4 Estimation of Parameters
The entire process of statistical design and analysis can be described briefly as
follows. The target of a scientist’s investigation is a population with certain
characteristic of interest: for example, a man’s systolic blood pressure or his
cholesterol level, or whether a leukemia patient responds to an investigative
drug. A numerical characteristic of a target population is called aparameter:
for example, the population meanm(average SBP) or the population propor-
tionp(a drug’s response rate). Generally, it would be too time consuming or
too costly to obtain the totality of population information in order to learn
about the parameter(s) of interest. For example, there are millions of men to
survey in a target population, and the value of the information may not justify
the high cost. Sometimes the population does not even exist. For example, in
the case of an investigative drug for leukemia, we are interested in future
patients as well as present patients. To deal with the problem, the researcher
may decide to take a sample or to conduct a small phase II clinical trial.
Chapters 1 and 2 provide methods by which we can learn about data from the
sample or samples. We learned how to organize data, how to summarize data,
and how to present them. The topic of probability in Chapter 3 sets the frame-
work for dealing with uncertainties. By this point the researcher is ready to
draw inferences about the population of interest based on what he or she
learned from his or her sample(s). Depending on the research’s objectives, we
can classify inferences into two categories: one in which we want to estimate
the value of a parameter, for example the response rate of a leukemia inves-
tigative drug, and one where we want to compare the parameters for two sub-
populations using statistical tests of significance. For example, we want to
know whether men have higher cholesterol levels, on average, than women. In
147