1. If Ni and Ni denote, respectively, the sum of the frequencies in the i th row and j th columns of a contingency table (the marginal frequencies), show that the expected frequency for the cell...

1. If Ni and Ni denote, respectively, the sum of the frequencies in the_ith row and_jth columns of a contingency table (the marginal frequencies), show that the expected frequency for the cell belonging to the_ith row and_jth column is NiNj / N, where N is the total frequency of all cells.

2. Extend the result of formula (9) of this chapter to 2 x k contingency tables, where k > 3.

3. (a) Prove that X²= for all contingency tables, where N is the total frequency of all cells.

(b) Using the result in part

4. By analogy with the ideas developed for h x k contingency tables, discuss h x k x l contingency tables, pointing out their possible applications.