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Financial Statistics: Statistical Significance
Statistical significance will tell you how to test if the result (here the coefficient of correlation) gives you a high degree of confidence that there is a relationship between X and Y.
In other words, we will show you in this section how to test that the correlation coefficient r is significantly different than 0.
Intuitively, we can say that it depends of the sample's size.
Without entering into details, we will test if r is significantly different than 0 by building an interval of confidence around r. If 0 is included in the interval, r will not be considered as significantly different than 0 and if 0 is not included in the interval, r will be considered as significantly different than 0.
To build that interval, we will use a Fisher's Z-transformation (1.96 in the above formula means that we work at the 95% confidence level).
The formula is:
n the sample size.
r the correlation coefficient.
the high end and low end case of the interval.
If 0 is not between the 2 , r is significantly different than 0.
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