Compute rank adjusted for ties.

[r, tieadj] = tiedrank (x) computes the ranks of the values in vector x. If any values in x are tied, tiedrank computes their average rank. The return value tieadj is an adjustment for ties required by the nonparametric tests signrank and ranksum, and for the computation of Spearman’s rank correlation.

[r, tieadj] = tiedrank (x, 1) computes the ranks of the values in the vector x. tieadj is a vector of three adjustments for ties required in the computation of Kendall’s tau. tiedrank (x, 0) is the same as tiedrank (x).

[r, tieadj] = tiedrank (x, 0, 1) computes the ranks from each end, so that the smallest and largest values get rank 1, the next smallest and largest get rank 2, etc. These ranks are used in the Ansari-Bradley test.

tieflag and bidir are read as an if reads a condition: each is set when it is not empty and all of its elements are nonzero, so an empty [] keeps the default, as in tiedrank (x, [], 1).

[r, tieadj] = tiedrank (x, tieflag, bidir, tol) treats two values as tied when they lie within a tolerance of each other rather than only when they are exactly equal. tol is either a scalar or an array the size of x giving each element its own tolerance, and two neighbouring values are tied when the gap between them does not exceed the sum of their two tolerances. The default is 0, which is exact comparison, and an empty tol takes it. signrank uses this to rank differences that are equal to within the precision of the values they came from.

Source Code: tiedrank