When trying to explain rank correlation, first thing that should come in front is the grading or rank given to a particular group of individuals.

For example, if we suppose that based on two characteristics n group of individuals are ranked then the equation will come as:

r = 1 – 6∑d_{i}^{2}/ n(n^{2} – 1)

Here (x, y;), *i*= 1,2…, n is the ranked individuals

Here, *d _{i}=Xi*–

One thing must be clarified before using – 1≤ r ≤ 1that one rank will not appear more than once. When the ranks are repeated then another correlation factor needs to be added. If we take that ranks are repeated m number of times then the equation will be added asm(m^{2} – 1) with Σd^{2}

Let us measure the correlation of coefficient of the data mentioned below:

X | 85 | 74 | 85 | 50 | 65 | 78 | 74 | 60 | 74 | 90 |

Y | 78 | 91 | 78 | 58 | 60 | 72 | 80 | 55 | 68 | 70 |

Here n = 10, so the solution is:

X | Y | Rank X (x) | Rank Y (y) | d = x – y | d^{2} |

85 74 85 50 65 78 74 60 74 90 | 78 91 78 58 60 72 80 55 68 70 | 2.5 6 2.5 10 8 4 6 9 6 1 | 3.5 1 3.5 9 8 5 2 10 7 6 | -1 5 -1 1 0 -1 4 -1 -1 -5 | 1 25 1 1 0 1 16 1 1 25 |

∑ | 0 | 72 |

In this solution, you can see that 85 are repeated two times for which the rank became 2.5 where it could be 2 and 3. Then 74 from the X series, is also repeated three times giving it the rank of 6 where it could be 5, 6, 7. Coming next to 78 from Y series which is repeated three times and getting the rank of 3.5 where it could have been 3 and 4.

As mentioned above, for the repeated ranks, a correlation factor will be added for each distribution, these are written below:

2(4 – 1)/12 = 1/2

3(9 -1)/12 = 2

2(4 – 1)/12 = 1/2

After measuring these three correlation factor we come to:

½ + 2 + ½ = 3

Hence we come to the rank correlation:

r = 1 – 6(72 + 3)/ 10 (100 – 1) = 0.545

**Links of Previous Main Topic:-**

- Introduction to statistics
- Knowledge of central tendency or location
- Definition of dispersion
- Moments
- Bivariate distribution
- Coefficient of correlation
- Regression of equations

**Links of Next Statistics Topics:-**

- Theorem of total probability addition theorem
- Random variable
- Binomial distribution
- What is sampling
- Estimation
- Statistical hypothesis and related terms
- Analysis of variance introduction
- Definition of stochastic process
- Introduction operations research
- Introduction and mathematical formulation in transportation problems
- Introduction and mathematical formulation
- Queuing theory introduction
- Inventory control introduction
- Simulation introduction
- Time calculations in network
- Introduction of game theory