I am performing an event study using the e-study function on Stata. I have the CAR calculated for multiple events including their SD and T-statistic. All my variables have the same number of observations, so I can simply take the average CAR of the three events to find the combined CAR. However, I want to test how significant this combined effect is.

Example: Event 1, CAR day 0 = 2%, T-stat = 1.89

Event 2, CAR day 0 = 3% T-stat = 2.2

Event 3, CAR day 0 = 7% T-stat = 1.0

AVG Event CAR = 4%. T-stat ?

Any help would be much appreciated