Goodman and Kruskal (1954) proposed an association measure (tau) for nominal variables based on…

Goodman and Kruskal (1954) proposed an association measure (tau) for nominal variables based on…

Goodman and Kruskal (1954) proposed an association measure (tau) for nominal variables based on variation measure

a. Show V(Y) is the probability that two independent observations on Y fall in different categories (called the Gini concentration index).

Show that V(Y) = 0 when π+j 1 for some j and V(Y) takes maximum value of (J — 1)/J when π+j = 1/J for all j.

b. For the proportional reduction in variation, show that E[V(Y |X)]  [The resulting measure (2.12) is called the concentration coefficient. Like U, T = 0 is equivalent to indepen­dence. Haberman (1982) presented generalized concentration and uncertainty coefficients.]

Looking for a similar assignment? Get help from our qualified experts!

Order Now

Related Posts