Z-Test

Prof. Fisher has  given a method  of testing the significance of the correlation coefficient in small  samples. According  to this method the  coefficient of correlation is transformed into Z  and hence the  name  transformation. The statistic Z given by  prof. Fisher is used  to test:

a.Whether  an observed value  of r differs significantly from some  hypothetical value or.

b.Whether two samples values of  r differ significantly,

For  testing whether r differs significantly from zero the t- test is preferable.

In order to apply the test  we have to calculate Z and by applying Fisher transformation and then  calculate the  value  of the standard  normal  variate.

                 Z- ε / 1/√n-3