3.33 For a 1 x 2 table (i.e., a single binomial Y based on n trials, with probabilities π and 1 – π), consider testing Ηο: π = πο.

a. Show that the Pearson residuals are

(γ – ηπο)/√ηπο and – (у – пπο)/√n(1 – πο), which have differing absolute values when πο ≠ 0.50.

b. Show that the standardized residuals are

(γ – ηπο)/√ηπο (1 – πο) and

(γ – ηπο)/√ηπο (1 – πο).

Explain why these are more suitable than Pearson residuals.