Post merger profitability analysis of shareholders. Evidence from ...

changes in beta implies the coefficient b is zero. A significant
negative t-statistic indicates a decrease in beta and a significant
positive t-statistic an increase in beta after the offer.
The null hypothesis is rejected if the test statistic exceeds a
significant value, here in the 5% tail region. In order to avoid Type
1 (the null hypothesis is falsely rejected) and Type 2 errors (the null
hypothesis is falsely accepted), a test statistic must be correctly
specified. A correctly-specified test statistic yields a Type 1 error
probability equal to the assumed size of the test. The second
concern is power, i.e. a test’s ability to detect abnormal
performance when it is present. Power can be measured as one
minus the probability of a Type 2 error. The standard t-test of mean
abnormal performance assumes that the mean abnormal
performance for the cross-section of securities is normally
distributed. The t-test compares sample means by calculating
Student’s t and displays the two-tailed probability of the difference
between the means. The t-test for independent data is (Berenson et
al., 2004):
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