Analyze data set with multiple trials

I have a data set of a reinforcement learning task. My goal is to analyze the difference between the reaction times of the two categories of a nominal variable. However, my data is currently coded with a lot of trials per participant, where every row corresponds to a trial.

How can I structure my data and which statistical test do need to use?

Even if I calculate the means per participant, I would still have two rows per participants - one for each category of the nominal variable. Or do I need to encode this into new variables?

If it's important: I will probably use SPSS for the analysis
I solved the structure part --> Aggregate and restructure in SPSS

Edit: Now I have a single line per subject with rows "RT_mean.0" and "RT_mean.1" with 0 and 1 coding the categories of the nominal variable. What test do I use for comparing them?
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