# ERP and impact of a signal trial

Dear Prof Cohen and EEG experts

What is the best way to evaluate the contribution of each epoch to the final ERP waveform?

General speaking (after cleaning data, of course) ERP waveform is equal to the sum_of_all_epochs

However, I like to find a way to estimate or assign a value to each epoch to determine its contribution to the final ERP. In my simple mind, I was thinking of ‘dot product’ (ERP_waveform*.signle_epoch)

I would love to hear your thoughts,

Karlo

Interesting question, Karlo. I suppose the real question is what a single-trial ERP looks like (if it exists).

If you assume that the ERP has the same shape on each trial but different amplitude, then you can regress the ERP on each single trial EEG (which is basically the dot product with some extra steps).

It would also be possible to fit the shape of the single trial waveform to the ERP, but I think that really increases the risk of overfitting. So I’d stick with the single trial regression approach.

Dear Mike,

Thanks for your response.

Although i am not familiar with how to regress out ERPwaveform from the signal trial; “dot product with some extra steps.” I would appreciate if you could elucidate it (maybe a reference)

And, my apologies if the question was not clear:
Suppose, the response to the event is not similar, even not in the waveform. Thus, i like to find the contribution of each trail (epoch) in shaping the final ERP waveform.

let say : ERP= sum (Epoch_i, i=1:100)
can we assign a contribution (or similarity) rate such as

Epoch_1 → 5%
Epoch_2 → 85%
Epoch_3–> 10%
Epoch_4 → 70%

Epoch_m → 45%
Epoch_n → 75%
Epoch_o–> 10%
Epoch_q → 90%

OK, I understand. My previous suggestion would have given you a number (beta coefficient) for each trial that encodes how much that single trial looks like the ERP. (You can google “regression” to learn more about how it works.)

But you want to know how much each trial contributes to the ERP. If you take the ERP as the trial average, then the “boring hypothesis” is that each trial contributes equally, i.e., (100/N)% for N trials. I think a way to quantify this is to remove each trial, re-compute the ERP, and then compute the root-mean-square error between the full ERP and the N-1 ERP. The larger the RMS, the more the contribution to the ERP.

On the other hand, I’ve never really thought about this issue. It’s possible there are existing solutions that I’m unaware of, because I don’t keep track of ERP methods. I recommend posting your question to the ERPlab or eeglab email list to see if there is a known solution.