of the Pearson Correlation, Sampling
Distribution of Pearson's r, Confidence
- State the standard error of z'
- Compute a confidence interval on ρ
The computation of a confidence interval on the
population value of Pearson's correlation (ρ) is complicated
by the fact that the sampling distribution of r is not normally
distributed. The solution lies with Fisher's z' transformation
described in the section on the sampling
distribution of Pearson's r. The steps in computing a confidence
interval for ρ are:
- Convert r to z'
- Compute a confidence interval in terms of z'
- Convert the confidence interval back to r.
The conversion of r to z' can be done using a table
The table contains only positive value of r, but that is not a
problem. The value of z' associated with an r of 0.654 is 0.78.
Therefore, the z' associated with an r of -0.654 is -0.78.
The sampling distribution of z' is approximately
normally distributed and has a standard error of
The final step is to convert the endpoints of
the interval back to r using a table
To calculate the 99% confidence interval, you use the Z for a
99% confidence interval of 2.58. Naturally, the 99% confidence
interval is wider than the 95% confidence interval.