The Kendall Tau Formula

This Kendall tau calculator compares every pair of observations (i, j). A pair is concordant when both values move in the same direction and discordant when they move oppositely. Tau-b, the version computed here, divides the difference of concordant minus discordant pairs by a tie-adjusted denominator.

Reading the Coefficient

Tau ranges from −1 (perfect inverse ordering) through 0 (no monotonic relationship) to +1 (perfect agreement). Its magnitude reflects how consistently the two variables rank together; unlike Pearson's r it detects any monotonic trend, not just linear ones.

Ties and Small Samples

The tau-b correction keeps the coefficient within [−1, 1] when ranks repeat. With small samples Kendall's tau is also less sensitive to outliers than Pearson's r, making it a dependable choice for survey data and ranked judgments.