Deleting trials or the deleting participant which scattered is not clear

Thank you for your answer, but do you mean that there is not a clear principle in deleting trials or deleting participant? If not, is there any way to know which one (of the possible principles mentioned in my question) is beteer?

Deleting data is not a good idea. Try robust statistical methods. I've attached an old paper that might be helpful. Best wishes. P.S. You might also look at Maronna et al, Robust Statistics, Wiley. The idea is to calculate your estimates by  down-weighting the outliers. Identify the outliers and put them aside for further study. They often contain useful information.

Thank you, Pro David. The fact is in most papers of my area, the outliers would be removed before analysis based on some hypothesis, for instance, a very fast response (e.g., with reaction time less than 200ms) is thought to be the result of anticipation, rather than a normal response. However, I think the down-weighting method of outliers as you mentioned is probably a better method. Unfortunately, the paper you attached lost half of pages (the even pages). I wonder if a full version could be attached. Many many thanks.

Sorry, couldn't find another of that one. I attached some others instead that should be helpful. Please contact me if you have questions. I'd start with RobustR.pdf. Best wishes.

I will learn from that. Thank you again very much.

We usually do it, per subject but not per condition

Thanks for your reply, Ariel. I know that many people just do as you do, including me. But now I tend to think if we plan to delete the outliers, we have to take the difference between the conditions into consideration. Imagine that, if we define the three standard deviations based on all conditions, it is likely we would delete more trials >3SD from the slower response condition, and more trials