What is Kendall's tau-b?

To get Kendall's tau-b, choose Stat > Tables > Cross Tabulation and Chi-Square, click Other Stats, and select Measures of concordance for ordinal categories.

Kendall's tau-b is a nonparametric measure of association for ordinal data. Ordinal data are categorical variables that have three or more levels with a natural ordering, such as strongly disagree, disagree, neutral, agree, and strongly agree.

Kendall's tau-b is used in cross tabulation to measure the association between two ordinal variables. For example, an athletic shoe manufacturer gives pairs of newly designed workout shoes to several costumers to assess how comfortable the shoes are. Each customer is asked to rate their own fitness level (low, medium, high) and their comfort in the new shoes (not comfortable, somewhat comfortable, very comfortable). The manufacturer to determine the relationship between fitness level and shoe comfort using Kendall's tau-b.

Kendall's tau-b ranges from -1.0 (all pairs disagree) to 1.0 (all pairs agree). A positive value indicates of both variables increase together. A negative value indicates that both variables decrease together.

If Kendall's tau-b for the fitness level/comfort level is 0.6129, the data indicates that comfort level is positively related to fitness level. So as a customer's fitness assessment increases, so does the customer's rating of comfort of shoes.

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