Information Technology Reference
In-Depth Information
limits of a particular confidence interval
are random variables because they
depend upon the sample that is
drawn.
Confidence intervals can be used
both to evaluate and to report on the
precision of estimates (see Chapter 4)
and the significance of hypothesis tests
(see Chapter 5). The probability the
interval covers the true value of the
parameter of interest and the method
used to derive the interval must also be
reported.
In interpreting a confidence interval
based on a test of significance, it is
essential to realize that the center of the
interval is no more likely than any other
value, and the confidence to be placed
in the interval is no greater than the
confidence we have in the experimental design and statistical test it is
based upon. (As always, GIGO.)
IMPORTANT TERMS
Acceptance Region,
A
(
q
0
). Set
of values of the statistic
T
[
X
]
for which we would accept
the hypothesis
H
:
q = q
0
. Its
complement is called the
rejection region.
Confidence Region,
S
(
X
).
Also referred to as a confi-
dence interval (for a single
parameter) or a confidence
ellipse (for multiple parame-
ters). Set of values of the
parameter
q
for which given
the set of observations
X
=
{
x
1
,
x
2
,...,
x
n
} and the
statistic
T
[
X
] we would
accept the corresponding
responding hypothesis.
Multiple Tests
Whether we report
p
values or confidence intervals, we need to correct for
multiple tests as described in Chapter 5. The correction should be based
on the number of tests we
perform
, which in most cases will be larger than
the number on which we report.
RECOGNIZING AND REPORTING BIASES
Very few studies can avoid bias at some point in sample selection, study
conduct, and results interpretation. We focus on the wrong endpoints;
participants and co-investigators see through our blinding schemes; the
effects of neglected and unobserved confounding factors overwhelm and
outweigh the effects of our variables of interest. With careful and pro-
longed planning, we may reduce or eliminate many potential sources of
bias, but seldom will we be able to eliminate all of them. Accept bias as
inevitable and then endeavor to recognize and report all exceptions that
do slip through the cracks.
Most biases occur during data collection, often as a result of taking
observations from an unrepresentative subset of the population rather than
from the population as a whole. The example of the erroneous forecast of
Landon over Roosevelt was cited in Chapter 3. In Chapter 5, we consid-
