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.
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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.
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$\begingroup$ 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. $\endgroup$– alexJul 30, 2016 at 17:08
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$\begingroup$ 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 $\endgroup$– alexJul 30, 2016 at 17:38