How can the significance of Spearman’s rank correlation be tested?
Let us assume
Ho:ρs=0 vs H1=ρs≠0
The test statistics is
t=[rs*SQRT(n-2)] / SQRT(1- rs2)
t has (n-2) degrees of freedom.
The formula for rs is based on the usual Pearsonian formula for the correlation coefficient. Here it is assumed that no ties occur in the ranks within a sample.
The value of rs lies between -1 and +1
If the ties occur within yhe samples, how the formula for rank correlation is amended?
Often the measurements are taken on individuals and then ranked. In such a situation, sometimes ties do occur.
If so, then a correlation has to be made in rank correlation. If the number of tied observations in X for a particular rank is tX. There can be more than one tX in X samples.
Let’s calculate the significance of Spearman’s Rank Correlation based on two judges’ ratings.
Following are the rank awarded to seven debaters in a competition by two judges.
Let’s calculate the rank correlation and test the significance.
First, we need to calculate the difference d’s which are:
d: -2, -4, -2, -1, 3, 2, 4
Also Sum of d square=54
To test Ho: ρs=0 vs H1=ρs≠0
Calculated value of t=0.080<2.571,
The Calculated value less than the tabled value. It means that there is a dissociation between the ranks awarded by two judges.