3.37 Consider an I × J table with ordered columns and unordered rows. Ridits (Bross 1958) are data-based column scores. The jth sample ridit is the average cumulative proportion within category j, j-1 P₁ = ++ (2) P+j.

k=1 The sample mean ridit in row i is R₁ = ∑;jPjli. Show that Σ; P+jfj = 0.50 and

Σ₁ Pi+R₁ = 0.50. [For ridit analyses, see Agresti (2010, Sec. 2.1), Beder and Heim

(1990), Bross (1958), Fleiss et al. (2003, Sec. 9.4), and Landis et al. (1978).]