Question

What is the formula to calculate Spearman's rank correlation coefficient when ranks are not repeated?
A. $R = \dfrac{{6\sum {d_i^2} }}{{n({n^2} - 1)}}$
B. $R = 1 - \dfrac{{6\sum {d_i^2} }}{{n({n^2} - 1)}}$
C. $R = - \dfrac{{6\sum {d_i^2} }}{{n({n^2} - 1)}}$
D. $R = 1 + \dfrac{{6\sum {d_i^2} }}{{n({n^2} - 1)}}$

Answer 1

Hint: The spearman’s rank correlation coefficient is the measure or relationship between the two sets of the data. The data set is the set which contains observations or numbers which are taken. The relation established between the two sets of data are the spearman’s rank correlation coefficient.

Complete step by step answer:
Given,
The ranks are not repeated, there must be nothing like repetition of ranks in the data set.
To find the spearman’s rank correlation coefficient where ranks are not repeated.
We need to find basic terms used in the spearman’s rank correlation coefficient, they are
n is the number of solutions (this is total number of ranks given) and
${d_i}$ is the difference between the data sets (there are two different sets of ranks given)
Spearman’s rank correlation coefficient is used to identify the relation between two given sets of data. This is very useful in finding the common things too. There are totally $i$ terms.
We represent the spearman's rank correlation coefficient as R.
$R = 1 - \dfrac{{6\sum {d_i^2} }}{{n({n^2} - 1)}}$
Where R is the spearman’s rank correlation coefficient,
n is the number of solutions
${d_i}$ is the difference between the data set (rank of $i$ th observation).
There is only theoretical explanation to the spearman’s rank correlation coefficient because practical theories are more difficult. The theoretical value gives the most accurate results.

So, the correct answer is “Option B”.

Note:
 The terms should be correctly placed. Check whether the rank is repeated or not repeated. The summation symbol should be used. The plus and minus sign should be correctly done. The value should not be negative. The value of spearman’s rank correlation coefficient has the coefficient of $6$ . The denominator should be written correctly without leaving a single term.