For the DOS, compute the indices, Pearson correlation, Spearman correlation, Goodman-Kruskal \(\gamma\), Kendall's \(\tau_{b}\), Stuart's \(\tau_{c}\), Somers' D, lambda coefficients, and uncertainty coefficients, for assessing association between education (dichotomized with cut-point 12) and depression using two different score systems for the depression outcome specified in (a) and(b) below.

(a) Scores for depression are 0 for no, 1 for minor, and 2 for major depression.

(b) Scores for depression are 0 for no, 1 for minor, and 3 for major depression.

(c) Compare results from (a) and (b) and state which indices are unchanged under the different scoring methods.

(d) Is the invariance true under all score systems that preserve orientation?