factors b. factor levels blocks d. experimental unit measurement unit f. replications treatments

b. A medical specialist wants to compare two different treatments T

1 , T 2 for treating a particular illness. She will use eight hospitals for the study. She believes there may be differences in the response among hospitals. Each hospital has four wards of patients. She will randomly select four patients in each ward to participate in the study. Within each hospital, two wards are randomly assigned to get T 1 ; the other two wards will receive T 2 . All patients in a ward will get the same treatment. A single response variable is measured on each patient.

c. In the design described in b make the following change. Within each hospital, the

two treatments will be randomly assigned to the patients, with two patients in each ward receiving T 1 and two patients receiving T 2 .

d. An experiment is planned to compare three types of schools—public, private-

nonparochial, and parochial—all with respect to the reading abilities of students in sixth-grade classes. The researcher selects two large cities in each of five geographical regions of the United States for the study. In each city, she randomly selects one school of each of the three types and randomly selects a single sixth-grade class within each school. The scores on a standardized test are recorded for each of 20 students in each classroom. The researcher is concerned about differences in family income levels among the 30 schools, so she obtains the family income for each of the students who participated in the study. Bio. 2.16 A research specialist for a large seafood company plans to investigate bacterial growth on oysters and mussels subjected to three different storage temperatures. Nine cold-storage units are available. She plans to use three storage units for each of the three temperatures. One package of oysters and one package of mussels will be stored in each of the storage units for 2 weeks. At the end of the storage period, the packages will be removed and the bacterial count made for two samples from each package. The treatment factors of interest are temperature levels: 0, 5, 10°C and seafood levels: oysters, mussels. She will also record the bacterial count for each package prior to placing seafood in the cooler. Identify each of the following components of the experimental design.

a. factors b. factor levels

c. blocks d. experimental unit

e. measurement unit f. replications

g. treatments

2.17 In each of the following situations, identify whether the design is a completely randomized design, randomized block design, or Latin square. If there is a factorial structure of treatments, specify whether it has a two-factor or three-factor structure. If the experiment’s measurement unit is different from the experimental unit, identify both.

a. The 48 treatments comprised 3, 4, and 4 levels of fertilizers N, P, and K, respectively,

in all possible combinations. Five peanut farms were randomly selected and the 48 treat- ments assigned at random at each farm to 48 plots of peanut plants.

b. Ten different software packages were randomly assigned to 30 graduate students. The

time to complete a specified task was determined.

c. Four different glazes are applied to clay pots at two different thicknesses. The kiln

used in the glazing can hold eight pots at a time, and it takes 1 day to apply the glazes. The experimenter wants eight replications of the experiment. Because the conditions in the kiln vary somewhat from day to day, the experiment is conducted over an 8-day period. Each combination of a thickness and type of glaze is randomly assigned to one pot in the kiln each day. Bus. 2.18 A colleague has approached you for help with an experiment she is conducting. The ex- periment consists of asking a sample of consumers to taste five different recipes for meat loaf. When a consumer tastes a sample, he or she will give scores to several characteristics and these scores will be combined into a single overall score. Hence, there will be one value for each recipe for a consumer. The literature indicates that in this kind of study some consumers tend to give low scores to all samples; others tend to give high scores to all samples.