In The Last Few Years A Promising New Treatment

in the last few years, a promising new treatment for headaches has been developed. simply described, the treatment involves a series of injec

In the last few years, a promising new treatment for headaches has
been developed. Simply described, the treatment involves a series of
injections of a local anesthetic to the occipital nerve (located in
the back of the neck). The current treatment procedure is to schedule
the injections once a week for four weeks. However, it has been
suggested that another procedure may be better, one that features one
injection every other day for a total of four injections.
Additionally, some physicians recommend other combinations of drugs
that may increase the effectiveness of the injections. To analyze the
problem, an experiment was organized. It was decided to test for a
difference between the two schedules of injection and to determine
whether there are differences among four drug mixtures. Because of the
possibility of an interaction between the schedule and the drug, a
complete factorial experiment was chosen. Five headache patients were
randomly selected for each combination of schedule and drug. Forty
patients were treated and each was asked to report the frequency,
duration, and severity of his or her headache prior to treatment and
for the 30 days following the last injection. An index ranging from 0
to 100 was constructed for each patient, where 0 indicates no headache
pain and 100 specifies the worst headache pain. The improvement in the
headache index for each patient was recorded and reproduced in the
accompanying table. (A negative value indicates a worsening
condition.)
IMPROVEMENT IN HEADACHE INDEX
DRUG MIXTURE
SCHEDULE 1 2 3 4
17 24 14 10
One Injection 6 15 9 -1
Every Week 10 10 12 0
(Four Weeks) 12 16 0 3
14 14 6 -1
18 -2 20 -2
One Injection 9 0 16 7
Every Two Days 17 17 12 10
(Four Days) 21 2 17 6
15 6 18 7
The following sums of squares were computed.
SS(Total) = 1949.6
SS(Mixture) = 581.8
SS(Schedule) = 14.4
SS(Interaction) = 548.6
Suppose that the experiment on developing new IRS tax forms is redone
in the following way. Thirty taxpayers fill out each of the four
forms. However, 10 taxpayers in each group are in the low-income
bracket, 10 are in the next income bracket, and the remaining 10 are
in the highest bracket. The amount of time needed to complete the
returns is recorded.
The following sums of squares were computed.
SS(Total) = 106,317
SS(Income) = 6,719
SS(Form) = 6,280
SS(Interaction) = 5,102
Many college professors seek ways to encourage their students to
participate in class. A statistics professor at a community college in
upper New York State believes that the time of day and the
configuration of seats are two factors which influence participation.
Six classes of about 60 students each were scheduled for one semester.
Two classes were scheduled at 9:00 A.M., two at 1:00 P.m., and two at
4:00 P.m. At each of the three times, one of the classes was assigned
to a room where the seats were arranged in rows of 10 seats. The other
class was a U-shaped, tiered room, where students not only face the
instructor, but face their fellow students as well. In each of the six
classrooms, over five days, student participation was measured by
counting the number of times students asked and answered questions.
TIME
CLASS CONFIGURATION 9am 1pm. 4pm
Rows 10 9 7
7 12 12
9 12 9
6 14 0
8 8 7
U Shape 15 4 7
18 4 4
11 7 9
13 4 8
13 6 7
SS(Total) = 468.67
SS(Configuration) = 13.33
SS(Time) = 46.67
SS(Interaction) = 206.67
Detergent manufacturers frequently make claims about the effectiveness
of their products. A consumer-protection service decided to test the
five best-selling brands of detergent, each of whose manufacturers
claims that its product produces the 11 whitest whites" in all water
temperatures. The experiment was conducted in the following way. One
hundred fifty white sheets were equally soiled. Thirty sheets were
washed in each brand-10 with cold water, 10 with lukewarm water, and
10 with hot water. After washing, the "whiteness" scores for each
sheet were measured with laser equipment. The results are stored in
file XR]5-29 using the following format
The following sums of squares were computed.
SS(Total) = 24,267
SS(Temperature) = 3,937
SS(Detergent) = 2,967
SS(Interaction) = 2,452