor?  

Many thanks for your expertise and time once again,
Regards,
Kris



On Wed, Jan 18, 2012 at 9:51 AM, Kris Baetens <[log in to unmask]> wrote:

    Dear SPM’ers,

    I'm sorry for the somewhat basic questions, but I'm very confused by the second-level analysis of some parametric modulations, and haven't found another post that was completely comparable.

    Participants conducted four different tasks during an experiment. After each trial they rated how difficult they had experienced this trial to be.

    On the first level I defined four conditions with a parametric modulator each (the difficulty rating). As helpfully suggested earlier on this list, I have asked a contrast for each condition and two contrasts for each parametric modulator (positive - negative regression slope).
    1.      How are the resulting images of the condition contrasts – if at all – influenced by including the parametric modulators in the first level? Is it useful to compare these images to those that result from a first-level analysis without modulators?


In theory, these should be the same since one is orthogonal to the other; however, in practice they will be slighltly different because of multiple tasks. I would stick with one model.

 

    On the second level, I conducted a within-subjects one-way ANOVA (with equal variance, no independence) to investigate the effect of the conditions themselves.
    To investigate the effect of difficulty on a group level, I made use of a flexible factorial design. I am absolutely uncertain whether what I did here makes sense. I specified two factors (condition and positive/negative difficulty regressor slope). I specified conditions/subject in an 8x2 double (1 1 , 2 1, 3 1, 4 1, 1 2, 2 2, 3 2, 4 2), meaning that I only input the 8 con images of the first level representing the parametric modulators. Then in the contrast manager, I specified a t-contrast for each of the 8 parametric modulations (4 conditions x 2). For example, for increasing difficulty ratings in the first condition, I entered the vector 1 0 0 0 1 0 0 0 0 0 0 0.
    2.      Is this approach correct?


No. The positive and negative slopes have a perfect correlation. Just use the ones with a positive slope. To test negative slopes invert the contrast.
 

    3.      Is it correct to interpret the results as representing regions in which there was a significant interaction between a given condition and difficulty?


In the new model yes. Make sure you have columns for each subject as well.
 

    4.      Is it normal that the condition contrast images are not required in this step of the analysis?


For the question you are asking, yes.
 

    5.      Is it correct to input “No independence” and “Equal variance” here for both factors?


Yes. But you only need one factor as described above.
 

    6.      Is it customary to investigate the impact of the conditions themselves and the parametric modulators in two different analyses? Can they be combined?


You will want one first level analysis and two second level analyses.

 


    Thanks in advance for any help,
    Kris