Goodman and Kruskal's gamma

In statistics, Goodman and Kruskal's gamma is a measure of rank correlation, i.e., the similarity of the orderings of the data when ranked by each of the quantities. It measures the strength of association of the cross tabulated data when both variables are measured at the ordinal level. It makes no adjustment for either table size or ties. Values range from −1 (100% negative association, or perfect inversion) to +1 (100% positive association, or perfect agreement). A value of zero indicates the absence of association.

This statistic (which is distinct from Goodman and Kruskal's lambda) is named after Leo Goodman and William Kruskal, who proposed it in a series of papers from 1954 to 1972.[1][2][3][4]

  1. ^ Goodman, Leo A.; Kruskal, William H. (1954). "Measures of Association for Cross Classifications". Journal of the American Statistical Association. 49 (268): 732–764. doi:10.2307/2281536. JSTOR 2281536.
  2. ^ Goodman, Leo A.; Kruskal, William H. (1959). "Measures of Association for Cross Classifications. II: Further Discussion and References". Journal of the American Statistical Association. 54 (285): 123–163. doi:10.1080/01621459.1959.10501503. JSTOR 2282143.
  3. ^ Goodman, Leo A.; Kruskal, William H. (1963). "Measures of Association for Cross Classifications III: Approximate Sampling Theory". Journal of the American Statistical Association. 58 (302): 310–364. doi:10.1080/01621459.1963.10500850. JSTOR 2283271.
  4. ^ Goodman, Leo A.; Kruskal, William H. (1972). "Measures of Association for Cross Classifications, IV: Simplification of Asymptotic Variances". Journal of the American Statistical Association. 67 (338): 415–421. doi:10.1080/01621459.1972.10482401. JSTOR 2284396.