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GEOSTATS: independence vs correlation

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  • Donald Myers
    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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