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I have conducted 2 tests for my event study.

One is the parametric T test which rejected the null hypothesis, and my returns on event day is very significant.

However, I have conducts the non-parametric rank test. No matter using event window 1 day to 20 days, I couldn’t reject any null hypothesis. My return on the event day is way higher than the rest of the days, still it cannot reject the null hypothesis

Does anyone know what could affect on this? I have tested the normality, it is not normally distributed.

EDIT: @jbowman @EdM The event study deals with announcement returns of a large M&A transaction in the US. Data for the returns was obtained from Thomson Reuters. Assuming the data to be normally distributed I started using the market model and t-test. For the market returns I use the S&P 500 index. I use different event windows to see if for example, insider trading occurs before the event date. My estimation window is 220 days, event window in the largest specification 41 days.

The non-parametric rank test is the Corrado test, based on his paper from 1989 (see link below). I use this test since it is easily implemented in Excel, and it was recommended by my finance lecture as check for parametric tests. In the Corrado test abnormal returns obtained from the market model are ranked and compared to the average return.

On the announcement date I have large abnormal returns (31%) that are highly statistically significant at the 1% level (t-value 16.4). The abnormal return on the event date is ranked 1st, however for the announcement date I only obtain a p-value of 8%. Therefore, I wonder why a return ranked first, is not significant at conventional levels. I have checked my calculation multiple times, and do not think i have made an error. The file provided by my university shows similar results for announcement returns of another company, that has large abnormal returns on the announcement date. If I extend the event window, with multiple extreme returns occurring after another, the rank test becomes significant.

Corrado (1989):https://econpapers.repec.org/article/eeejfinec/v_3a23_3ay_3a1989_3ai_3a2_3ap_3a385-395.htm

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    $\begingroup$ I provided an answer. For future reference note that callouts like @Stephie_lin only work in comments on this site; if they are in the text of a question or answer the individual isn't notified. I luckily just happened to come by this question today. $\endgroup$
    – EdM
    Jan 1, 2020 at 18:47

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A couple of thoughts, although time-series analysis is outside my expertise.

First, a non-parametric test will often have lower power than a parametric test. If the assumptions regarding the parametric test are met, then you have a test based explicitly on the underlying probability distribution of the statistic of interest. Non-parametric tests are generally based on rank-orderings and associated uniform distributions. (The magnitude of the difference in power will depend on the specifics of the data and the test.) So it's not surprising to get lower apparent "significance" with a non-parametric test.

Second, it's possible for a parametric test to give a false-positive result if its assumptions aren't met. A footnote on page 386 of the paper that you linked notes this explicitly for your type of work:

Brown and Warner (1985, pp. 23-24 [J. Finan. Econ. 14:3-31]) show that doubling the day 0 return variance almost triples the probability of a Type I error [false positive] using the parametric t-test.

So it's possible that high variances on the announcement dates are making your t-tests apparently significant only because your data don't meet the assumptions needed for t-test validity with this type of data, leading to false-positive findings. That seems to be exactly the problem that the non-parametric method proposed in the paper that you linked attempts to solve.

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