My best guess here would be to look hard at non-parametric tests.  Kendall's coefficient makes sense for your question, but you have two nested layers here - within participant across trial and within trial across participants.  That could generate a number of possible tests.  Start with a good basic text on non-parametric statistics (I like Conover's Practical Nonparametric Statistics, but it is from 1999, so you might want something more recent).

Your use of the word correlation is confusing me.  What precisely do you want to know?  Is it: Do participants select the same color across 8 trial? or is it: Is there a relationship between the letter and color chosen over 8 trials? Or...?  If you wanted that last one in 1 trial, I would suggest Kendall's coefficient of concordance, and I think you could also estimate a 2nd layer Kendall's coefficient by trial, but I am not certain that kind of calculation would fit your data.

Thank you Dr.Smith.

I basically want an outcome of colors that are consistently selected for a letter by 30 participants. For example, {b-blue}, {g-green}, {t-black}.

I kept 8 trials in the experiment to get a concrete data set. The question is not about selecting the same color across 8 trials by a participant. I am expecting a significantly chosen color for each letter among 30 participants.

My best guess here would be to look hard at non-parametric tests.  Kendall's coefficient makes sense for your question, but you have two nested layers here - within participant across trial and within trial across participants.  That could generate a number of possible tests.  Start with a good basic text on non-parametric statistics (I like Conover's Practical Nonparametric Statistics, but it is from 1999, so you might want something more recent).

Thank you Dr. Smith. It was useful.