What is Kendall's rank-order correlation?

Kendall's rank-order correlation is also known as Tau's coefficient of Kendall. Tau's coefficient assesses statistical association based on ranked data.

• Kendall's correlation is a non-parametric method for measuring the relationship between ranked data columns.  
• Tau's coefficient returns 1 to present the maximum correlation between two columns and 0 to show the minimum correlation.

Kendall's Tau formula

To calculate Kandell's coefficient, the following formula is used.

Where:

F = score of max relation – score of min relation on A and B

K = number of samples for both A and B

Tau's coefficient uses pair observations for analysis, where A and B are pairs of statements. 

For further understanding, we'll use an example numerical to clarify things.

Example

Suppose A and B show their preference for different samples and assign a score of ten for each instance. To see whether their importance is related to each other, we may use the following steps.

M, N, O, and P are the four samples.

Step 1: We rank the data for A and B based on score. We rank P to 1 as the score of P is minimum, and N to 4, as the value for N is maximum for A.

Step 2: 1 to K data arrangement of A.

Step 3: We arrange the data of B corresponding to A and calculate the relation score.

We need a score of max relation and min relation to calculate F. It can be estimated using the scores for B, starting from the left and counting the number of ranks to its right. This represents the max relationship.

We subtract the number of minimum rank values to its right. This shows the min relationship. If we do this for all the ranks and sum the result, we obtain an F.

The first value to the sum is +1, as moving left to right 4 and 3 are greater values making sum = +2. However, with a lesser value, 1, it causes subtraction in the value of sum = +2 -1 = +1. The same process is repeated for other values.

Step 4: We calculate the value of T.

F = -2 and K = 4 (the number of samples)

As a result, T = -0.33 is the measure of maximum relation between the A and B pair, as the Tau is negative, which shows the negative correlation between A and B.