## GEOSTATS: independence vs correlation

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• In the sense that it is used in statistics, i.e., as an assumption in applying a statistical test, a random sample from a population means a set of random
Message 1 of 1 , Oct 30, 1998
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In the sense that it is used in statistics, i.e., as an assumption in
applying a statistical test, a random sample from a population means a set
of random variables X1,...., Xn that are identically distributed and and
mutually independent (mutually independent is stronger than pairwise
independence). The random variables are mutually independent if their
joint distribution is equal to the product of their marginal distributions.

In the case of joint normality, independence is equivalent to zero
correlation but not in general. Independence will imply zero correlation
(if the random variables have second moments) but not conversely. Not that
not all random variables have a first moment let alone a second moment and
hence there may not be a correlation coefficient.

However if the correlation coefficient of two random variables
(theoretical) is not zero then the random variables are not independent.
Zero correlation is sort of the next best thing to independence but it is
not equivalent to it.

For some purposes zero correlation is sufficient but not for most
statistical tests.

Donald E. Myers
Department of Mathematics
University of Arizona
Tucson, AZ 85721

myers@...

http://www.u.arizona.edu/~donaldm

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