Q:

Aggregating and comparing data across days using paired t-test

I have two groups of data (with and without stimulus) from the same subject.  For each experimental session, I measure a score (let say reaction times, n_with_stim=50, n_without_stim=50).  For each day, the subject participates in four sessions (hence, n_with_stim_total=200, n_without_stim_total=200).  My ultimate goal is to test whether the stimulus has any effect.  The problems are (i) his baseline score changes across session; The later in the day, the slower his reaction time, and (ii) his baseline score may change across day.  
How can I aggregate and compare the results across sessions?  Can I just combine all the data across sessions within the day to see whether there is an effect on that particular day?  
Is it ok to combine data across sessions and days to compare?  
Is paired t-test an appropriate test for me to use?  
Thank you in advance.  

A:

To me it sounds like a case for simple 2-way repeated-measures ANOVA. 
The results of the ANOVA will tell you how much variance is accounted for by (1)Stim condition (2) Trail number, and (3) 1x2 interaction (does stim affect the change across trials)
Tutorials for running repeated-measures ANOVA in your favorite software are pretty googlable; and/or I bet you could get software-specific advice here. 
This is probably more of a 'comment' than an 'answer' but I haven't got quite enough reputation points to comment yet. :)