Next section: Difference between correlations

The number of standard deviations from the mean can be calculated with the formula:

where: z is the number of standard deviations above the z' associated with the population correlation, z' is the value of Fisher's z' for the sample correlation (z' =.97 in this case), μ is the value of z' for the population correlation (.55 in this case) and is the mean of the sampling distribution of z'. is the standard error of Fisher's z'; it was previously calculated to be .25 for N = 19.

Plugging the numbers into the formula: z = (.97 - .55)/.25 = 1.68.
Therefore, a correlation of .75 is associated with a value 1.68
standard deviations above the mean. As shown
previously, a z table can be used to
determine the probability of a value more than 1.68 standard
deviations above the mean. The probability is .95. Therefore there is
a .05 probability of obtaining a Pearson's r of .75 or greater when
the "true" correlation is only .50.

Next section: Difference between correlations