Did you look at the variance in your behavioural data? As Stephen said, behavioural and EEG measures may not be measuring the same thing. 

Thanks a lot for both of your answers. I checked SDs of behavioral and ERPs data. Behavioral's SDs seem fine, but ERPs' SDs are big, M=10.2, SD=7.7, for example. What would these suggest?  Plus, I'm not sure what does the "noisy" raised by Stephen mean? You mean some  extra variables might be involved? Or?...

Thanks a lot! It makes much sense. I have some extra questions about my results.

I focused on two components: ERN (error-related negativity) and Pe (error positivity. ERN is a sharp negative deflection that typically peaks within 100 ms after the commission of an error. Pe  is a slow positive deflection typically peaking between 200-250 ms following the peak of ERN. Both of them are source localized in the ACC. In general, Pe reflects the conscious awareness of errors, whereas ERN reflects error monitoring following both consciously and unconsciously recognized errors.

I found the experimental manipulation (X) significantly increased Pe (but not ERN) after error commission.

1) How to explain? Does it suggest X only had an effect on (or is more sensitive in) consciously (but not unconsciously) error responses? Or some other possibilities?

2) Previous research usually found Pe showed a frontoparietal distribution (e.g., Cz, CPz, Pz), but my  topographical map of grand-averaged  Pe ( of all participants’ data) showed a frontocentral distribution, and it was most salient at FCz. So I chose FCz as the target site to calculate Pe. Does it make sense to justify my choice? (I tried Cz site or other sites, but seemed only a marginally significant effect).

You can try to standardize (Z-score) your behavioral and ERP data to get rid of the scale difference issue, but yes this is not surprising to not have any correlation between your ERP and behavioral data.

You could also try to add behavioral performance as a covariate in your ERP analyses, as this will provide you information on how the two measures are related.

Thanks for your suggestions. But if I get something after putting the behavioral performance as the covariate, what can this tell? How to understand this?

I will bring you information on how behavioral performance account for the observed ERP effects. It can also clarify the inter-individual variance in this effect.

Hope this helps !

Thomas

Additionally to the comments of Stephen, to be fair in your comparisons, you could normalize each recording to achieve zero mean and unitary variance, this is similar to Thomas' proposition. This procedure must be done per channel and recording. The intention of this is to reduce the effect caused by the recording conditions. But now, your unit are arb. units, and no uV as initially it was. But now you are able to compare different subjects and different recordings of the same subject. The procedure is a piece of cake, you have to remove mean value and scale data to keep variance=1.

regards.

Two further, related, thoughts on this:

In relation to noise, is your study adequately powered to detect individual differences? You could do a sensitivity analysis to find out what kind of effect size you had a good chance of detecting, even though post-hoc power analysis isn't informative.

Sometimes a null finding, if the study was well powered, might be telling you that the behavioural measure and the ERP effect aren't related as you thought. You might find this paper (out shortly from David Donaldson's lab) interesting, soon out in Frontiers, although the authors don't yet know why an expected effect wasn't found, this was informative:

https://www.frontiersin.org/articles/10.3389/fnhum.2017.00580/abstract

cheers

Alexa