Standard Error

Hypothesis testing under the Z test of significance of correlation coefficients in small samples, the reliability of a partial coefficient of correlation is also be studied through Fisher’s transformation technique.

According to this technique, the given partial correlation coefficient is to be transformed first, in to Z by the model,

Z = 1.1513 log₁₀ (1+r)/(1-r)

Then, the testing of the reliability of such a coefficient is to be compared at a desired significance level with its standard error.

As mentioned earlier, the standard error of Z corresponding to a simple r is given by = SE_Z  1/√(n-3)

But in this case the above model will be slightly revised according to the order of the coefficient as under:

In case of a first order coefficient in which one more degree of freedom is lost by keeping one variable as constant, the stander error of Z is to be obtained by

SE_Z(r123) =  1/√(n-3-1) or 1/√(n-5)