Should raw response time data be transformed? I am a statistician and doing some data analysis in cognitive sciences. 
I noticed that the distribution of response time (RT) is chisq-squared-like, and I want to do Box-cox transformation to make it look normal distributed. Because before I did not think much for this transform, my question is:


Does a box-cox transformation  need to be applied to response times? 
If so, what do the results mean? 
For t-test, ANOVA and other tests, will the result be valid for the original response time data? 
If not, should we transform the data since analysis of these data is based on the normality hypothesis?
You can transform RT, i.e., by log(1/RT). This makes the distribution roughly normal.  The problem is that you don't usually run the ANOVA on the RT values collected at each trial, but on the average for each participant. So the distribution across participants need to be normal. A trick is to transform the single RT values, calculate the mean for each participant and condition, and then transform the value back with the inverse.

Alternatively, you can run ANOVAs without corrections if you use the appropriate one (i.e., normality not assumed... this will lead to oddly-looking DOF with decimal values).