To this point, we have primarily used multiple regression to study relationships among two or more continuous variables and used analysis of variance (traditional, regression and MLE implementations) to study how one continuous variable depends on discrete levels of one or more grouping or treatment factors. These grouping factors are described with one or more categorical variables.
We have also encountered situations in which these two approaches can be mixed. The "More Dummies on Mars" and "Protein Synthesis in Newborns and Adults" examples in Chapter 3 and the "Reduced Nausea Cigarettes" examples in Chapter 10 included categorical variables in regression analyses using dummy variables. Combining dummy variables and continuous variables in regression analyses allowed us to build models to interpret data from a wide variety of experimental designs. By so doing, we could study how relationships between continuous variables, such as Martian weight and height, were affected by discrete experimental interventions, such as secondhand smoke.
There is another perspective on mixing continuous and categorical variables in a statistical analysis: analysis of covariance (ANCOVA). In a traditional ANCOVA, the focus is on the categorical variables that identify grouping or treatment factors, with an adjustment for the effects of at least one continuous variable. In contrast to the regression perspective, in ANCOVA, the continuous variables are of secondary importance.*
Preeclampsia is a condition in which high blood pressure (hypertension) occurs during pregnancy in some women. The cause of preeclampsia is not completely understood, but the fats carried in the blood as lipids and lipoproteins increase in women who will develop preeclampsia well before clinical signs appear. There is also improper functioning of the inside layer of the uterus, the endometrium, including in the small blood vessels that determine the resistance to blood flow in the uterine lining. Hayman and colleagues* hypothesized that aberrations in lipoprotein metabolism contribute to blood vessel dysfunction in preeclampsia. To test this hypothesis, they studied the effect of drugs on small endometrial artery contraction in the presence of serum from two groups of women, those with normal pregnancies and those with preeclampsia. They were particularly interested in the ability of the arteries to relax from a previously contracted state in response to a drug that requires normally functioning endothelial cells to relax the muscle in the artery wall. Their response variable was percent residual contraction, R, defined as the percentage of pre-contracted state that remained after administering a drug that causes endothelium-dependent relaxation. The smaller the value of R, the more effectively the drug relaxes the vessel wall. Because of their interest in lipid metabolism in relation to vessel ...