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.
We can find the probable error if and only if the given below conditions are taken care of.
- The data that we have must be a bell-shaped curve. This means that the data has to give us a normal frequency curve
- It is important to take the probable error for measuring the statistics from the sample only
- It is compulsory that the sample items are taken off in an unbiased manner and must remain independent of each other’s value.
step 1. Calculation of correlation coeffficient r
1. It is calculaeted through ρ by using the transmutation formula. The value is r = 2 sin (πρ/6).
assumption ρ=k
step 2 The formula is given by:
P. E rfound from ρ = 0.7063 (1 – r2)√N {1 + 1.042r2 + 0.008r4 + .002r6}
Example For k=0.8
we get r= 2 sin (180ρ/6).
r= 0.81347
so correlation coefficent =0.81347
Step 2 Now for r=0.81347 and N=9
Probable error = 0.7063 (1 – r2)√N {1 + 1.042r2 + 0.008r4 + .002r6}=0.13429
Boundary condition 0< r < 1
