# CAAR t-test for event-study

I have a set of data that I have gathered for an event-study. I computed the CARs, CAARs (cumulated average abnormal returns) and now I have to do a t-test to test if CAARs are significantly different from zero. I work with excel and I am not sure how to do that.

You will need a One sample bilateral t-test.

Let say your cum abnormal returns are:

-0,15   -0,2    -0,02   -0,19   0,17    0,06    0,05    -0,1    0,03    0,12
-0,14    0,02   -0,2     0     -0,33   -0,1    -0,14    -0,28   -0,19   -0,29
0,09   -0,33   -0,03   -0,4    -0,24  -0,26    0,12    0,22    -0,33   -0,02
-0,15   -0,03   -0,06   -0,1    0,14    -0,14   -0,43   -0,18   0,09    0,08


Then you have:

Mean              -0,096
Standard error     0,02620139
Standard deviation 0,165712138
Sum               -3,84
Count              40


In your case the null hypothesis will be $\mu=0$.

The main statistic to be computed is the observed $t$:

$t_{obs}= \frac{\bar{x}-\mu}{s/\sqrt{n}}=\frac{-0,096-0}{0,02620139}=-3,6639278$.

In Excel you can compute the theoretical $t$ with $\alpha=5\%$. You can use the following function $t_{crit}=T.INV(0,025;40-1)=-2,02269092$. *1.

Or you can compute the p-value with the following function $pval=2*T.DIST(-3,6639278;40-1;1)=0,000737103$. *1.

In any case you reject the Null (H0)($|t_{obs}|>|t_{crit}|$, or $pval<\alpha$).

*1. It is considered the half of $\alpha$ in $T.INV$ or double the $T.DIST$ result because of the bilateral test.

• Hey thanks for your answer. The thing is I have cumulative average abnormal returns (CAARs) and not (CARs) so I don't know if what you wrote applies to my case. Anyway thanks a lot.
– alex
Jul 30 '16 at 17:08
• Ok I think I got it thanks to you. For the CAAR i will do tCAAR = (CAAR-0)/ (sCAAR*n^(1/2)). I have to do this for each day of the event window right ? So for exemple for day -1 I will have a certain t-value for day 0 another t-value ?Thanks again
– alex
Jul 30 '16 at 17:38