Suppose a one-way layout has ordered levels for the c groups, such as dose levels in a dose–response assessment. The model E( yij) = ????0 + ????i treats the groups as a qualitative factor. The model E( yij) = ????0 + ????xi has a quantitative predictor that assumes monotone group scores {xi}.

a. Explain why the quantitative-predictor model is a special case of the qualitative-predictor model. Given the qualitative-predictor model, show how the null hypothesis that the quantitative-predictor model is adequate is a special case of the general linear hypothesis. Illustrate by showing ????

for the case c = 5 with {xi = i}.

b. Explain how to use an F test to compare the models, specifying the df values.

c. Describe an advantage and disadvantage of each way of handling ordered categories.