Chapter 2.8, Problem 18E

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.

2.18 Researchers in an education department at a large state university have designed a study to compare the math abilities of students in junior high. They will also examine the impact of three types of schools — public, private nonparochial, and parochial — on the scores the students receive in a standardized math test. Two large cities in each of four geographical regions of the United States were selected for the study. In each city, one school of each of the three types was randomly selected, and a single eighth-grade class was randomly selected within each school.

The scores on the test were recorded for each student in the selected classrooms. The researcher was concerned about differences in socio-economie status among the 8 cities, so she obtained a measure of socioeconomic status for each of the students that participated in the study.

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