Kendall's Coefficient of Concordance

Kendall's coefficient of concordance is a nonparametric statistic test that measures the agreement among ranks of the variables.

It assesses the consistency of ranks in the test sets and can measure concordance for three or more sets of ranks.

Consider an example where four different researchers measure humidity at 10 different altitudes on a mountain.

To estimate the concordance, first, assign the ranks to humidity measurements by each b = 4 researchers separately. Further, sum these ranks for a = 10 altitudes.

Kendall's W is calculated using the following expression.

Different quantities, such as the parts, P, Q, and R of this equation can be calculated separately to compute the numerator as shown.

Now, divide this quantity by b ✕ (a﹣1) and calculate Kendall's W — the coefficient of concordance.

Values of Kendall's W range between 0 and 1, 0 suggesting the ranks are random and 1 suggesting ranks are in perfect concordance.

In this case the humidity measurements by the four researchers are in a perfect concordance.