 Estimating the Population Value of rho on the Basis of Several Observed Sample Values of r
 Test for the Heterogeneity of several Values of r
The measures of linear correlation observed within several samples can be aggregated to provide an estimate of rho, the correlation that exists within the general population of bivariate XY values from which the samples have been randomly and independently drawn. The method of aggregation involves taking the weighted average of the Fisher
rtoz transformations of the several sample values of r, as described in
 Edwards, Allen L., An Introduction to Linear Regression and Correlation
(2nd ed.), New York: W.H. Freeman, 1984, pp. 7076.

and then translating this weighted average back into the recognizable terms of the Pearson productmoment correlation coefficient.
This page will perform the procedure for up to
k=12 sample values of r, with a minimum
of k=2. It will also perform a chisquare test for the heterogeneity of the k values of r, with
df=k1. A significant value of chisquare can be taken to suggest that the several values
of r are heterogeneous.
To perform the estimate, enter the sample values of r and n into the designated cells, then click the «Calculate» button. For purposes of this calculation, the value of n for each sample must be equal to or greater than 4.
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©Richard Lowry 2001
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