By Ruben Geert van den Berg on March 28, 2016 under SPSS Correlation Tools.

SPSS Confidence Intervals for Correlations Tool

SPSS - Confidence Intervals for Correlations Tool - Dialog

Summary

What's the easiest way to obtain confidence intervals for Pearson correlations? Sadly, we couldn't find these often requested statistics anywhere in SPSS. The best we encountered on the web were some ancient macros that, well... how to say this delicately... didn't excel in user friendliness.
This tutorial therefore proposes a freely downloadable, menu based tool for computing one or many confidence intervals for Pearson correlations.

How to Use the Tool?

Output

Running the tool results in SPSS creating a new dataset as shown below.

SPSS - Confidence Intervals for Correlations Tool - Result

If you're unsure which confidence level you requested, switch from data view to variable view. The confidence level is added to the variable labels of the lower and upper bounds as shown below.

SPSS - Confidence Intervals for Correlations Tool - Variable Label

Theory

The sampling distribution for a correlation approaches a normal distribution only as the sample size becomes very large. However, the result of the following non linear transformation reasonably approximates a normal distribution when n > 10:
$$E(Z_F) \approx \frac{1}{2} \ln \frac{1 + \rho}{1 - \rho} + \frac{\rho}{2(n - 1)}$$
This formula is known as Fisher’s z-transformation. After applying it, the standard normal distribution is used for computing confidence intervals for the transformed correlations.
Finally, the upper and lower bounds for the transformed correlations are converted back to “normal correlations” by reversing the aforementioned formula by means of a Newton-Raphson approximation.
We'd like to thank our colleague Reinoud Hamming from TNS NIPO for his kind assistance with the formulas.

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