Analysis of Asset Allocation

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Financial Statistics: Statistical Significance

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:

with

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.

Do you want to know more on the subject? Visit our selection of books

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