In Exercise 1.46, we investigated the e¤ects of the three binary pre-
operative variables (x-ray, grade, and stage); in this exercise, we focus on
the e¤ects of the two continuous factors (age and acid phosphatase). The
53 patients are divided into two groups by the finding at surgery, a group
with nodal involvement and a group without (denoted by 1 or 0 in the
sixth column). For each group and for each of the two factors age at
diagnosis and level of serum acid phosphatase, calculate the meanx,
variances^2 , and standard deviations.2.33 Refer to the data on cancer of the prostate in Exercise 2.32. Investigate
the relationship between age at diagnosis and level of serum acid phos-
phatase by calculating Pearson’s correlation coe‰cient and draw your
conclusion. Repeat this analysis, but analyze the data separately for the
two groups, the group with nodal involvement and the group without.
Does the nodal involvement seem to have any e¤ect on the strength of
this relationship?
2.34 A study was undertaken to examine the data for 44 physicians working
for an emergency department at a major hospital so as to determine-
which of a number of factors are related to the number of complaints
received during the preceding year. In addition to the number of com-
plaints, data available consist of the number of visits—which serves as
thesizefor the observation unit, the physician—and four other factors
under investigation. Table E2.34 presents the complete data set. For
each of the 44 physicians there are two continuous explanatory factors,
revenue (dollars per hour) and workload at the emergency service
(hours), and two binary variables, gender (female/male) and residency
training in emergency services (no/yes). Divide the number of complaints
by the number of visits and use this ratio (number of complaints per
visit) as the primaryoutcomeorendpoint X.
(a) For each of the two binary factors, gender (female/male) and resi-
dency training in emergency services (no/yes), which divide the 44
physicians into two subgroups—say, men and women—calculate the
meanxand standard deviationsfor the endpointX.
(b)Investigate the relationship between the outcome, number of com-
plaints per visit, and each of two continuous explanatory factors,
revenue (dollars per hour) and workload at the emergency service
(hours), by calculating Pearson’s correlation coe‰cient, and draw
your conclusion.
(c) Draw a scatter diagram to show the association, if any, between the
number of complaints per visit and the workload at the emergency
service. Does it appear to be linear?
EXERCISES 105