Having established that there certainly is a correlation in the wider population, we might want to quantify the range of values we expect to lie within by calculating a confidence interval. As in the previous chapter with the mean, the confidence interval of r expresses the probability (expressed as a percentage) that the population parameter lies between two specific values.

However, a complication arises when trying to calculate the standard error of the correlation coefficient that didn't exist for the mean. Because the absolute value of r cannot exceed 1, the distribution of possible samples of r is skewed as r approaches the limit of its range.

The previous graph shows the negatively skewed distribution of r samples for a of 0.6.

Fortunately, a transformation called the Fisher z-transformation will stabilize the variance of r throughout its range. This is analogous to how our weight data became normally distributed when we took the logarithm.

The equation for the...