Page 205 - Computational Statistics Handbook with MATLAB

192 Computational Statistics Handbook with MATLAB

for estimating the bias and variance of estimates is presented in Section 6.4.
Finally, Sections 6.5 and 6.6 conclude the chapter with information about
available MATLAB code and references on Monte Carlo simulation and the
bootstrap.

6.2 Classical Inferential Statistics

In this section, we will cover two of the main methods in inferential statistics:
hypothesis testing and calculating confidence intervals. With confidence
intervals, we are interested in obtaining an interval of real numbers that we
expect (with specified confidence) contains the true value of a population
parameter. In hypothesis testing, our goal is to make a decision about not
rejecting or rejecting some statement about the population based on data
from a random sample. We give a brief summary of the concepts in classical
inferential statistics, endeavoring to keep the theory to a minimum. There are
many books available that contain more information on these topics. We rec-
ommend Casella and Berger [1990], Walpole and Myers [1985], Bickel and
Doksum [1977], Lindgren [1993], Montgomery, Runger and Hubele [1998],
and Mood, Graybill and Boes [1974].

gg
TTestinestin
Testin
HHyypothesispothesis estin g g
Hy
Hypothesis pothesis T
In hypothesis testing, we start with a statistical hypothesis, which is a con-
jecture about one or more populations. Some examples of these are:
• A transportation official in the Washington, D.C. area thinks that
the mean travel time to work for northern Virginia residents has
increased from the average time it took in 1995.
• A medical researcher would like to determine whether aspirin
decreases the risk of heart attacks.
• A pharmaceutical company needs to decide whether a new vaccine
is superior to the one currently in use.
• An engineer has to determine whether there is a difference in
accuracy between two types of instruments.

We generally formulate our statistical hypotheses in two parts. The first is
, which denotes the hypothesis we
the null hypothesis represented by H 0
would like to test. Usually, we are searching for departures from this state-
ment. Using one of the examples given above, the engineer would have the
null hypothesis that there is no difference in the accuracy between the two
instruments.

© 2002 by Chapman & Hall/CRC