Biostatistics

162 CHAPTER 6 ESTIMATION
LEARNING OUTCOMES
After studying this chapter, the student will
1. understand the importance and basic principles of estimation.
2. be able to calculate interval estimates for a variety of parameters.
3. be able to interpret a confidence interval from both a practical and a probabilistic
viewpoint.
4. understand the basic properties and uses of the t distribution, chi-square distribution,
and F distribution.
6.1 INTRODUCTION
We come now to a consideration of estimation, the first of the two general areas of statistical
inference. The second general area, hypothesis testing, is examined in the next chapter.
We learned in Chapter 1 that inferential statistics is defined as follows.
DEFINITION
Statistical inference is the procedure by which we reach a conclusion
about a population on the basis of the information contained in a sample
drawn from that population.
The process of estimation entails calculating, from the data of a sample, some
statistic that is offered as an approximation of the corresponding parameter of the
population from which the sample was drawn.
The rationale behind estimation in the health sciences field rests on the assumption
that workers in this field have an interest in the parameters, such as means and proportions,
of various populations. If this is the case, there is a good reason why one must rely on
estimating procedures to obtain information regarding these parameters. Many populations
of interest, although finite, are so large that a 100 percent examination would be prohibitive
from the standpoint of cost.
Suppose the administrator of a large hospital is interested in the mean age of patients
admitted to his hospital during a given year. He may consider it too expensive to go through
the records of all patients admitted during that particular year and, consequently, elect to
examine a sample of the records from which he can compute an estimate of the mean age of
patients admitted that year.
A physician in general practice may be interested in knowing what proportion of a
certain type of individual, treated with a particular drug, suffers undesirable side effects.
No doubt, her concept of the population consists of all those persons who ever have been or
ever will be treated with this drug. Deferring a conclusion until the entire population has
been observed could have an adverse effect on her practice.
These two examples have implied an interest in estimating, respectively, a population
mean and a population proportion. Other parameters, the estimation of which we will cover
in this chapter, are the difference between two means, the difference between two
proportions, the population variance, and the ratio of two variances.