Probable error
probable error is the coefficient of correlation that supports in finding out about the accurate values of the coefficients. It also helps in determining the reliability of the coefficient.
The calculation of the correlation coefficient usually takes place from the samples. These samples are in pairs. The pairs generally come from a very large population. It is quite an easy job to find out about the limits and bounds of the correlation coefficient.
The correlation coefficient for a population is usually based on the knowledge and the sample relating to the correlation coefficient. Therefore, probable error is the easy way to find out or obtain the correlation coefficient of any population. Hence, the definition is:
probable error = \[0.6745\] \[\frac{1-r^2}{\sqrt{N}}\]
where r = coefficient of correlation for any random sample
N= total no of pairs pf observations
Question: Find the probable error. Assume that the correlation coefficient is 0.8 and the pairs of samples are 25.
Solution: We will use the most common method to calculate the outcome of the following.
Here, r = 0.8 and N = 25.
We know that, probable error = \[0.6745\] \[\frac{1-0.8^2}{\sqrt{25}}\]=0.0486
Question: If the value of r = 0.7 and that of N = 64, then find the P. E. of the correlation of coefficient
Solution: Here, we have to calculate the probable error. Given, r = 0.7 and N = 64. We know that,
probable error = \[0.6745\] \[\frac{1-0.7^2}{\sqrt{64}}\]=\[0.043\]
