Chapter 2.8, Problem 16E

In the descriptions of experiments given in Exercises 2.15–2.18, identify the important features of each design. Include as many of the components listed in Exercise 2.14 as needed to adequately describe the design.

2.16 A medical study is designed to evaluate a new drug, D₁, for treating a particular illness. There is a widely used treatment, D₂, for this disease to which the new drug will be compared. A placebo will also be included in the study. The researcher has selected 10 hospitals for the study. She does a thorough evaluation of the hospitals and concludes that there may be aspects of the hospitals that may result in the elevation of responses at some of the hospitals. Each hospital has six wards of patients. She will randomly select six patients in each ward to participate in the study. Within each hospital, two wards are randomly assigned to administer D₁, two wards to administer D₂, and two wards administer the placebo. All six patients in each of the wards will be given the same treatment. Age, BMI, blood pressure, and a measure of degree of illness are recorded for each patient upon entry into the hospital. The response is an assessment of the degree of illness after 6 days of treatment.

2.14 The process engineer designed a study to evaluate the quality of plastic irrigation pipes. The study involved a total of 48 pipes; 24 pipes were randomly selected from each of the company’s two manufacturing plants. The pipes were heat-treated at one one of four temperatures (175, 200, 225, 250°F). The pipes were chemically treated with one of three types of hardeners (H₁, H₂, H₃). The deviations from the nominal compressive strength were measured at five locations on each of the pipes.

Identify each of the following components of the experimental design.

1. a. Factors
2. b. Factor levels
3. c. Blocks
4. d. Experimental unit
5. e. Measurement unit
6. f. Replications
7. g. Covariates
8. h. Treatments