Standard Error is basically the standard deviation of any mean. It is the sampling distribution of the standard deviation. The standard error is generally used to refer to any sort of estimate belonging to the standard deviation. Therefore, we use probable error to calculate and check the reliability associated with the coefficient.
Advantages of Standard Error
1. It helps in finding and reducing the sample errors as well as the measurement errors.
2. The standard error of any mean tells about the accuracy of the estimate clearly enough.
Formula for standard error of the correlation coefficient =\[\frac{1-r^2}{\sqrt{N}}\]
Question: If the value of r = 0.5 and that of N = 81, then find the Standard error of the correlation of coefficient.
Solution
Standard error S.E =\[\frac{1-r^2}{\sqrt{N}}\]
here r=0.5 and N=81
On putting these values in the formulas S.E =\[\frac{1-0.5^2}{\sqrt{81}}\]=\[0.08333\]
