To check the abnormality of return due to event, t-test is applied. One of the assumption of t-test is normality. Now, in my 5 days of event window, is it required to test normality?
There are 300 news/events in 5 years for a single company, in that case degree of freedom cross 200. Is it required to test normality?
If non-parametric test is applied then there is no significant difference in final result. So, is it required to test normality?
I agree with jochen , a t test having degree of freedom 200+ does not make any sense.
First thing there is no such maximum sample size limit for applying t test. If you are manually applying the test (you are going to compare computed t value with the tabulated t value), the standard t distribution table has degrees-of-freedom values of more than 30. If you use SPSS, it accepts (and does not warn you) if you have more than 30 sample size per group.
Note that the t-distribution becomes closer to the normal distribution as degree of freedom increases. When df approaches 30, it will be practically the same as normal distribution.
So basically "t-test is used when the samples are less than 30", just because there is no need to use is anymore with a higher number. Of course you can still use t-test with more samples.
I didn't mean to point out that a t-test on many d.f. is not different to a z-test. I really meant if a test (any test!) done on that many d.f. might not make much sense.
When the daily stock prices are used to checked the event impact, the daily stock prices are not normal. But research paper viewed that it is not required to apply normality. (Brown and Warner 1985) had explained in their research paper that "The Central Limit Theorem [see Billingsley (1979, pp. 308-319)] guarantees that if the excess returns in the cross-section of securities are independent and identically distributed drawings from finite variance distributions, the distribution of the sample mean excess return converges to normality as the number of securities increases."
Is it required to test normality?
Thanks for reply Mr. Jochen
I have used Gretl software to check the normality of abnormal return and output is as below
Doornik-Hansen test = 34.8962, with p-value 2.6447e-008
Shapiro-Wilk W = 0.960947, with p-value 0.000700518
Lilliefors test = 0.0619472, with p-value ~= 0.23
Jarque-Bera test = 47.2043, with p-value 5.61987e-011
Remember too that a t-test is a lot more robust than some of the tests you're referring to. Theoretically the population should be normal, but diversions from normality don't seem to affect it unless they are large. Dr. Wilhelm is correct in suggesting that a t-test is generally a small sample test statistic.
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