<p>You will need a One sample bilateral t-test.</p>

<p>Let say your cum abnormal returns are:</p>

<pre><code>-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
</code></pre>

<p>Then you have:</p>

<pre><code>Mean              -0,096
Standard error     0,02620139
Standard deviation 0,165712138
Sum               -3,84
Count              40
</code></pre>

<p>In your case the null hypothesis will be $\mu=0$.</p>

<p>The main statistic to be computed is the observed $t$:</p>

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

<p>In <em>Excel</em> 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.</p>

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

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

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

CC BY-SA 3.0
2016-07-30T17:08:06.667Z
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
CC BY-SA 3.0
2016-07-30T17:38:48.983Z
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
CC BY-SA 3.0
2016-07-29T17:59:49.343Z
2016-07-29T18:07:17.500Z
2016-07-29T18:07:17.500Z
Robert
<p>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.</p>

<econometrics><mathematical-economics>
CAAR t-test for event-study
alex
# CAAR t-test for event-study

(Asked by: username_0 on 2016-07-28)

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.

**Tags:** econometrics, mathematical-economics

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## 1 answers

### Answer by username_1 on 2016-07-29. Score: 1

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.

> **Comments:**
> **username_0**: 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.  
> **username_0**: 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  

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