In article <[EMAIL PROTECTED]>,
Bruno Facon <[EMAIL PROTECTED]> wrote:
>Dear Sir,
>I work in the area of intelligence differentiation. I would like to know
>how to use the khi2 statistic to determine whether the number of
>statistically different correlations between two groups is due or not to
>random variations. In particular I would like to know how to determine
>the expected numbers of statistically different correlations due to
>chance.
>Let me take an example. Suppose I compare two correlations matrices of
>45 coefficients obtained from two independent groups (A and B). If there
>is no true difference between the two matrices, the number of
>statistically different correlations should be equal to 1.25 in favor of
1.125
>group A and equal to 1.25 in favor of group B (in case of alpha = .05).
1.125
>Consequently, the expected number of nonsignificant differences should
>be 42.75. Is my reasoning correct?
This is correct IF you have the correct distribution of
the correlation coefficient; this is NOT easy, and is
very highly dependent on normality.
Also, and you did not ask this question, but indicated
it, the closeness of the various sample correlation
coefficients are highly dependent, so one could not
use the chi-squared test on the set of numbers.
One would be much safer to use covariances, rather
than correlations. They are still quite dependent,
but not as much, but their distributions are still
dependent on normality. If one wants to test the
equality of covariance matrices under normality,
the Wilks-Lawley test properly takes into account
the dependence. This should be found in multivariate
texts.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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