Chapter 10 Analysis of Variance 427
can you explain it? As a hint, con-
sider that the college is in Vermont,
which has a small population. Why is
that relevant here?
c. Perform a one-way analysis of vari-
ance to compare tiers. Are there sig-
nifi cant differences among tiers in the
percentage of instate students?
d. Create a matrix of paired mean dif-
ferences. Does the fi rst tier have sig-
nifi cantly fewer instate students in
comparison to the other three tiers?
e. Redo the analysis in parts b and c but
this time do not include the outlier.
How does this affect the results?
f. Save your changes to the workbook and
write a report summarizing your results.
- The Infi eld workbook data set has statis-
tics on 120 major league baseball infi eld-
ers at the start of the 2007 season. The
data include Salary, logSalary (the loga-
rithm of salary), and Position.
a. Open the Infi eld workbook and save
it as Infi eld Salary ANOVA.
b. Create multiple histograms and box-
plots to see the distribution of Salary
for each position. How would you de-
scribe the shape of the distribution?
c. Make the same plots for logSalary.
How does the shape of the distribution
change with the logarithm of the salary?
d. Perform a one-way ANOVA of logSal-
ary on Position to see whether there
is any signifi cant difference of salary
among positions.
e. Save your changes to the workbook and
write a report summarizing your results.
- The Infi eld workbook also contains the
SLG variable, the slugging percentage of
each infi eld player. Analyze the relation-
ship between slugging percentage and
position.
a. Open the Infi eld workbook from the
Chapter10 data folder and save it as
Infi eld SLG ANOVA.
b. Create multiple histograms and box-
plots of the SLG variable against
Position. Describe the shape of the
distributions. Is there any reason to
doubt the validity of the ANOVA
assumptions?
c. Perform a one-way ANOVA of SLG
against Position.
d. Create a matrix of paired mean dif-
ferences to compare infi eld positions
(use the Bonferroni correction factor).
Which positions differ signifi cantly?
Can you explain why?
e. Save your changes to the workbook
and write a report summarizing your
results.
- The Honda25 workbook contains the
prices of used Hondas and indicates the
age (in years) and whether the transmis-
sion is 5 speed or automatic.
a. Open the Honda25 workbook from
the Chapter10 data folder and save it
as Honda25 ANOVA.
b. Perform a two-sample t test for the
price data on the basis of the trans-
mission type.
c. Perform a one-way ANOVA with
price as the dependent variable and
transmission as the grouping variable.
d. Compare the value of the t statistic
in the t test to the value of the F ratio
in the F test. Do you fi nd that the F
ratios for ANOVA are the same as the
squares of the t values from the t test
and that the p values are the same?
e. Use one-way ANOVA to compare the
ages of the Hondas for the two types of
transmissions. Does this explain why
the difference in price is so large?
f. Perform two regressions of price vs.
age—the fi rst for automatic transmis-
sions and the second for 5-speed
transmissions. Compare the two lin-
ear regression lines. Do they appear to
be the same? What problems do you
see with this approach?
