Kendall's Tau Test

Consider an example where 35 pieces of vintage porcelain teacups are ranked independently by an artisan and an ordinary buyer.

Kendall's tau test can be used to find if any association between these two rankings exists.

Here, the null hypothesis states that there is no correlation between the artisan's rankings and the buyer's. The alternative hypothesis is that a correlation exists between these two rankings.

First, arrange the data in a specific order, for instance, per the artisan's ranking.

These paired ranks are required to be converted into counts.

In the conventional method of calculating counts, first, locate a rank and count the total number of ranks higher than that in the same column. Repeat this process for all the ranks in the data.

The test statistic tau can be calculated using the following equation.

The significance of this quantity can be obtained using a suitable computer-based tool.

Kendall's tau is particularly useful for finding linear or non-linear monotonic associations between the variables when there are no ties in the data.