# Event study - varying sample size per event window allowed?

#### Eventstudy17

##### New Member
Hi all,

I am conducting an event study, analyzing how social media posts are affecting stock prices. Is it statistically allowed to have a different number of observations per event window?

E.g. to have in event window [0;1] 120 observations for which the abnormal returns are analyzed with the t-test; while having in event window [0;3] only 60 observations?

I controlled for confounding events - per respective event window. E.g. when earnings where released in t=2 I still used the observation in event window [0;1] but not in [0;3].

I wondering if its correct to then conclude e.g. that abnormal returns in [0;1] are significant, but not in [0;3].

Thank you so much!!!

PS: I followed McWilliams &Siegel (1997, S. 647) approach with the confounding events - but begin to think I did it wrong, because every other event study uses the same number of observations per event window...

#### staassis

##### Active Member
I did not understand your notation completely (e.g. what you mean by [0,1] and [0,3] windows). However, having event windows of random or varying size is fine as long as measurements in the windows are consistent with 1 unknown distribution. Example: by how many percent the stock drops from the time the CEO runs into a major scandal until the time he/she resigns.

#### Eventstudy17

##### New Member
Hi staassis,

With e.g. [0,1] I meant the time interval from day 0 (t=0, which is the day of the event, e.g. CEO scandal) to day 1 (t=1, which is the day after the event).

Let me explain it in a little more detail: I cumulate the abnormal returns in the event window [0,2] for one company (e.g. 1% in t=0, 2% in t=1 and 1% in t=3 lead to to cumulative abnormal return (CAR) of 4% in the [0,2] interval for company A). Secondly, I cumulate the (CAR) for company A, B, C etc. and then calculate the average of the cumulative abnormale returns (which is CAAR) over all companies. Finally, I test CAAR for its significance with the t-test.

Due to controlling for confounding events, I have to eliminate certain events/companies, e.g. when company B would have announced its earnings on day 2 (t=2), I would not consider its event (CEO scandal) for the [0,2] interval. However, I would still include it in my significance calculations in the time window [0,1]. This is why the sample size is varying and I am not sure if I am allowed to compare the overall significance of the CAAR during the different time intervals, because the sample (size) is different.

Your comment sounds promising though! What do you mean with:
measurements in the windows are consistent with 1 unknown distribution
- the calculation I mentioned above are exactly the same for each event window - always the average is tested.

Thanks again!!