Chapter 10 Analysis of Variance 429
c. Examine the ANOVA table. What
factors are signifi cant in the analysis
of variance? What percentage of the
total variance in reaction time can be
explained by the two factors? What is
the R^2 value?
d. Examine the means and standard de-
viations of the reaction times for each
of the three heats. Using these values,
form a hypothesis for how you think
reaction times vary with rounds.
e. Test your hypothesis by performing
a paired t test on the difference in
reaction times between each pair of
rounds (1 vs. 2, 2 vs. 3, and 1 vs. 3).
Which pairs show signifi cant dif-
ferences at the 5% level? Does this
confi rm your hypothesis from the pre-
vious step?
f. Because there is no replication of a rac-
er’s reaction time within a round, you
cannot add an interaction term to the
analysis of variance. You can still cre-
ate an interaction plot, however. Create
an interaction plot with round on the
x-axis and the reaction time for each
racer as a separate line in the chart.
On the appearance of the chart, do
you believe that there is an interaction
between round and the racer involved?
What impact does this have on your
overall conclusions as to whether
reaction time varies with round?
g. Save your changes to the workbook
and report your observations.
- Researchers are examining the effect of
exercise on heart rate. They’ve asked
volunteers to exercise by going up and
down a set of stairs. The experiment has
two factors: step height and rate of step-
ping. The step heights are 5.75 inches
(coded as 0) and 11.5 inches (coded as 1).
The stepping rates are 14 steps/min
(coded as 0), 21 steps/min (coded as 1),
and 28 steps/min (coded as 2). The ex-
perimenters recorded both the
resting heart rate (before the exercise)
and the heart rate afterward. Analyze
their fi ndings.
a. Open the Heart workbook from the
Chapter10 data folder and save it as
Heart ANOVA.
b. Create a two-way table using StatPlus.
Place frequency in the row area of the
table, place height in the column area
of the table, and use heart rate after
the exercise as the response variable.
c. Analyze the values in the two-way
table with a two-way ANOVA (with
replication). Is there a signifi cant in-
teraction between the frequency at
which subjects climb the stairs and
the height of the stairs as it affects the
subject’s heart rate?
d. Create an interaction plot. Discuss
why the interaction plot supports
your fi ndings from the previous step.
e. Create a new variable named Change,
which is the change in heart rate due
to the exercise. Repeat parts a–c for
this new variable and answer the
question of whether there is an inter-
action between frequency and height
in affecting the change in heart rate.
f. Save your changes to the workbook
and write a report summarizing your
conclusions.
- The Noise workbook contains data from
a statement by Texaco, Inc. to the Air and
Water Pollution Subcommittee of the
Senate Public Works Committee on June
26, 1973. Mr. John McKinley, president
of Texaco, cited an automobile fi lter de-
veloped by Associated Octel Company as
effective in reducing pollution. However,
questions had been raised about the ef-
fects of fi lters on vehicle performance,
fuel consumption, exhaust gas back-
pressure, and silencing. On the last ques-
tion, he referred to the data included here
as evidence that the silencing properties
