## Obtaining an averaged correlation

This spreadsheet evaluates the average correlation for a set of upto 100 inputted correlations.

The program Fisher z-transforms the raw correlations, works out the average of the transformed correlation and then backtransforms it. Fisher z transformed correlations are used in areas such as meta-analysis for computing overall estimates of correlations such as those obtained by pooling over studies (Field AP and Gillett R, 2010). Fisher z-transformed correlations are also usually used when comparing average correlations between groups.

Bonett DG (2008) further recommends and illustrates a simple way of computing a variance for the average of correlations obtained from different studies which he then uses to obtain a 95% confidence interval for the average correlation. This method uses the mean of the raw correlations as a point estimate. Bonett performs a series of simulation studies which show his derived 95% confidence intervals have better coverage than the more traditional approaches such as Hedges-Olkin (1985). In one example (which is the one in the spreadsheet mentioned below), he finds the supposed 95% confidence interval using Hedges-Olkin is only a 57% one!

This spreadsheet evaluates Bonett's (2008) recommended confidence interval for the average correlation and one of the older methods which uses the mean of the Fisher z-transformed correlations, the Hedges-Olkin (1985).

If one is using time series data it may be worth considering removing autocorrelations by differencing successive observations prior to computing a correlation in order to remove this.

Reference

Bonett, DG (2008) Meta-analytic interval estimation for bivariate correlations. *Psychological Methods* **13(3)** 173-181. (This paper is downloadable by CBSU users for free using ScienceDirect).

Field, AP and Gillett, R (2010) How to do a meta-analysis. *British Journal of Mathematical and Statistical Psychology* **63** 665-694.

Hedges, LV, & Olkin, I (1985) Statistical methods in metaanalysis. Orlando, FL: Academic Press.