1. Each of the following is a description of a three factor study. Identify the three factors and state if they are random or fixed.

Also, state the relationship between the three factors. For example, labeling the three factors as A, B and C, some possible answers are:

a. Thirty randomly selected subjects were tested in an experiment on the effects of sunglasses on visual acuity. The tests were conducted using all possible combinations of two types of sunglasses and five different lighting conditions. In addition, each subject was tested under three different levels of initial light adaptation. A single visual acuity score was obtained from each subject under each level of adaptation.

Subjects=Random (A)

Sunglasses=Fixed (B)

Lighting Conditions=Fixed (C)

A*B*C

b. Six randomly selected first-grade teachers were each assigned 12 randomly selected pupils. Each teacher taught the pupils two subjects, reading and arithmetic. At the end of the year all six classes were given the same standard tests in these two subjects. The data were the test scores of the individual pupils in each of the two subjects.

Teachers =Random (A)

Pupils= Random (B)

Subjects=Fixed (C)

B(A)*C

c. Two cancer treatments were being compared. Thirty randomly selected hospitals participated in the experiment, with ten hospitals using each treatment, and ten using traditional treatments (as a control). In each hospital, fifteen patients were treated, each having one of three types of cancer (i.e., there were five patients with each type of cancer). The health of each patient was rated on a ten-point scale after one week, two weeks, and three weeks of treatment.

Treatments=Fixed (A)

Hospitals=Random (B)

Patients= Fixed (C)

C(B)*A