For Multiple Sample 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 r-to-z 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. 70-76.
and then translating this weighted average back into the recognizable terms of the Pearson product-moment 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 chi-square test for the heterogeneity of the k values of r, with df=k-1. A significant value of chi-square 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.

Data Entry

 Chi-Square  df P

Confidence Intervals

.95 CI   
.99 CI   

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