Tests of Pearson's Correlation (4 of 6)
Other Null Hypotheses
For other null hypotheses, the significance test of r is done using Fisher's z' transformation. The formulas used in the fourth step of hypothesis testing are shown below:
where
is the value
of r converted to z', 
is
the value of ρ converted to z', and 
is the standard error of z'. This standard error can be
computed as:
Once z is computed, a z table is used to calculate the p value.