Z – Test of the Significance of the Correlation Coefficient

Prof. Fisher has given a method of testing the significance of the correlation coefficient in small samples. According to this method of coefficient of correlation is transformed into Z and hence the name Z- transformation. The statistics Z given by Prof. Fisher is used to test (i) whether an observed value of r differs significantly from some hypothetical value, or (ii) 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 ξ by applying Fisher’s transformation and then calculate the value of the standard normal variate

        Z – ξ
       1/√n-3

If the absolute value of this statistics exceeds 1.96, the difference is significant at 5 % level.
Here       


p refers to the population correlation coefficient.

        S.E.z = 1/√n-3

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