deaths per 1000 live births) for certain selected countries before World
War II.
(a) Draw a scatter diagram to show the association, if any, between
between the average daily number of calories per person and the
infant mortality rate.
(b)Calculate Pearson’s correlation coe‰cient, Kendall’s tau, and
Spearman’s rho rank correlation coe‰cients.2.31 In an assay of heparin, a standard preparation is compared with a test
preparation by observing the log clotting times (y, in seconds) of blood
containing di¤erent doses of heparin (xis the log dose) (Table E2.31).
Replicate readings are made at each dose level.
TABLE E2.31
Log Clotting Times
Standard Test Log Dose
1.806 1.756 1.799 1.763 0.72
1.851 1.785 1.826 1.832 0.87
1.954 1.929 1.898 1.875 1.02
2.124 1.996 1.973 1.982 1.17
2.262 2.161 2.140 2.100 1.32(a) Draw a scatter diagram to show the association, if any, between
between the log clotting times and log dose separately for the stan-
dard preparation and the test preparation. Do they appear to be
linear?
(b)Calculate Pearson’s correlation coe‰cient for log clotting times and
log dose separately for the standard preparation and the test prepa-
ration. Do they appear to be di¤erent?2.32 When a patient is diagnosed as having cancer of the prostate, an impor-
tant question in deciding on treatment strategy for the patient is whether
or not the cancer has spread to the neighboring lymph nodes. The ques-
tion is so critical in prognosis and treatment that it is customary to
operate on the patient (i.e., perform a laparotomy) for the sole purpose
of examining the nodes and removing tissue samples to examine under
the microscope for evidence of cancer. However, certain variables that
can be measured without surgery are predictive of the nodal involve-
ment; and the purpose of the study presented here was to examine the
data for 53 prostate cancer patients receiving surgery, to determine
which of five preoperative variables are predictive of nodal involvement.
Table E2.32 presents the complete data set. For each of the 53 patients,
EXERCISES 103