Refer to the previous exercise. Denote the cell counts in the 2 × 2 table by

{nij}. For the case ????1 = 0 (the independence model), the fitted values in the cells of that table are { ̂????ij = ni+n+j∕n}. These have a common value for the four |nij − ̂????ij|.

a. Construct the Pearson residuals. Explain why all four may differ in absolute value.

b. The standardized residuals in this case are rij = (nij − ̂????ij)∕

√

̂????ij[1 − (ni+∕n)][1 − (n+j∕n)].

Show that all four are identical in absolute value, thus appropriately recognizing that residual df = 1 for the independence model.